diff --git a/lectures/07-inprogress-lecture.pdf b/lectures/07-inprogress-lecture.pdf new file mode 100644 index 0000000..58e5eed Binary files /dev/null and b/lectures/07-inprogress-lecture.pdf differ diff --git a/lectures/07-regressions_robust_lasso.ipynb b/lectures/07-regressions_robust_lasso.ipynb new file mode 100644 index 0000000..9285be4 --- /dev/null +++ b/lectures/07-regressions_robust_lasso.ipynb @@ -0,0 +1 @@ +{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"07-regressions_robust_lasso.ipynb","provenance":[]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"code","metadata":{"id":"w4aUIfZjRSAe","colab_type":"code","colab":{}},"source":["%matplotlib inline"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"LzZuMm-aTYvh","colab_type":"code","colab":{}},"source":["import numpy as np\n","import numpy.linalg as npl\n","import pandas as pd\n","\n","import sklearn.linear_model\n","\n","import matplotlib.pyplot as plt\n","import seaborn as sns\n","sns.set_style('whitegrid')"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"WktR6j1_rw3M","colab_type":"text"},"source":["# Noisy polynomials"]},{"cell_type":"code","metadata":{"id":"qUwtqPO9r56o","colab_type":"code","colab":{}},"source":["def gen_data(n=10, sigma_noise=.2, sorted=True, fun='sin'):\n"," X = 2 * np.random.rand(1, n) - 1.0\n"," eps = np.random.randn(1, n) * sigma_noise\n"," if fun=='poly1':\n"," Y = 0.3 + .7*X + eps\n"," elif fun=='poly2':\n"," Y = 0.3 + .7*X -1.1*X**2 + eps\n"," elif fun =='log':\n"," Y = np.log(X+1)**.5 + eps\n"," elif fun == 'sin':\n"," Y = np.sin(2*np.pi*X) + eps\n"," else:\n"," raise ValueError(f\"Unknown fun type: {fun}.\")\n"," if sorted:\n"," xind = np.argsort(X[0, :])\n"," X= X[:, xind]\n"," Y= Y[:, xind]\n"," return X, Y\n"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"-CnfmEui0zu3","colab_type":"code","outputId":"7fafe1ab-cdaf-4146-c3aa-eda78ec5e742","executionInfo":{"status":"ok","timestamp":1574930308906,"user_tz":-60,"elapsed":3507,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":281}},"source":["XC,YC = gen_data(n=1000, sigma_noise=0)\n","fig = plt.figure()\n","plt.plot(XC.T,YC.T,'-') #note: plot assumes that each column is a data series\n","plt.title('The clean X-Y relation')\n","plt.show()"],"execution_count":4,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYIAAAEICAYAAABS0fM3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDacsECGxZXo9i6d/KIJezyLnvnHoJ+z9s92YQX54bmYMdkoV+KygzP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8AKBGQ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\nOHPmjHGb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"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"RrFuRqJG03ZF","colab_type":"code","colab":{}},"source":["def expandX(X, deg=1):\n"," return X**np.arange(deg + 1)[:, np.newaxis]\n","\n","def expandRBF(X, N=100, sigma=1):\n"," Xmin = X.min()\n"," Xmax = X.max()\n"," return np.exp(-((np.linspace(Xmin, Xmax, N)[:, np.newaxis] - X) / sigma)**2)\n","\n","def polyfit(X, Y, C=0.0):\n"," theta = npl.inv(X.dot(X.T) + np.eye(X.shape[0])*C).dot(X).dot(Y.T)\n"," return theta"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"7iib0Lst1mW7","colab_type":"code","outputId":"09bfb1d2-e194-4728-f652-8bb055451e19","executionInfo":{"status":"ok","timestamp":1574930309507,"user_tz":-60,"elapsed":4031,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":265}},"source":["plt.figure()\n","plt.plot(XC.T,YC.T,'-r', linewidth=2, label='clean')\n","for deg in [0,1,2,5,7,10,20]:\n"," XE = expandX(XC,deg)\n"," #XE = expandRBF(XC,deg)\n"," theta = polyfit(XE, YC)\n"," plt.plot(XC.T, theta.T.dot(XE).T,'-', label='deg %d' % deg, )\n","plt.legend(loc='upper right')\n","plt.show()"],"execution_count":6,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAD4CAYAAADvsV2wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIl0A4eBh8tKVSNVS5D5ZHCyeRNG5Sqbc3Zfecc0L+8kVMsa8MIvjT36MF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2qPjg3nXMJj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\n52+gVrvoYmTaEkqVguumdaHcYIXrR2KoOIo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7762vt3nzZjFmzBiRlJQk3n333frjWVlZ\n4qabbhLJycni4YcfFmazucW0lZaWirvuukukpKSIWbNmibKyMiGEEGlpaeLvf/97fb3s7GwxYsQI\nYbfbG7S/8847xaRJk8TEiRPFn//8Z1FVVdVquvbu3SsmTZokUlNTxaRJk8SiRYvq2ztrzC5H19Kl\nS0WPHqIa1foAAAERSURBVD3E5MmT6/8dOXJECNHy43Wxe+aNN94QGzZsEEIIYTKZxMMPPyySk5PF\nTTfdJLKysurbvvvuuyIpKUmMGTNGbN68uVk6rlTXrFmzxLBhw+rHZ+7cuUKI3/9MW0PXq6++KiZM\nmCBSU1PFHXfcITIyMurbfvvttyI5OVkkJyeLxYsXt6ouIYR46623xCuvvNKgnbPH67HHHhPDhw8X\nPXr0ECNHjhSLFi0SX331lfjqq6+EEEI4HA7xzDPPiKSkJDFp0qQGXojNHS85PLKMjIxMB6FdL+nI\nyMjIyJxHNvgyMjIyHQTZ4MvIyMh0EGSDLyMjI9NBkA2+jIyMTAdBNvgyMjIyHQTZ4MvIyMh0EP4f\nua0y031lCqQAAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"OyFVjPcY1mMC","colab_type":"code","outputId":"23c2a9af-c153-4100-9ac8-76aecee1bbe2","executionInfo":{"status":"ok","timestamp":1574930310653,"user_tz":-60,"elapsed":5143,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":269}},"source":["num = 20\n","lambda_ = 0\n","\n","X,Y = gen_data(num, sigma_noise=0.4)\n","plt.figure()\n","plt.plot(X.T,Y.T,'o', label='data', alpha=1.0)\n","plt.plot(XC.T,YC.T,'-r', linewidth=2, label='clean')\n","\n","for deg in [1, 2, 5, 10, 20, 30]:\n"," XE = expandX(X, deg)\n"," theta = polyfit(XE, Y, lambda_)\n"," plt.plot(XC.T, theta.T.dot(expandX(XC,deg)).T,'-', label='deg %d' % deg, )\n","plt.legend(loc='upper right', ncol=3)\n","plt.xlim([-1.1, 1.1])\n","plt.ylim([-2,2.5])\n","plt.show()"],"execution_count":7,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ndmdV2cOHD2MoKw+4X2N5KQD5eXng55yZjEZq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5q5xu3SUfDqRJTFKS/dEA1pXpTOtSqR7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H1hOFsW1nFqq+Kev1dJLuCGKUQa07BVffnuWEjQtdpuOUWqpKSiB4xHM78e5uPg34Nxavg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\nKkFx+AoKCgpXCf8f/2rdmnLRukcAAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"FRRVrVJu1lb_","colab_type":"code","outputId":"bea879a4-ff8a-4339-acf8-4c7f34cabd4e","executionInfo":{"status":"ok","timestamp":1574930310654,"user_tz":-60,"elapsed":5055,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":281}},"source":["#Hint: change the degree and number of samples\n","deg = 50\n","num = 15\n","lambda_ = 1e-2\n","\n","plt.figure()\n","plt.title('Various degree=%d fits' % deg)\n","plt.plot(XC.T, YC.T, '-r', linewidth=2, label='Clean rel.')\n","for run in range(5):\n"," X,Y = gen_data(num, sigma_noise=0.4)\n"," XE = expandX(X,deg)\n"," theta = polyfit(XE, Y, lambda_)\n"," XCE = expandX(XC,deg)\n"," plt.plot(XC.T, theta.T.dot(XCE).T,'-' )\n","\n","plt.xlim([-1.1, 1.1])\n","plt.ylim([-2, 2])\n","plt.show()"],"execution_count":8,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAEICAYAAABcVE8dAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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3boQPGR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\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XX30F8+aJqXQSDuGrk19x1pTKku9ScJ04A/5j7NPP5XF8SyLxhzMQBIFG7XwwNtDxwYmL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\nRU5ErkJggg==\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"GszVgLYHr1zY","colab_type":"text"},"source":["# Outliers and robust regression"]},{"cell_type":"code","metadata":{"id":"O2DwA8ka6Ai5","colab_type":"code","outputId":"e498c8de-099f-4459-8947-1e0aec6432a9","executionInfo":{"status":"ok","timestamp":1574930310664,"user_tz":-60,"elapsed":5026,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["XC.shape"],"execution_count":9,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(1, 1000)"]},"metadata":{"tags":[]},"execution_count":9}]},{"cell_type":"code","metadata":{"id":"kKblHNkO5FGh","colab_type":"code","outputId":"a52e94c1-32c4-4279-ab7b-68a21f3b8dd3","executionInfo":{"status":"ok","timestamp":1574930310669,"user_tz":-60,"elapsed":4999,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":281}},"source":["XC,YC = gen_data(n=30, sigma_noise=0.2, fun='poly1')\n","# now append some outliers\n","\n","XO = np.concatenate([XC, [[-1, -0.9, -0.75]]], axis=1)\n","YO = np.concatenate([YC, [[3, 3, 3]]], axis=1)\n","fig = plt.figure()\n","plt.plot(XO.T,YO.T,'o') #note: plot assumes that each column is a data series\n","plt.title('X-Y relation with outliers')\n","plt.show()"],"execution_count":10,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAEICAYAAABcVE8dAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nam+7vVOnTkmqR+r6jsK67OOqdQnhurWxLvt4Wl19rSdLLx2DwYC8v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iIiO0gO/EmTJuH8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\niEghGPhERArBwCciUoj/D4zpV4uS/vTKAAAAAElFTkSuQmCC\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"1VUFhrjS6fpg","colab_type":"code","outputId":"84b79ab6-03bc-4d63-cc48-5705abd88b50","executionInfo":{"status":"ok","timestamp":1574930311163,"user_tz":-60,"elapsed":5070,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":353}},"source":["fig = plt.figure()\n","plt.plot(XO.T,YO.T,'o') #note: plot assumes that each column is a data series\n","\n","XE = expandX(XC, 1)\n","poly = sklearn.linear_model.LinearRegression()\n","YFit = poly.fit(XE.T, YC.T)\n","plt.plot(XC.T, poly.predict(XE.T), label='Lin Reg no outliers')\n","\n","poly = sklearn.linear_model.HuberRegressor()\n","YFit = poly.fit(XE.T, YC.T)\n","plt.plot(XC.T, poly.predict(XE.T), label='Huber Reg no outliers')\n","\n","# Models on outliers\n","if 1:\n"," XE = expandX(XO, 1)\n"," poly = sklearn.linear_model.LinearRegression()\n"," YFit = poly.fit(XE.T, YO.T)\n"," plt.plot(XO.T, poly.predict(XE.T), label='Lin Reg with outliers')\n","\n"," poly = sklearn.linear_model.HuberRegressor()\n"," YFit = poly.fit(XE.T, YO.T)\n"," plt.plot(XO.T, poly.predict(XE.T), label='Huber Reg with outliers')\n","\n","_ = plt.legend()"],"execution_count":11,"outputs":[{"output_type":"stream","text":["/usr/local/lib/python3.6/dist-packages/sklearn/utils/validation.py:724: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"," y = column_or_1d(y, warn=True)\n","/usr/local/lib/python3.6/dist-packages/sklearn/utils/validation.py:724: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n"," y = column_or_1d(y, warn=True)\n"],"name":"stderr"},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAD4CAYAAADvsV2wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niau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WEX5RVZOg05HgE0Bi92AuGU03KvrpfIjQRxA96Ddg/8K19kn4Tz/9NIcPH6agoIC7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\nLhTms7dyAnnFE9FUXl9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3zmH+kZNsv54+fYonT54ACHRQy8zMxOnpqSTz/064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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"YjVuX0bxrzuQ","colab_type":"text"},"source":["# Forward stagewise"]},{"cell_type":"code","metadata":{"id":"T5utaWkdTjn-","colab_type":"code","outputId":"a1bd6dbe-86e5-4c79-9593-dbac4f0f3d31","executionInfo":{"status":"ok","timestamp":1574930312245,"user_tz":-60,"elapsed":6110,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":238}},"source":["# Load the data\n","\n","cancer_df = pd.read_csv(\n"," 'https://web.stanford.edu/~hastie/ElemStatLearn/datasets/prostate.data',\n"," sep='\\t', header=0, index_col=0)\n","\n","train_id = cancer_df['train']\n","del cancer_df['train']\n","\n","# Standardize the whole data, as per its readme\n","# https://web.stanford.edu/~hastie/ElemStatLearn/datasets/prostate.info.txt\n","# NB, usually you should standardize based on train set only!!\n","\n","cancer_df -= cancer_df.mean(0, numeric_only=True)\n","cancer_df /= cancer_df.std(0, numeric_only=True)\n","\n","cancer_train_df = cancer_df[train_id=='T']\n","cancer_test_df = cancer_df[train_id=='F']\n","\n","X_cols = [c for c in cancer_df.columns if c!='lpsa']\n","Y_col = 'lpsa'\n","\n","print(f'Train nas {len(cancer_train_df)} saples\\n'\n"," f'Test nas {len(cancer_test_df)} saples')\n","\n","cancer_train_df.head()"],"execution_count":12,"outputs":[{"output_type":"stream","text":["Train nas 67 saples\n","Test nas 30 saples\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/html":["
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lcavollweightagelbphsvilcpgleasonpgg45lpsa
1-1.637356-2.006212-1.862426-1.024706-0.522941-0.863171-1.042157-0.864467-2.520226
2-1.988980-0.722009-0.787896-1.024706-0.522941-0.863171-1.042157-0.864467-2.287827
3-1.578819-2.1887841.361163-1.024706-0.522941-0.8631710.342627-0.155348-2.287827
4-2.166917-0.807994-0.787896-1.024706-0.522941-0.863171-1.042157-0.864467-2.287827
5-0.507874-0.458834-0.250631-1.024706-0.522941-0.863171-1.042157-0.864467-1.825150
\n","
"],"text/plain":[" lcavol lweight age ... gleason pgg45 lpsa\n","1 -1.637356 -2.006212 -1.862426 ... -1.042157 -0.864467 -2.520226\n","2 -1.988980 -0.722009 -0.787896 ... -1.042157 -0.864467 -2.287827\n","3 -1.578819 -2.188784 1.361163 ... 0.342627 -0.155348 -2.287827\n","4 -2.166917 -0.807994 -0.787896 ... -1.042157 -0.864467 -2.287827\n","5 -0.507874 -0.458834 -0.250631 ... -1.042157 -0.864467 -1.825150\n","\n","[5 rows x 9 columns]"]},"metadata":{"tags":[]},"execution_count":12}]},{"cell_type":"code","metadata":{"id":"oJSNLK8etmVN","colab_type":"code","outputId":"46018b5e-2294-4839-e638-2db1044074d9","executionInfo":{"status":"ok","timestamp":1574930312247,"user_tz":-60,"elapsed":6078,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":265}},"source":["# Forward stagewise\n","\n","epsilon = 1e-1\n","theta = np.zeros((len(X_cols),))\n","X = np.array(cancer_train_df[X_cols])\n","r = np.array(cancer_train_df[Y_col])\n","\n","coefs = [np.array(theta)]\n","errs = []\n","last_err = np.sum(r**2)\n","\n","for _ in range(1000000):\n"," # compute correlations\n"," residual_correlations = r @ X\n"," best_feat = np.argmax(np.abs(residual_correlations))\n"," max_corr = residual_correlations[best_feat]\n"," \n"," theta[best_feat] += epsilon * np.sign(max_corr)\n"," r -= epsilon * np.sign(max_corr) * X[:, best_feat]\n"," cur_err = np.sum(r**2)\n","\n"," if last_err - cur_err < 0:\n"," break\n"," last_err = cur_err\n"," errs.append(cur_err)\n"," coefs.append(np.array(theta))\n","\n","\n","coefs = np.array(coefs).T\n","tau = np.abs(coefs).sum(0)\n","\n","for i, name in enumerate(X_cols):\n"," plt.plot(tau, coefs[i], label=name)\n","#_ = plt.legend()"],"execution_count":13,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAD4CAYAAADvsV2wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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ww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\nAAAAAElFTkSuQmCC\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"ZmbKn55tUTUs","colab_type":"code","cellView":"both","outputId":"1f4f669c-266e-4741-e2a9-767697e82781","executionInfo":{"status":"ok","timestamp":1574930312248,"user_tz":-60,"elapsed":6045,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":265}},"source":["#@title Lasso LARS\n","\n","(alphas, active, coefs\n"," ) = sklearn.linear_model.lars_path(np.array(cancer_train_df[X_cols]), \n"," np.array(cancer_train_df[Y_col]))\n"," \n","# coefs is D x n_steps\n","tau = np.abs(coefs).sum(0)\n","\n","for i, name in enumerate(X_cols):\n"," plt.plot(tau, coefs[i], label=name)\n","_ = plt.legend()"],"execution_count":14,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXwAAAD4CAYAAADvsV2wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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cgq6WCMKgwGFXo8sgIzTAg2hVBeBw+WmtN6KNkhJdGjgLJvu09gt8M2z8OXT4GyGUTfBpCUQ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\nNH78ePULR3MbQ4DVq1eTlJR0VX/o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"]},"metadata":{"tags":[]}}]},{"cell_type":"code","metadata":{"id":"3YHQ81B9ZotY","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]}]} \ No newline at end of file diff --git a/lectures/08-generative_discriminative.ipynb b/lectures/08-generative_discriminative.ipynb new file mode 100644 index 0000000..6173597 --- /dev/null +++ b/lectures/08-generative_discriminative.ipynb @@ -0,0 +1 @@ +{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"08-generative_discriminative.ipynb","provenance":[],"collapsed_sections":[]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"code","execution_count":0,"metadata":{"cellView":"form","colab":{},"colab_type":"code","id":"ZA0ntr1QI4KP"},"outputs":[],"source":["#@title Imports\n","%matplotlib inline\n","\n","import numpy as np\n","import matplotlib.colors\n","import matplotlib.pyplot as plt\n","\n","import sklearn.linear_model\n","import sklearn.discriminant_analysis\n","\n","import seaborn as sns\n","sns.set_style('whitegrid')"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"egFAw8SX7t4J"},"source":["# Generative and discriminative classifiers\n","\n","Suppose you have a dataset of $x^{(i)}, y^{(i)}$ pairs, where $x^{(i)}\\in\\mathbb{R}^D$ and $y^{(i)}\\in\\{0, 1, ..., C\\}$.\n","\n","A *classifier* is tasked with finding the label (or class) $y$ of a givan sample $x$. In probabilistic terms, the classifier should find\n","$$\n","p(y|x).\n","$$\n","\n","The classification task can be oslved in two ways:\n","1. Directly, by modeling $p(y|x)$. We call such classifiers **discriminative**.\n"," \n"," E.g. logistic regression, with the model fit to data using the maximum likelihood principle.\n","\n","2. Indirectly, by first modeling $p(y)$ and $p(x|y)$, then using the Bayes theorem to get $p(y|x)$. We call such models **generative**\n","\n"," E.g. the Naive Bayes and the Gaussian Discriminant Analysis, defined below, are both generative. They are fit by modeling separately points belinging to the same class.\n","\n","Generatively and discriminatively trained models approach the classification problem from two directions:\n","- generative models first learn to describe samples belongign to each class. Then, classification of a new sample amounts to finding a class that makes the observation the most probable.\n","- on the other hand, discriminative models are trained to find the few features that can set the two classes apart. Ideally, they will only focus on the few discriminating traits, and ignore everything else.\n"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"U6EYUur4Jmkq"},"source":["# Gaussian Discriminant Analysis\n","\n","The GDA models a joint distribution $p(x,y) = p(x|y)p(y)$ with:\n","$$\n","\\begin{align}\n","y &\\sim \\text{Bernoulli}(\\phi) \\\\\n","x|y=0 & \\sim\\mathcal{N}(\\mu_0, \\Sigma_0) \\\\\n","x|y=1 & \\sim\\mathcal{N}(\\mu_1, \\Sigma_1)\n","\\end{align}\n","$$\n","\n","Which corresponds to the following expressions of probality:\n","$$\n","\\begin{align}\n","p(y) &= \\phi^y(1-\\phi)^{1-y}\\\\\n","p(x|y=0) &= \\frac{1}{(2\\pi)^{d/2}|\\Sigma_0|^{1/2}}\\exp\\left(-\\frac{1}{2}(x-\\mu_0)^T\\Sigma_0^{-1}(x-\\mu_0)\\right) \\\\\n","p(x|y=1) &= \\frac{1}{(2\\pi)^{d/2}|\\Sigma_1|^{1/2}}\\exp\\left(-\\frac{1}{2}(x-\\mu_1)^T\\Sigma_1^{-1}(x-\\mu_1)\\right)\n","\\end{align}\n","$$\n","\n","Using the Bayes theorem, we recover the decision boundary:\n","$$\n","\\begin{split}\n","p(y=1|x) &= \\frac{p(x|y=1)p(y=1)}{p(x|y=1)p(y=1) + p(x|y=0)p(y=0)} \n"," &= \\frac{1}{1+\\frac{p(x|y=0)p(y=0)}{p(x|y=1)p(y=1)}}\n","\\end{split}\n","$$\n","\n","Let's expand the term in the denominator:\n","$$\n","\\begin{split}\n","&\\frac{p(x|y=0)p(y=0)}{p(x|y=1)p(y=1)} = \\\\\n","&\\frac{\\frac{1}{(2\\pi)^{d/2}|\\Sigma_0|^{1/2}}\\exp\\left(-\\frac{1}{2}(x-\\mu_0)^T\\Sigma_0^{-1}(x-\\mu_0)\\right) (1-\\phi)}{\\frac{1}{(2\\pi)^{d/2}|\\Sigma_1|^{1/2}}\\exp\\left(-\\frac{1}{2}(x-\\mu_1)^T\\Sigma_1^{-1}(x-\\mu_1)\\right) \\phi}\n","\\end{split}\n","$$\n","\n","This leads to a quadratic boundary function and the resulting model is ofetn called \"Quadratic disrciminant Analysis\".\n","\n","An interesintg simplification happens when $\\Sigma_0=\\Sigma_1=\\Sigma$, i.e. when we asume that samles belonging to all classes have the same covariance matrix. Then:\n","\n","$$\n","\\begin{split}\n","&\\frac{p(x|y=0)p(y=0)}{p(x|y=1)p(y=1)} = \\\\\n","&\\frac{1-\\phi}{\\phi}exp\\left(-\\frac{1}{2}(x-\\mu_0)^T\\Sigma^{-1}(x-\\mu_0) +\\frac{1}{2}(x-\\mu_1)^T\\Sigma^{-1}(x-\\mu_1) \\right) =\\\\\n","&= \\exp(-\\Theta^T x)\n","\\end{split}\n","$$\n","For a certain value of $\\Theta$. Thus, the GDA's decision boundary is liear and the resulting model is called \"Linear Discriminant Analysis\" (LDA).\n","\n","We note that while it computes the decision boundry using a firmula similar to logistic regression, i.e.\n","$$\n","p(y=1|x) = \\frac{1}{1+\\exp(-\\Theta^T x)}\n","$$\n","it is trained in a very different fashion.\n","\n","\n","## LDA training\n","We fit the LDA model by maximizing the joint loglikelihood equal to\n","$$\n","\\begin{split}\n","\\mathcal{l}(\\phi,\\mu_0,\\mu_1, \\Sigma) &= \\log\\prod_{i=1}^{N}p(x^{(i)}, y^{(i)}; \\phi,\\mu_0,\\mu_1, \\Sigma) \\\\\n","&= \\log\\prod_{i=1}^{N}p(x^{(i)} | y^{(i)}; \\mu_0,\\mu_1, \\Sigma)p(y^{(i)}; \\phi)\n","\\end{split}\n","$$\n","\n","Maximizing the likelihood leads to intuitive formulas for the parameters:\n","\n","$$\n","\\begin{align}\n","\\phi &= \\frac{1}{N}\\sum_{i=1}^{N}[y^{(i)}=1] \\\\\n","\\mu_0 &= \\frac{\\sum_{i=1}^{N}[y^{(i)}=0]x^{(i)}}{\\sum_{i=1}^{N}[y^{(i)}=0]} \\\\\n","\\mu_1 &= \\frac{\\sum_{i=1}^{N}[y^{(i)}=1]x^{(i)}}{\\sum_{i=1}^{N}[y^{(i)}=1]} \\\\\n","\\Sigma &= \\frac{1}{N}\\sum_{i=1}^{N}(x^{(i)} - \\mu_{y^{(i)}})(x^{(i)} - \\mu_{y^{(i)}})^T \\\\\n","&= (1-\\phi) \\frac{\\sum_{i: y^{(i)}=0}(x^{(i)} - \\mu_{0})(x^{(i)} - \\mu_{0})^T}{\\sum_{i: y^{(i)}=0}1} + \\phi \\frac{\\sum_{i: y^{(i)}=1}(x^{(i)} - \\mu_{1})(x^{(i)} - \\mu_{1})^T}{\\sum_{i:y^{(i)}=1}1}\n","\\end{align}\n","$$\n","\n","We see that $\\phi$ simply equals to the fration of samples belonging to class $1$, that the means $\\mu_0$ and $\\mu_1$ correspond to the means of samples in both classes and finally that the covariance matrix is just the weighted mean of the covariance matrices for each class."]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"vdwRn7hIjx72"},"source":["## LDA vs Logistic regression\n","\n","Once trained, LDA and logistic regression's predictions can be computed using the same formula. However, the classifiers are fitted using a different objective and thus will be different. Let's plot them on some exemplary data."]},{"cell_type":"code","execution_count":0,"metadata":{"colab":{},"colab_type":"code","id":"GMgZlq5VkDjx"},"outputs":[],"source":["## Helper function\n","def plot_dec_boundary(X, Y, model, class_threshold=0.5):\n"," plt.scatter(X[0, :], X[1,:], c=Y, cmap='spring', edgecolors='black')\n"," nx, ny = 200, 100\n"," x_min, x_max = plt.xlim()\n"," y_min, y_max = plt.ylim()\n"," xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),\n"," np.linspace(y_min, y_max, ny))\n"," Z = model.predict_proba(np.c_[xx.ravel(), yy.ravel()])\n"," Z = Z[:, 1].reshape(xx.shape)\n"," plt.pcolormesh(xx, yy, Z, cmap='spring',\n"," norm=matplotlib.colors.Normalize(0., 1.), zorder=0)\n"," plt.contour(xx, yy, Z, [class_threshold], linewidths=1., colors='white')"]},{"cell_type":"code","execution_count":3,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":545},"colab_type":"code","executionInfo":{"elapsed":2760,"status":"ok","timestamp":1574904830071,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"},"user_tz":-60},"id":"paUMJiiVjwpD","outputId":"da7d1f16-54e8-441e-8986-f12e55410cf5"},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXIAAAEICAYAAABCnX+uAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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5pEtzAoto047PZqhhbJyZT755wOEjMhUqKLsaNVIWMv5ybjyffujj9K+ZXj21VKoMcxeYOHRQ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\nOHKBQCDwcIQjFwgEAg/n/wG10K6vO0/xZwAAAABJRU5ErkJggg==\n","text/plain":["
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j3x8by9btibz1lqx6B72rp08PLZMn2NtgouDoCJZ/tEuS3ObklP79Gg2sXSub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\nIBAIajnCkQsEAkEtRzhygUAgqOX8P1QM6lgQp3hkAAAAAElFTkSuQmCC\n","text/plain":["
"]},"metadata":{"tags":[]},"output_type":"display_data"}],"source":["## Gen some data\n","Sigma = np.array([\n"," [1.0, 0.8],\n"," [0.8, 2.0]])\n","Mu0 = np.array([[-2], [-2]]) # Try also -1 , -1\n","Mu1 = np.array([[2], [2]])\n","N0 = 50\n","N1 = 30\n","\n","X = np.concatenate([\n"," Mu0 + Sigma @ np.random.randn(2, N0),\n"," Mu1 + Sigma @ np.random.randn(2, N1)], axis=-1)\n","Y = np.concatenate([\n"," np.zeros(N0), np.ones(N1)], axis=0)\n","\n","\n","for model in [\n"," sklearn.linear_model.LogisticRegression(solver='lbfgs'),\n"," sklearn.discriminant_analysis.LinearDiscriminantAnalysis(),\n","]:\n"," model.fit(X.T, Y)\n","\n"," plt.figure()\n"," plot_dec_boundary(X, Y, model)\n"," plt.title(model.__class__.__name__)"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"T1FDM09OkUSr"},"source":["When the data is generated according to the LDA model the two classifiers act similarly. However, differences start to show up when the data is generated form a distribution that deviates from the normality assumtions."]},{"cell_type":"code","execution_count":4,"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":545},"colab_type":"code","executionInfo":{"elapsed":3503,"status":"ok","timestamp":1574904830837,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"},"user_tz":-60},"id":"ZS5Bh-LhksKn","outputId":"0f10f9d0-ba05-4050-df5e-6b868312af80"},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYQAAAEICAYAAABfz4NwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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90KcL+PpmefezPgugakVvatYU2T8nfaji+4W+1K4l/xlKJO6A1BCMsTLnHKAK4DWlHwMZyBKW\nEEQQpznNWMbytepL02vtwVhTcIanj7Wv+tTaPfQfFC0BbbvBhlXYNHykJ9CerXpmv328YNqkPEyZ\nqJCUrCMg79O+dWahPsyRnkcSSZYgP83s4Eu+5AXKUJ7ylKAELWnJON6jk6qTq0XLGBsOQr480LCR\nS7r39FQRECDtBhKJuyEHBDvwUfkwSzWLq6rL/Kw6wCXVBQZ5DHK1WBlHq4NVG6FOPSjzgqulkUgk\nboKcMjInlamFvOQjL/mclz9BP0Wi9Uzftemta43YBFi9BXp1haV34MH9jC2Mc3ZeBXvzJ0hXVInE\n6UgNITdz4Qoc+A269QQv9/k2SExUOHBQx+/HdLhxdHaJJMfhPm8BdyMjQfD09dNrYDbPRWzeriN5\njs3rmxuBd56BEs9B886wbX362kyrrwywdn0yb7+bzAtl4P4D8FDBuh+8eKmy0bORrqgSSabgsIZw\n48YN+vbtS5s2bWjbti3Lly+3qPPbb79Rq1YtOnbsSMeOHZk9e7aj3UqcyY/boXgRqFXbpWLE/K1j\n+Jhkdu2CX3+DmBgYOxbad9Gg0ciXt0SS2TisIXh6ejJ+/HgqV67M48eP6dq1Kw0bNqRs2bIm9WrX\nrs38+fMd7S7rSU8QPPP6GdEU0rmA7ZHuMQ90j3hOKZT+0T1FvgRYuB3e6QqxsXDtqo16Vn6nJwRG\nGmXLVmp4cyBUry5+q1Twen/46mt4tZ+GFUu98PVVcf++wvLvtfz5F7z4Irzez4PAZ+HXIzB3vo4b\nN6BBAxg2VEVQsB0ySU1BIgGcoCEEBQVRubKI55M3b17KlClDXFycw4JJUuexLp43br9H8YuNqHWl\nM+X/a03kg30Zb/DWA/jxJwjvDnnyOE/QdHD3vo5ixS3LK1SAs+cVBgzWcOGCQtVaGo4eV6hdVyH6\nT4WqNbVMn6Glc7iOGjXgndFiXKvXQCE2Vr7sJRJ7caoN4erVq8TExFCtWjWLcydPnqRDhw4EBQUx\nbtw4ypUr58yuMxc7g+DZLLP1dWyeb1jnYffX6oAH4/FNeoaLXKKAUoCD2oP0uNKdohSlbv4XrcuY\nFsevQ/G/oFMP+GEZKDY8fmxpCOm1HehzMD8lrJEP3y3T8NZb4PH0U+XWLdi3D377DV5+WeHBAw2D\n3oQPPhTnBw+GL7+Ajz+B3buhTh1R3ro1jBwBX30FX30pF61JJPbgNC+j+Ph4RowYwYQJE8ibN6/J\nucqVK7N37142b95M3759GTZsmLO6zZVc1V5nT9Ih5rOAghREhYpQQhmvjGf23R8ca3z3IdBooVlz\n5wibDsI7euPt6cErr0BEBCxcCI0bw9tvQ7lyUL0a7N6r8NYQ0+vCmopQGPrBQE/vV2Hf/iwTXyLJ\n9jhlQEhOTmbEiBG0b9+eFi1aWJzPmzcveZ5OQ4SGhqLRaLhrHDg/u5Can761c8Zl+mNrZToPsRmf\n15fpPMQ6Ba1nyu+ryXGUUZXBH3+T7qpSjUvqWFD7iC3JV2xqH3jiJ7ZEf9tbQgDE+8PS3VC+ErxQ\nC+LzGLaEALEZX6Nv94mfoT/jfpO9TTeNl2HT39fTzdvDi21r8+Hr6cFHH8HevTB9OkyeDAkJcPKU\nmM168MD0MXt5wcOHIv+CMZcuwbOBdvzdGf99SSS5GIcHBEVRmDhxImXKlKF///5W69y6dSvFnzw6\nOhqdTkdB4xjIknRR0bM8Z5VzXOOaSXkUW6nj95LjHSQkwcpN0LEZFA5yvL104OenYuHMvNy+DaEh\nEBoKZ89Czx7QqrkHr73qyYcfgvbpbJNOB9/MguLFYdxYSE4W5Vevwv/+B4PelC95icReHLYhHD9+\nnMjISMqXL0/Hjh0BGD16NNevXwegV69e7Nixg9WrV+Pp6Ymfnx/Tp09HpZL/UTNKfo9nGB0wmDYJ\nrfmMaTzP86xlDas9fuC3Ak5aS3D9JkTtgx49YOUsUD9xTrt2UKqkBzs35OH9yU8YMVJLwYIw8DUv\nJk3wQqOBrr11lCun0LAh/PorFC+mYkeUireG6ShZEp5/XrisjntPRdeu8t+ZRGIvKsWNl4LGfB9D\nxX4VXS2GdVIzQFo7Z16mUqyX6Q3M+nPGZUZ7xUPDSnUE8xKXEae7RahvfSYWHEoZr1Lg/fQz2Xjv\noxbHvkmGvd/Tl7z/07kWvycQkGBa1utlKBQAa9dCwNOczAEJlvX8Ew3t6fe+SYb+9P0by+T1NHWm\nfu+pNRia9XsPneX9qxSOndDw1xmFF1+EunVUIjuoSuHcOYUbsVC1CuQvYPZsrR3bQhqYJdmUmJgz\nVKyYsfemXKmcTVGpVPT17U7fgK6iwEtj4bXjFLbuhSE9oHEjOL7D+e1nkNq1PKhdC6MXt9iXLavC\nsARGvtQlkvQgB4SMYuaqqFW0bGQjUWwjjxJAH/pQ36OezfomBkzjMvNwFpD1OZnNj5dvgeF94fp1\n+O8/+66x1bYzDLfGC/hSC4YHjgXBS6uORJLDkMHtjIglloMc5DrX03WdVtHSje58zhfUox4lKEE3\nujNdNyOTJM1iHj0WkVE7dYYCBdKuL5FIsiW5ZkBYxjIqUhFvvKlJTTaxKeWcBg1DGEIlKjGBCbzE\nSwxgAGrUaTesqNjCVi5xicMc5i3eYhzjOcIRPuFT4nQ3LeqjqDivnGeYZgT1NQ3pqenDEd2vJufT\ndEU1d0nVepq6dGq8LF0+k70tXVKTfE1dR625oiYEwF93Yd9vEN4L1M9YuqCau6Oau6Tq+zXe7HBF\nNXa3NdlSe05mzzrVhXRWNJa1axWqVlPw9FKoVAm+/96ef2ESSfYnVwwIC1nINKaxkIU85jFTmcrb\nvM1WtgIwjWmc5SwXuMAhDnGZy8QRx0d8ZFf729nOa7yGDz4pZcUpThhh7GGPRf2/lb9poGtEIQrx\nNdMJUULoou3OJm2kU+430zh0HG7egbbtXCbCuf90DBv9hIZNE+k78Am/HzNMGSUlKZyK1nH9esan\neSIiFMaNhxkz4MkTmDcPPv4YVqxwhvQSiXuT420ICgpTmMJ61lMbEc2zFa34ju+YylTa0Y4FLGAb\n28hPfgDykpdZzKIe9ZjCFFSkPu+dj3zcxXKh3R3ukI98FgHyPlE+ZTTvMI7xADSkIRWpxGDdYDp6\ndBAuufovV+NwFqmFybb7gaQRZC6tOf6VB2FMV6gYCseOpW0bSCPPst3ngL9itIR1fMygQTDtCzh+\nTKFdeBLL5vlyI07L+//T8OyzIo5R44Yqliz0pFAhszZthc5+ytTPFBYsgKZNxe+QEFi2DAYMgH79\nUhVPIsn25Hi30wQSKEQhnmDqR3+Xu5ShDPe5TwABxBLLMzyTcl6NGn/8SSYZjzQUqZOcpBWtOMxh\nXkCkpNzKVt7kTS5yAV+Vr8mAUFpXht3spiyGiLAKCs/yLGe8ThGsMgrRaeyeauySasUV1cJlU7/3\n0hjcPfUunj5qgyuofu/3xOAmauxOqj/Wu5oW94W3e8PqNXD3X8M5e11R9Xvz/q3JaeSK2uPNB9Rr\nqGH0u4bH89NPMPxteJIE27fDSy+JFctj34OLF1Rs2eRleGZP97dvK6z/UeHRY2jVEqpUMQwIfgE6\n7t4VoTD0KAp4eoJGY4ixJJG4K464neb4f97++FOEIhznuEn5YQ5TEfHQmtCE1aw2Ob+GNTSmcZqD\nAUB1qjOZydSmNu1oRyMaMZjBbGSDGAzAZD47mGD+w9Rb5xa30KDhGSW/7Xlw4/nytOwJ5rYFW7YE\n482WLUFvL9BvV9Sw7icI7wYehS3P27IjmIe3sGVTMLYrGN3HwV+0dOtu+uxbtoRr12H0aDEYAPj7\ni5DZvx5VuHxZMXmO27YpVKik4+fDCleuKLRsrTD6XUNmtooV4dAh0z4OHxaxlDxU1m0OEklOIcdP\nGalQ8T7v04c+LGYxdanLXvYylKHMYQ4AU5lKC1pwhSuEEMIv/MIc5rCFLXb3M4hBdKMbe9lLHgII\nIwwflY/VukMZwnu8RyUqUYISPOQhwxhGH17FX+Vv9Rq3I+Y8FP8TwsNhRdZYXYODVJw/r1CihKEs\nNlbsn0ZgT8HXV4SziLupULKkeIknJCi89oaOrVtFvgSAyZ9AvXrQuhU0bw4TxsOgQbBokQib8csv\nYrpo0ofOuYfHj2HNGhGOo1o16NpVyCqRuAM5XkMA8bIewxj60x8ffBjLWGYykw50AMQX/hGO8JjH\nfMEX3OY2hzhEfeqnq5+CFKQrXWmlamVzMADoRz960J1qT/+UpjR5COArjy8cus8sZ/dhETyoebMs\n6W7Ia368Oxpu3BC/Hz2CYUOh2ksqNpvZ48+dg8uXoVJFwxf93n0KVaoYBgMQXrRD3oJ1EUJD6NbN\ngy+mwbvvgp8fDB0KH/0P+vVzXDP47z8xcEVFiX6XLIFatUSIb4nEHcjxGgIILWHA0z8KilUj8Qu8\nwExmOqU/jaIlllgKUZAAVYDFeZVKxUQmMpIRnOUsxShGkCroqcHTvLKVHM06D+cYmO0lNcPwyp9g\nRF8xb3P+aOrXOdj/oD55uHZdoVKlRJ4vDRcuQud2Xkxf4kuTtvF4ekK37nD+vPAM+vgDL/IEeIhn\nqlJQFOs2AE8vYSfQ0727B931U1P25tS2gxEjYPhwGDNG/H7/fVE2aRLMnZvu5iQSp5PjjcpZzRKW\nMIlJaNHyhCe8QX+mMQ1vlbdlZWuxjMyPbZWZxzyyFvPH2LhsbGDW7/UGXGPjrnnMI78nljGP/BMN\nBuSABCgaBIPCYe0CuB1ralw2NzQbG5mNDcz6/q3FYTKT/UF8MmcvJlOimAfBRcSpGzc1zJij5uBh\nLcHBKt4a4EXrVh4mzyk+XqHkCxp27hRf5iC0jHr14OsvPGjdBktsvfjTOSAkJUH+/FgYrC9cgJdf\nNmg9EomjyFhGRpzgBJvYhCeedKNbiuE4K4gkkk/4hC1soQY1uMEN3uANxjOer/na8gJr7o9mrpAn\nlZMcUg5ThCK092hrMFKbh25whqZgT84Aa/z3GDbvh479RFabBKP2MDvOSPtm1+TPA7WrPr1frbj/\nokHwxSdmz0RRTJ5TngAVi+d70KKFjs6dIDAQ1qyFtm2gVSusf/mnN6e2DVQqsWk0puVqtcjnIJG4\nAznKhjCJSbSnPWrUPOABoYTyLd9mWf+zmMVXfEUNagBQlKIsYQlLWEqCkpDG1aZoFS39tK/TQduF\nP3VnmKdbSHlNZc4oZzJDdMc5cQbO/QedO0Ma6zZcSaeOnpz+w4uXKnmQJ8CD9Ws8+W62Z6aHY/fx\ngfbtYdo0Q5lOB59+imF6SiJxMTnm2+QEJ1jCEk5ykmd5FoCRjKQGNehEJ0pQIo0WHOcSl6hCFZOy\nohTFDz/ucpcALO0JgNXAa0uUpZznAv/wT0pmtIUsoK+mP8e8fkXlYbRwDUwDvrmKjYdgcHeo3RIO\n/Gy/NuAsTcIcawECPXQ89xyMGuFp1Kf4ylcn6/D2FjaeVHNkW5PdDk1h1ixo0QL27xfpPvftE8bl\n775Lxz1JJJlIjtEQNrGJvvRNGQwASlKSjnRMl/uoI9ShDtvYZlJ2ghOAiKXUUenEUGUo0Uq0SZ1H\nyiO2K9s5qBxEq4j58tXKGsYxjl3soglNKE1ptvMTV7jKOc5lyf2kG60Ovt8iJugNMajdnvU/6qhc\nTUNAPh0lSuuYMdOwLsGZFC0KJ07AhAlQujTMnAkHDkC+fE7vSiLJEDlGQ/DE02owOjVqvLLoNt/n\nfZohXDDb0IZoohnNaFSoOMd/vM7rxHCG5rRgobKADqoOrFBWMIp3qEY1HigPuM99fiSCZDQc5CDr\nWc/XfE01qrGNbexkJyd0pyinKmfaeXo9jxz5Ak8tWFyCAiujoF9HWHwbEuyIHJuZi72shf0wMs5v\n267jnTE6VqyAJk3g9Gl44w2F5GQVY99Lp6Zgh5bg5QXtXBcKSiJJFad4GR08eJApU6ag0+no1q0b\ngwYNMjmvVqsZO3Ysf/31FwUKFGDGjBkUL148zXbT42UUQwyhhHKMY5SkJAB/8ReNaUwMMQQTnEYL\nziGaaKYyld/5nVKUogAFKE5xvuGblDoHOEB/+rORDbSgJfvYRyUqAbCOdbzLuwxjKJ/zBbvZTS1q\npVw7m9nsZQ8bvNeJgrQ8j/R7c88jD51lxjJjzyNjDyRzbyDfJEuvoYAE0xAXDWtAvcrwwxzQJJt6\nJYFpSAxjzyP9sTXPJ+OwFtayrVm7R2thP4yeWZPmaoaPEAvE9Pzzj4hhdO2yB15WnMOc5XkkkWQG\nLvUy0mq1TJ48maVLlxIcHEx4eDhhYWGUNZoyiIiI4JlnnmHXrl1ERUXx1VdfMXOmc3z+9VSkIh/y\nITWoQUc6okbNNrYxhzmZPhgkksg7vJMyNVWJSuxlL6UoRTWqMYEJJvVDCEGDhm/5lsEMShkMALrT\nnW/5lsIEoaBwhStMYAJxxNGYxvSgB1/ypfWv6vR4HjnB28eizPh41z9Qsig0DYeNVqK4ptW/s7QG\n82dhllDn37PC7dSYChWE98+DBxAYmHmeRxKJu+GwDSE6OppSpUpRokQJfHx8aNu2LXv2mIZ83rt3\nL507dwagZcuWHDlyJFPmaIcznJOcpDa1CSGEGGLoRS+n92OMDh11qMM61jGGMSxmccpAcI1rFKSg\nRcKdRBJ5xCOSSCKYIhZtBhOMFx7o0PEe7zGAASxiEXnIQxe6UNTKNW7J+p1QJBjq1na1JDZ5qZKK\n/ftNy06dgjx5ZC4gSe7DYQ0hLi6OIkUML6jg4GCio6Mt6hQtWlR06OVFvnz5uHfvHoUKFXK0ewtK\nUIKhDHV6u7bYznYuc5nd7KYudQERXtsff0YxigEMYBKTaEADClMYLVo+4AOa0IQOdOBrpjOYwSl2\njlhi2ctePuczAHawgzKUAaA2tXnMY65xNcvuzyGSNbAmAgb2h3sX4dplV0tkwYSxXvTsl4yvr/AA\n+uMPGDIEJr6vwtPTfd1nJZLMIMcYlV3FT/xEfvKnDAZ6+tGP7nRnHev4m78pT3lqUpOznKUsZVnH\nOgqQn6UsI4wwBjKQ+9xjJrMYw7vc5wFlnv4xphvdmGg8BeXo1JE59uYvsHdK51oCrN0J4X1gwSJI\nuGl5vbNcTfXXe2kszxk/C6NpoyYhnqxcApM/0zBggMLzpWHCWA/69TOEvLA6FeQkV1SJxJ1weEAI\nDg4mVh9yEqENBAcHW9S5ceMGRYoUQaPR8OjRIwoWLOho125BGcpwj3vEE08e8qSUX+ISBSiAChVT\nmMJIRnKSkxSjGJV5GppTpRCpbGI1q4kiijwEsIiFhKnCuKZc4wpXSCQxZR0CwN/EUIxiWX2bjvH3\nefHp3T0c1s0TK7LciGZNPWjW1MfU4GwRVEoiyfk4bEOoUqUKFy9e5MqVK6jVaqKioggLCzOpExYW\nxsaNGwHYsWMH9evXz/SVoVnFQAbigw9jGJPi9nqVq4xhDKMZnVIviCBa0MIwGAAoKrzxoZ+qH2tV\na1iiWkKYKozdym560JNkkhnMYB7zGIA/+INPmcJQj7dSzx+cWg7m1PIoGOcfMM5LYC13QnryMScE\nwLbjkKCBRh0hPo/thAeJ+AAAIABJREFU/AnmeRRSy59gnpfZPLe0tbzMtvIwp7aZP2NjUgv3IXMn\nSLIZDg8IXl5eTJo0iYEDB9KmTRtat25NuXLlmDVrVopxOTw8nPv379O8eXOWLl3KGH24xxxAPvKx\nhS1sYhNBBFGZypSnPJ3pTB/6WNQ/xSnWsIZTnLLa3kHlIK/Sh1GM4m/+Jo44ggmmJCVpT3s+Ywqh\nqtA05dIqWo7pjnNKF50pBvx0owA/bIPy5aDqS05vPvGJjjWRiUyf/5hfj6vd454lkmyGjHbqRH7m\nZ25xi6Y0TcnPrCeeeLrTndOcpj71OcxhSlCCBSygKlVFJZVCG6UtPejBa7yWcu0v/EJb2jKTGRRX\nFaMJTfA0j+NsNF+9R9nDG9pB5CUvatR448Uqn6XU8KhuujZBf42x37619Jv6OXnjNQrmUVF9kyzT\nZRqvNdDvXwiAwd1g+ffw6KIoM16jYF7feG2CcRpOo7UJZ84l0WrwJSpVVqjwokJUlIrqFX1YPS8/\n3n5W1iboj9NYo2CzzPw4tTJ7zkkkTkSm0HQTGtOYLnSxGAwAJjKRZ3iGc5yjFKVIIAEdOl7hFTrQ\ngYc8BMRiuhBCUq5TUNjOdtSo2UQk45T3qahU5l/lX6sy3FBu0EP7KotZzF/8xb/8ywd8QDt1VxKV\nxMy58fRw4zZE7oOe3cDXz+HmFEXhtYnX+PB/On7aqTDrGzgTo3AvQc285ekLKJhR1GqF2FgFjUa+\n9CXZGzkgZAJ3ucsYxlCe8lShClOZyjKWMY1pLGEJBznIOc5xlKPc4AaFKcwIRoCiogIVOMKRlLY2\ns5kIIrjEJTaykWMc4x1G0V3XC8XYNvt0vnql7ge60DklhIYKFb15lSq8xGZtlKntQD//bTzPbi0f\ns36zlpPZeI7fnnzMCQFw+DKcuQhtekGilfPGdgXznMxmdoWLF+FqXDJvDDA8Ch8fGDtOYd2WJ5b3\nY3yP5raU9NgUFBU6LXz0sY7niitUra5QqjTM/c7GoJDR0OISSRYiBwQn84QnvMIrPOQh61nPQhby\nC7/wmMcUohCLWMRnfEYggQD44MNXfMUGNhBPPGN5jzGMYTvb0aFjDnMYz3iToH1vMYSHPOQ0py36\nv8UtSlHaorw0pbmJG+Vq3HJA5KgMDUm7bipodQqeHpaZ0Ly9QaN1qOk0mfqZwq7d8PvvcPMmbN8O\nM7+BH36QmoIkeyIHBCcTQQTBBDOf+VSlKvWpz0Y2ko98LGABd7lr4TZagAJ4481jHtOM5sxnPhOY\ngBdenOQkhTBdwKdCRQEKEE+8xVdrqCqEH/kRDQZf/Hji2UoUoYSk7oFk/NVsS0tITVMw/4K35j2k\n1wAe+8GybVCzJhSral1L0GsKqWgJLwTlo2BebyIiDM9Hq4WZ01V0bp7HUkOwphlkQEvQahW+ma2w\nbBk8/7zot2pV+PZbmDET6XkkyZbIAcHJHOMYrWhlkrfZG28a05gpTCEPeVjJSpNrfuInilKUIIIA\naE97Tqj+QEMyE5nAQhaiGPnFH+MY17lOTWpa9N+KVgQTRGtas4lNrGUtr/AKrVQtqOpRxaK+S3kU\nDyu3Quf2kMF1KSqVisUTyzB8mAd9eqv45BOoW1vF47s+DH898+JKx8eLzTzKd7VqcPFipnUrkWQq\ncqWykylNaasupZe5TGlKE0oos5nNTW7Sjnac4ASzmc1KVpoMIgAeKg/eVN5kMUtoRCNe53XOc57F\nLOY7ZhvSaRrhqfIk0nMDi3VLmKt8hzfejPAcSm+Pnpl2zw5x8Trs/xl6hsOq74D0G77rVs5LzIYX\n+WHnHa5fTebjoT60Dg3A008DZM4iuHz5oFgxOHQIGjc2lP/0E9SskSldSiSZjhwQnExf+vI5n7OM\nZfShD8kk8wVfoEZNLWqxghVUohKrWc1e9hJGGHvZy//bO/e4qKrtgX+H4SkqGsrgA+2SmKYolvbT\nxBcqZYj4NsKbmo9ES/GZpt1S812W2c2L2g1fkaZIKimKCiii3EzDBz5LxURQxEeBwDDn98fAOMMM\nMAgzg7S/fPicM3vvs/eafeCss/bae+3WFJubXzi08Dmfk0027WnPD/zAda7TgAb40Vd/D+bCc1vs\nCLYKJlg2XrtC/cW3ptiX2cB3KJNDKeDaFHoPgZ/CS66nlPqecYB3hxT+OdvmqfVAvsyoaw1iVboi\nkcmsWPCxRFCQxGefQfv2EBMDc+ZAxDatNkVoC8FThFAIlUw96rGHPUxkIiGEoEJFV7qyj300pjHX\nuc5FLtKc5uSQw0EOcoYzuOOut8VmOuks51POcx7XwginEhKv8Rqb2MRYxlriK5qGbTEweSi81AlO\nJJZdvgowbKicWrVUfLpCxW+/QxtP2Bkpo2NH4ScQPJ0IhWAC2tGOoxzlNrexwYY6PI6j3IQmuOHG\ndKaziU34489NbhJCCD/yI//H4+D8iSTijbdGGYDaoRxIIPvZr1YIBvZj1rEaiucZorR9mc3hBC1q\n479RMHkYXLsLdy6Yvl1jKMNSeL2PFa/3sSr2ti+C4AmeToRCMCH1qW8wfRe72MteLnBBoyx+5EeG\nMYwrXEGOegN4Z5y5znUkJB3/QirXcabyQ4dbnLv3IWIXDBsAYf+Gvx5aWiKB4G+FmGVkAb7ne6Yw\nRcdyCCCAOtThGMc0aZ3pjBIlX/EVqkLnaDLJ/JuvGcUoVkuraS49j61kR0fVK0RL0eoLDQVl0z4v\n6Vd72qWh4HflnYpaUhC8osVrhqaZ/poGCachYDjk1ix90VrxYHiGguBpB78r/mvsdFRzBMET01EF\nVQChECxAHnnYox+2wQEHTcRUACus2MlOvuVbmtGMl3mZnvRkBZ9xkIP8h1A2sIEHPGAWsxghjSJW\nijWJzD8rTxL08B1evtebtx9M5pzShEM6B45DTg682st0bQgEAj3EkJEFCCCA1axmKEOxxRaAJJK4\nwhU60UmnbDOacYITnOY0D3jAS7yENXIa40YccbSgBQD96c9DHrJUWk53WXf1xYbeOov7F4pjYObR\nfuVBhueMYw4f8B7TiM09RPfcweypE85L9gYil5ZknRQvU9pb8cb9EPIm3Pg/uJRUel0lYYwc5aEM\nf4IGAzO/dOQoyWdQWp5AYAaEQrAAgQSygx20pz1v8AZppBFOON/wjZ7lkEsuD3lIa1pjVWjQ3eQP\nVKg0yqCILnRhLnMrXd7Zj+axlrX0ox8AHenIMzjzrz+XEWW/odLbA+BRLoTtggmDIDwVMtJM045A\nINAghozMQC65ZJGlWW1sjTXb2MYylnGXu7jiyglOEECA5po88pjOdFxxxQMPnud5wglnDnPwpA1Z\nZOGJJ/vYp7kmgQS1kihtDFuScUL1C0MLAmmR70nf/P4cKogrcXOdXFUeydIZ+tJXp7qBDCRBmaTr\nUyg+Xm/Il2BsMLy/HOFKDkTEwcAgUD1TcniLkkJcaLel7d8oya9QyeEtdPrd0L0whPAnCCyIUAgm\n5C/+Iphg6lOfpjTFCy/2sx9Q+wde4zU+5VPmMIemNNW5dhrTOMc5znCGu9zlv/yXSUxiH/v4H/8j\njzwWsYgggjjKUaKIYjrTeZ+ZpcqUKCXymsqPrlJXIohgMEMIKhjBjwU7DZa3wYZa1OIqV3XSL3GJ\nBjKFwWsqlZMXIOUiDAkAxINSIDAlFRoyWrp0KYcOHcLGxoYmTZqwePFiateurVfOx8cHR0dHrKys\nkMvlREREVKTZp4bRjEaFirnMZR/7eMhDBjKQeOJpR8nxDR7wgI1s5DKXNVFOu9CF5SxnK1txxx1Q\nxzz6kA/xxZcWtNDsx1wa81QLWM5yRjISgBd4gUY0YqpqCv2kvhTf2dRKZkWw9WiCleP5jnCccS5c\nNzGZCfajnrxzykP0QXg7CLr0gMMHzdOmQPA3pEIKoXPnzkybNg1ra2uWL19OaGgoM2bMMFh2/fr1\nPPNMNZw7XwLXuc5+9tOJTkQTzWQmo0TJEpYQRBDnOFfitZe5TG1q64S8BvDCixWs0EnrSEda0IKf\nZf/Tr8jAwqfjJLGJzTrFetGLi1zikZSLg1Rs9pPKio9s5jBVmkWzgmY0phE3+IN3bcfwrs14KHjC\nWEHlHRr5dg9MDYSrdyA1+cnaLGq3MngSB7P255LSjMkTCExEhYaMvL29sbZW6xQvLy9u3bpVKUJV\nB65xDVdcucY19rKXfvTTWAdZZJFEksHr8shjAhPIIotLXNLJ28MePUfyAQ7gzDNMl6bzifQJaVLp\nztcmNOEsZ3XSLnMZJ5ywQz9YHoCNzIZVdp9xpUYy79tOYah1f1JVN9mavwOlpDR4TaXzMBu+j4AB\nfaHu3+fFQiAwJ5XmQ9i+fTtdu5a82cno0aMZOHAgW7ZsqawmqzQtackVrjCAAdhgo0m3x55BDCKO\nOIPXbWc7dtgxj3kEEMBe9nKVq6xkJUtYQgopmrAYa1jDQhZyhrN8SxifsJDmPM8MqZgfQeuteBLv\n8h7vaZTNH/zBGMbwrmwCVshLXrCmsuK7/B+YlfcRzyo96KTsyhc5ofR/8JZ660jtxWpFjlntxWrG\nLlor7lzWPr+QBdHHYcA/Id/JuAVrxR3ZhhatGbt4TcuxfOiQxOv9c2nW6hEBQ/JITJTKv4BN+/6I\n/RMEVYAyh4xGjhzJnTt39NJDQkLo1Uu9cGj16tXI5XL69etnsI7w8HAUCgWZmZmMGjUKd3d3OnTo\nUEHRqzb1qIc33pznvF7eNa7xMi8bvC6BBAYykMlMRoGCj/mYP/gDBxwIIQQXXBjDGNJIoylNccVV\ns8eCJ578zM8MYACukoJpsml69b8te5ss6R6v8Ao1qFHo1+hPO7xIl9JRyFwMypUpZfJh/gJOcpJn\neRZQ+0i6FHgTkb+LodaG732lk/AruNeD1wfAj1vN02Yxdu9RMnbyI5YuhY4dIS5ORcDQPLZusqF7\nNzFPQ/D0IpMkqUKDlBEREWzZsoWwsDAcHBzKLL9q1Spq1KjB6NGjyyybsjGFlm+1rIh4FuU2t/HA\ng01swg8/ALaylRBCuMQlalJT75q5zOUAB5AhwxFH3uIthjOcznRmLnN5ndc1ZXvQgwtcYBe7eImX\nNOmxxNKf/vzKKZrKdGcvFY1J50q5JEunCWEKN7lJc5qTRBLBsndYaLUAmZVWeZnE9oIdfKvcyG6i\ndKoLJZRE63jCHL8GeeGelUXj69bKx2nWhUNLNvmPj7aFq7KLjna5YP9Ifa59dCjcI6FGtvpYOw9C\nhsAvp+HXuMd5RflFR4ccw/XZ5eq2W3S0yX8sX5G88oLH54Xfy6t7FkuWSbz22uN+CA+H0NUyYvfZ\nPR73L+w77X7XOTfkHyjNZyD8CQIjSEk5R8uWT/bcrNDrTHx8POvWrWP16tUlKoPs7Gz+/PNPzXlC\nQgIeHh4VafapoT712c1uQgihBS3wwIOP+Zjd7DaoDHLIYSc7aUhDFrGIYIL5gi/oRS8yyMAXX53y\n1lhzi1t6O6e1pz2PeMRnfFaibHYy9bCUN525whWiieYSl/hJ2stm6Tudso+kRyRKxzjNGT7hE25w\nQ5OXyR1qyfS/i0nJL4DvtkO3TuD2rFmbViolTp+V8NW9Ffj5wf9OiAe24OmmQrOMFixYQF5eHqNG\nqacftm3blvnz55Oens7cuXNZu3YtmZmZTJw4EYCCggL69u1bqq+huuGNNxe5SDLJWGGFJ556O6MV\nsZnNNKIR29imKdOTnrjhxo/8iHWx2xVIIL/wC4c4hA+Pp5vGEMPzPE+iVqA8DYVj0rdI4yiJbGO7\nZgV0PerxMR/zpWolw62CALgv3aeHsjf1qMdMZnKGM7SjHRFE4IYb/+ZrIuXhumGzKyNkRGkb20gy\n+CMbNu+HN4fB199CdobhcpU5Bm+tRC6TULjIOHdOorVW1I7kZGjaBHU/lDYDyVAo8vLOPCopXyCo\nIBVSCPv37zeYrlAoWLt2LQBubm7s3Gl40dPfBSusaEMboolmDWtwxJEggmhDG51yCSQwiEE6CsMJ\nJ3zxJZ10vXpHMIJv+IahDOUbvqETnYgjjslMZhjD9BaTafOAB9Smtl6ojAY04B73NZ8/LViBJ20I\nI0wj12u8xkAGqhfH2XxEB/lLmGqrylK5cA2On4DAgfDdWrM0KZPJCHnHnrFjcgj/Hp59Fi5ehIkT\nIWSiTZnXCwRVGRHLyAyoUPFP/slpTjOCEdzjHr74Mo95vMM7mnINaKA31VRC4jKXaUADvXrlyEkg\ngfa05z3eI5tsWtGKD/mQJSzhG74pMWDac1IzZMiIJ56uPLbY1hNGb3pq3kZ3S3v4mq91lFQ/+iFH\nziHbvbwo96o8XfAkb/N7ToGrG/TwhwORT9Zeae0ayJse7EjOI4n2Lz3Czh7y82HmZFvGjrR+PCsL\nSrYUSgowaKylYEy+QPAECIVgBqKI4gxnSCJJ80Y+ilG8yIsMZjDOOAPwNm/TiU70oQ/d6Y4SJStY\ngRIlXehSYv2xxBJMMLvYxQ1usIAFLGQhvSg5fLRcJudLvmCwNJj3eJcWtCSSSJJIIsEqXlPOAXse\nortRTX7hTwOZa/FqzY8EfBcN04ZBhhecPmXyJq2sZHw0swbvT3LgdpYShYsMW3sJZBawkgSCSkTM\nkTMDu9nN27ytMzzjjjvd6U4MMZq0ZjRjAxsYyUia0YxGNGJ34Y9VKbeqJjXZyEaucIWf+IlrXGMU\nZYeV8Jf5c0C2nwwyCOc7vGhLklUiLlpTT4fL3uQTPiGbbE3aCj7DS9aGBjJ9q8UiPMqDzduhZx9Q\nmE9J2dvLcGtsha2tWCsgqB4IC8EMOOCg95YN8JCHOKA7O6sPfbjCFc5zHkccNXP+jcEZZ+pSlw1s\nYDObecQjvPHmsnSZn/gJO+wI5A0WsQgnmRNIMjxpwyqrL3XqkVQSsbJD/KDaTgFK7LHDHXd605vz\nnCebv/jJJlJ3yKP4XszloZxDNgbTrmbDrn3qyKjffg2Pcsquu7wyGVuX1l4SZTqYi9dbnv0TtK8V\nQ0eCSkBYCGYgiCD+w390pmvGEMM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lPniQG/bvv9J+BfPzoJ9/HnbsMA2rWxfefVc6y7l9++I5GICLrYxUKhWq4tpT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\nHyy84ZKOVfdjAAAAAElFTkSuQmCC\n","text/plain":["
"]},"metadata":{"tags":[]},"output_type":"display_data"}],"source":["## Gen some data\n","Sigma = np.array([\n"," [1.0, -0.6],\n"," [-0.6, 2.0]])\n","Mu0 = np.array([[-2], [-2]]) # Try also -1 , -1\n","Mu11 = np.array([[2], [2]])\n","Mu12 = np.array([[10], [10]])\n","N0 = 50\n","N1 = 30\n","\n","X = np.concatenate([\n"," Mu0 + Sigma @ np.random.randn(2, N0),\n"," Mu11 + Sigma @ np.random.randn(2, N1//2),\n"," Mu12 + Sigma @ np.random.randn(2, N1//2)], axis=-1)\n","Y = np.concatenate([\n"," np.zeros(N0), np.ones(N1)], axis=0)\n","\n","\n","for model in [\n"," sklearn.linear_model.LogisticRegression(solver='lbfgs'),\n"," sklearn.discriminant_analysis.LinearDiscriminantAnalysis(),\n","]:\n"," model.fit(X.T, Y)\n","\n"," plt.figure()\n"," plot_dec_boundary(X, Y, model)\n"," plt.title(model.__class__.__name__)"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"vXmz567OY4-P"},"source":["# The relationship between LDA and Logistic Regression\n","\n","While both classifiers separate the two classes using a hyperplane, they make different assumptions about the data:\n","- GDA (and in turn LDA and QGA) assume that the class-conditional data densities are normally distributed. Whtn this is satisfied, they have a better smaple efficiency than logistic regresion\n","- Logistic Regression makes no assumptions about the class conditional densities, and instead directly models the probability $p(y|x)$. This makes it more robust, but less sample efficient when the data is indeed normal.\n","\n","In practice, Logistic Regression often works better!"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"OeTLyvjWl-Zh"},"source":["# Naive Bayes and Logistic Regression\n","\n","It turns out, that Naive Bayes and Logistic Regression are simiar as well.\n","\n","Assume that each sample is described using $F$ discrete features, with $x_f$ denoting the value of the $f$-th feature.\n","\n","Assume that the data is discrete. For Naive bayes we can model it directly, while for Logistic Regression we will need to encode each feature using a 1-hot encoding, in which we replace each discrete feature with a binary vector which is all zeros, except for a single one at the location corresponding to the discrete value.\n","\n","For both classifiers the decision boundary takes the form:\n","$$\n","\\sum_f \\theta_{f,x_f} > c.\n","$$\n","In naive Bayes, $\\theta_{f,x_f} = \\log p(f=x_f|y=1) - \\log p(f=x_f|y=0)$, while in the case of Logistic Regression $\\Theta_{f,x_f}$ is the coefficeint of the $x_f$'s value of feature $f$ determined using optimization.\n","\n","The two classifiers behave in a similar way:\n","- Naive Bayes has a stronger inductive bias, often working better on very small datasets and saturating to a worse error rates\n","- Logistic Regression needs more data to work well, but oftensaturates at better error rates than naive Bayes."]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"kftyoKuRnrpj"},"source":["## Empirical comparision of generative and discriminative classifiers\n","\n","Andrew Ng made an extensive comparision of performance of generative and discriminative classifiers, with main results summarised in [Figure 1](https://ai.stanford.edu/~ang/papers/nips01-discriminativegenerative.pdf).\n","\n"]},{"cell_type":"markdown","metadata":{"colab_type":"text","id":"kqil6ofIn-Qi"},"source":["# Further reading\n","- CS229 lecture notes on discriminative classifiers http://cs229.stanford.edu/notes2019fall/cs229-notes2.pdf\n","- Andrew Ng, Michael Jordan, \"On discriminative vs. Generative classifiers: A comparison of logistic regression and naive bayes\" https://ai.stanford.edu/~ang/papers/nips01-discriminativegenerative.pdf\n","- Bradley Efron \"The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis\" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.476.3459&rep=rep1&type=pdf\n"]},{"cell_type":"code","execution_count":0,"metadata":{"colab":{},"colab_type":"code","id":"c2oL74YBpDIs"},"outputs":[],"source":[]}]} \ No newline at end of file diff --git a/lectures/08-gradient-boosting-demo.ipynb b/lectures/08-gradient-boosting-demo.ipynb new file mode 100644 index 0000000..ef92418 --- /dev/null +++ b/lectures/08-gradient-boosting-demo.ipynb @@ -0,0 +1 @@ +{"nbformat":4,"nbformat_minor":0,"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.7.3"},"colab":{"name":"07-gradient-boosting-demo.ipynb","provenance":[]}},"cells":[{"cell_type":"code","metadata":{"id":"QGBVCkcmMr6w","colab_type":"code","colab":{}},"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","import sklearn\n","\n","from ipywidgets import interact, interactive, fixed, interact_manual\n","import ipywidgets as widgets"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"38h8IMBtMr69","colab_type":"text"},"source":["# Least Squares Regression with Gradient Boosting"]},{"cell_type":"code","metadata":{"id":"nsMKS_WJMr6_","colab_type":"code","outputId":"fd61cc00-7b77-415e-a2f4-6c3088ab63d4","executionInfo":{"status":"ok","timestamp":1574339831061,"user_tz":-60,"elapsed":1610,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":320}},"source":["x = np.linspace(-5,20, 200)\n","data_x = x \n","data_y = 1/np.sqrt(2*np.pi) * np. exp( -(x+2)**2 / (2) ) +\\\n"," 1/np.sqrt(2*np.pi) * np. exp( -(x-4)**2 / (2) ) *0.8 +\\\n"," 1/np.sqrt(2*np.pi) * np. exp( -(x-15)**2 / (5) ) * 3\n","data_y -= np.mean(data_y)\n","\n","data_y += np.random.rand(200)/4\n","\n","plt.figure(figsize=(12,5))\n","plt.scatter(data_x, data_y);"],"execution_count":2,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAssAAAEvCAYAAACzNYzSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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s3sj8zsSwn/7ZP0fkl/TdLVkp6U9O9r3VkAeb3S3X9S6yk37zSzn6l7h1A+Xy/xRJmn\nduK63EJm9gOSPiHpV9z9/w4/F8v5fHHdO1And39NlteZ2W9L+h8l7w6q0ZN0+dDvl/UfQ8u4e6//\n71Nm9kmtp+B8tt69Qkm+YWYvc/cnzexlkp6qe4cQnrt/Y/Az1+V2MLNZrQfK/83d7+s/HN353Ome\n5XH6X9DA35f0pbTXolEelHSFme0wsxdIulHSkZr3CYGZ2V8ys5cMfpb0c+IcbrMjkt7a//mtkn6/\nxn1BSbgut4uZmaTfkfRld//NoaeiO59ZlCSFmX1Y60M9Lulrkv7JUA4NGqxfbuh9kmYk3e3u/7bm\nXUJgZvZXJX2y/+vFkn6P77kdzOyjkq6VdKmkb0h6j6TDkj4maZukr0t6s7szOazBUr7na8V1uTXM\n7JWS/pekU5K+33/4X2k9bzmq85lgGQAAAEhBGgYAAACQgmAZAAAASEGwDAAAAKQgWAYAAABSECwD\nAAAAKQiWAQAAgBQEywAAAEAKgmUAAAAgxf8HLR0baMTOv6MAAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"RFNzVX48Mr7I","colab_type":"text"},"source":["## 1. fit a regressor with high bias"]},{"cell_type":"markdown","metadata":{"id":"j7l59ykoMr7K","colab_type":"text"},"source":["We choose a shallow decision tree regressor"]},{"cell_type":"code","metadata":{"id":"NhdUQvtPMr7L","colab_type":"code","colab":{}},"source":["from sklearn.tree import DecisionTreeRegressor\n","\n","def weak_learner(data, target, max_depth=1):\n"," tree = DecisionTreeRegressor(criterion='mse', max_depth=max_depth)\n"," tree.fit(data[:,None], target)\n"," pred = tree.predict(data[:,None]);\n"," return pred"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"pVI8oL5xMr7S","colab_type":"text"},"source":["### Compute residuals\n","\n","### $r_{im} = \\frac{\\partial}{\\partial F(x_i)} L(F(x_i), y_i) = y_i - F(x_i)\\text{, for } i = 1,...,n.$"]},{"cell_type":"code","metadata":{"id":"3HPaMlBeMr7T","colab_type":"code","outputId":"cb12a0ae-7874-4450-f756-37d4d45b4679","executionInfo":{"status":"ok","timestamp":1574339832578,"user_tz":-60,"elapsed":3101,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["pred_y = []\n","pred_y.append( weak_learner(data_x, data_y) )\n","\n","plt.figure(figsize=(18,5))\n","plt.subplot(121); plt.plot(data_x, pred_y[-1], color='orange', linewidth=4);\n","plt.scatter(data_x, data_y); plt.title(\"orignal data with prediction\"); ylim = plt.ylim();\n","\n","residuals = data_y - pred_y[-1]\n","plt.subplot(122); plt.scatter(data_x, residuals); plt.title(\"residuals\");"],"execution_count":4,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAABBoAAAE/CAYAAADohaB9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkE73DLSLK0UVXWLqKQAA0I9250f3fUm782Pultecel1nJqZEB0gREW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rpRbvfSwYEgLwY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\nNoJF9fvStav09+df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"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"QCXldCd8Mr7Z","colab_type":"text"},"source":["## 2. fit next regressor to the residuals"]},{"cell_type":"code","metadata":{"id":"oRxvFLitMr7b","colab_type":"code","outputId":"e6e98b10-eb4b-4268-9255-49b9c5517adb","executionInfo":{"status":"ok","timestamp":1574339833172,"user_tz":-60,"elapsed":3674,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["pred_y.append( weak_learner(data_x, residuals) )\n","\n","plt.figure(figsize=(18,5))\n","plt.subplot(121); plt.plot(data_x, pred_y[-1], color='orange', linewidth=4);\n","plt.scatter(data_x, residuals); plt.title(\"previus residuals with prediction\");\n","\n","residuals = residuals - pred_y[-1]\n","plt.subplot(122); plt.scatter(data_x, residuals); plt.title(\"residuals\");"],"execution_count":5,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAABBoAAAE/CAYAAADohaB9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nOMtAzc0v6vrddw5gb4DsmNkrzOxOM7vLzCZCtrnMzA6Z2UEz+/Sg9x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14q6SzMnjfSkiz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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"VhNzTR3qMr7h","colab_type":"text"},"source":["**To simplify, we omit choosing weight for the classifier!**"]},{"cell_type":"markdown","metadata":{"id":"_dEOnHGzMr7j","colab_type":"text"},"source":["## 3. repeat M times"]},{"cell_type":"code","metadata":{"scrolled":true,"id":"fK28ySs2Mr7l","colab_type":"code","outputId":"f8bc3c30-8e2e-469c-a191-bfbb6a557fcf","executionInfo":{"status":"ok","timestamp":1574339833869,"user_tz":-60,"elapsed":4349,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["for i in range(5):\n"," pred_y.append( weak_learner(data_x, residuals) )\n"," residuals = residuals - pred_y[-1]\n","\n","plt.figure(figsize=(18,5))\n","plt.subplot(121); plt.plot(data_x, pred_y[-1], color='orange', linewidth=4);\n","plt.scatter(data_x, residuals); plt.title(\"previus residuals with prediction\");\n","\n","residuals = residuals - pred_y[-1]\n","plt.subplot(122); plt.scatter(data_x, residuals); plt.title(\"residuals\");"],"execution_count":6,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAABBoAAAE/CAYAAADohaB9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABAaUg0AAAAAACA0rBGAwAg1ZadS7py2y7dvXuPTlo5p8vXn6ENa+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0H3Cs9TrO0VfR5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DXuGEg1t7uRD7OCzdu5Sdzt4OvbptOE9xIAOHcivqwnzcVNGBj9PUsWAUJ7ETxcT9Vt2LumKrTcv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\nAAAAAElFTkSuQmCC\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"IxKLYuMWMr7r","colab_type":"text"},"source":["We see that residuals become more and more noisy, when there's no information except this noise, overfitting will begin!"]},{"cell_type":"markdown","metadata":{"id":"iFyEoPxqMr7t","colab_type":"text"},"source":["## 4. connect regressors"]},{"cell_type":"code","metadata":{"id":"TpTDcjZaMr7v","colab_type":"code","outputId":"0a61bad9-dd95-46c2-93e2-d37206cecd9e","executionInfo":{"status":"ok","timestamp":1574339833871,"user_tz":-60,"elapsed":4332,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":336}},"source":["connected_predicitons = np.array(pred_y).sum(0)\n","\n","plt.figure(figsize=(9,5))\n","plt.plot(data_x, connected_predicitons, color='orange', linewidth=4);\n","plt.scatter(data_x, data_y); plt.title(\"orignal data with prediction\"); plt.ylim(ylim);"],"execution_count":7,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAiMAAAE/CAYAAACU1sPMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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GBkp\nPp4Kg3PpOEuYmmliUzDS5FR30JxU5yONMHtq8ZgYI/lhy3WcJUzBSGxqpmliqjtoXkF1PgAHRsb0\n+UlizjquOOgYcd2qJ6sHBSOxKRhpYqo7aF6FOp++3uIJtp4/MKqAUhJzwuzi5Pf03umqJ0vYms2D\n3Lr52eI7FYxUTcFIE1PdQXNbPtDP9CmlLaUKKCUxvkHP/uziAQUiCSpkp58/aEX3P7x9d8gzJIyC\nkSaWxNTfazYPsnT1ehauupOlq9frirzBFFBKXWnQs7oqZKf9E+Xd8/OdKW1R81Iw0sTiji+impP0\nJRFQioTScPB1VbhoKBQGFxw8pIuJaikYaWJxxxdRzUn6ogaUymBJTZQZqavCRcOoK86MzJ6axtY0\nN3XtbXJxxhdRE0H6Cp9due7ZmpVZovJ39b9j0X7meBdQZiRRK5ct4qrbHzo8fkvBqxfOTGmLmpeC\nkTamsS7SETQ2zIZV54cuXy6DpWBECoKC1meef4E53qt0ZUYSVfj+PbnhrqL7Tz6yJ2hxKUPNNG1M\nc9o0Xi11OspgSRRBQWsXo8ULKTOSuOUD/XzkgjOK71TX3qopM9JkahlxNew5UZoIpDZh+7yWLIcy\nWBJFUHDaY75gxJcZ0QjOCdGgZ7EpGGkitdQOVHqO5rRJXrl9XkuWo9Au7Q1ilMESv6CgtSQY8WRG\nVIuUIAUjsSXSTGNmF5jZFjPbamarAh7/iJk9amY/M7PvmdkJSay33dTS+0U9Zhqv3D6vpSuvZmWW\nKIKaXad0hGdG9NuQIAUjscXOjJhZJ3A98CZgO3C/ma11zj3qWWwzsMQ5d8DM3g/8DXB53HW3m1qu\nqsMeGxwaZunq9UrP1kG5z+mzl59ZU5ZDGSypJKjZ9YieCZjwLOTJjKgWKUEKRmJLopnmbGCrc+5J\nADO7GbgEOByMOOfu9ix/H/C7Cay37dRSOxD2HIPD9ys9m6xyn5PqdKSeSoLWm30nRU9mRLVICfIH\nI/7B5qSiJIKRfmCb5/Z24FVlln8P8B8JrLft1FI7EPQcA5xvOXUVTU6lz0lZDmkI50oGPXvt/93A\n9qER5vf1ct6p87ht06BqkZKgzEhsDe3aa2a/CywBrgt5fIWZbTSzjbt3a6Ih/6ibQNW1A956A4BO\ns5JApEDp2WSoxkMyYaK4XmTMdbBtaORwl/LbNg3ytrP6dZwmQcFIbElkRgaB4z23j8vfV8TM3gh8\nAni9cy4wh+WcuwG4AWDJkiVh58y2EFbpfu2li8sOkBWk8OPiv1r3U3o2Ocp+SOp8WRH//CnDo+Pc\ndN/T9Pf18tnLz9TxGoeCkdiSCEbuB04xs4XkgpArgHd4FzCzAeD/ARc453YlsM6WF2fUzaCxA4Je\nz0vp2WRo3AbJDF/dwshEd+BiqhlLQKeCkbhiByPOuTEz+yCwDugEbnTOPWJmnwY2OufWkmuWmQF8\nw8wAnnbOXRx33a2s1kr3sBroZaIAAB5gSURBVIxKuUCkXyfNRCQxboOCGUlMhcyIl2rGYlJmJLZE\nBj1zzt0F3OW772rP329MYj3tpNZK97CMSqcZ46605au/r7fqZh8JFncOGQ1CJYnyBSOjZYIRUM1Y\nLApGYtPcNBlV67wxYT8o486VfT1NUR9f3HEbwoKZj976oD4XqZ6vmeaIGTMOF7IHUc1YDApGYlMw\nklG19sgI+0EpPD/o9SpN3qZAJZpaRlf1KhdIRp1UT+QwX2Zk5rTpbFh1Pn93+ZmaIDNp/tmQFYxU\nTXPTZFi5HhlhtQXlxrgIe71Kw0Kr6SCauHPIhDXNealtXyLzD7yVP2Fq4L068BewjisYqZaCkSYU\npbagmh+acs0Lcesg2kncH/mgYCaI2vYlEl9mxDsUvLqeJ0zNNLEpGGlClQKEan9oyhXLav6K6sT5\nkfcHMx0hRcdq25dIQjIjUgcKRmJTzUgTSjpAKFcsG7cOQqqzfKCfDavO56nVF/GZy16htn2pnT8z\nomCkfsx3Xe/GwE0ELyuBlBlJWS3jSiQ9wVWl5oU4dRDtLs64IVGbfTQ2iQTyZ0Y6FYzUjVkuO+LJ\niJz719/hw8tKOx3o+xpMwUiKah1XIm6hZJCw5gUVu9UuiXFDKjX7aGwSCaXMSEON0k03k8HI7n37\nS76L+r6GUzNNiir1YgnT6InYvE0HG1ad3/Zfmqhq/Xyztg5pUsqMNNSB0eLTabeNlXwX9X0Np8xI\niuLUfqgaPjvC0q6NKP5VgbGEUmakoQ5NdOUmRMnrtjGg+Luo72s4ZUZSFLU4VIOOZVe5AePCPt8O\ns8Q+QxUYSyhlRhpqwoqH259io0Dxd1Hf13AKRlIUZcj3SqOjSrrKpV2DPl/Ijaia1GdY67QB0gaU\nGWmoGb3Tim5321jJd1Hf13AKRlIUpfaj0W2MysJUp1zatfD5duZmqi6S1GfY6PohaR6Pbd9ddHvL\nbo19UU8zphUHI/2zOku+i/q+hlPNSMoq1X40so1Rld7Vq9TNevlAP1fe8kDgc5P6DFU/JH5rNg/y\nzOPbOW3u5H3fefx5HjtqUMdKvfgGPrvpfw3AnOAeivoMSikzknGNbGNUpXepSpmiKGlXtRNLo123\nbgvmijMhL411tfV3ue40CmssCkYyrpFtjKr0LhalXidK2rVRn6Ga2KRgx9AwPfkCyoIR19223+WG\n8AUjH/jKffouVkHNNBnXyEHHkh7ZtdlFnSSwUto16c8wqCsxaHblduY/JvqmdR/uzVEwMtHdtt/l\nhvAFIy+89FLRRQzou1iOgpE6SHq430a1MVYa2bXdhjFOMlOU1GcYVtcztbtDsyu3qaBjorvDmNpR\nHIy4jh5Wvkm9NurGF4x0e4JBfRcrUzCSsGYuAi13Bd/M76tWWcwUhWVr/PcVKC3f+oKOidEJR29X\n8X2/ueRlLGnR72om+MZx6ckPelZQ6bvYbhd7fgpGEhY1tZ9VYVfwzf6+ahGUKTJygdjS1evr+mNR\n7aiuYZSWb31hx4T5xhlZ8rJjG7E57askM1IcjJT7LrbjxZ6fgpGERU3tN1sU3I7Frd5M0eDQMAa4\n/GP1/LEo98MUlq3p6+3m0NiEZlduQ2HHxBE9vinsNehZfZUJRip9F9vxYs9PvWkSFqUbZ6VeGlns\nFdGu3VMLkwT29/UeDkQK6tXtudpRXXu7O7nm4l/TYEotqtbu5ScfWTw8uYaDrzNfMHLUdIv0XVyz\neTAwmITWvtjzU2YkYZWKQKHyeB5ZSdd5szezervp7jRGxydPye105d3IzFClUV0hvGeOgo/WEiV9\nH3ZMHLUHOOB5MWVG6ssXjHz8gpP4+CkXlX1K4fMN46DuTcJZYc75r/eyYcmSJW7jxo1pb0Z0zsGj\n18ITN3JweB8vjYwxMeHo6DCm93QxtXsyCbV7/6HQl+noMCYmSj+Tjg7jyOk9Ac+oj4OjE+w/NJZ7\nXx5mhnPB76uVPffSSMM+lyTXdXB0gpdGxnhieD5/v/9Kfuv8C1r+Ry3LqmmeXbN5kI/e+iDjAb/R\n/X29bFh1fvmV/efZsPf+ydtvvhfmnhNn86WcjX8EP//85O2zPseaA28r+3kvXb0+NCvi1dtdOrR8\nszKzTc65Jf77lRlJyp574MFPADAVmNrJ5HTS4/l/efN82dMSpXOr5RyMtYVVmQpMrXR0+N5XKzvS\n+3n6Jfy5JLmuwrF45IznudL+L1d841g+dccjDB0YbYpapVZSTZFiYdmgQAQiZuQ0UV5j+TIjD2/b\nzVU/KP95R82stkP9SHtc1jbCc02UxZG29OvTfoGbGOX5A6OaAToF1Uy3ELSsV6RaLX8wopqR+vIF\nIxt+vqPi511NzV1QJ4is1RbGkUgwYmYXmNkWM9tqZqsCHp9iZrfkH/+xmZ2YxHoz5eCzaW+BSFnd\nNs78nuKZXKMW4bbaD18aqqk7KnfFHLlWa1yZkYbyBSPDhyp/3kHFx6VzfOdU0wmiGcVupjGzTuB6\n4E3AduB+M1vrnHvUs9h7gOedcyeb2RXAXwOXx113phx8pvj2mX8DC3+v6K7/eHgnf3XnYxwcm+xy\nN7Wrg49fdBoXnnFs0XJfuPsJntl3kGOOmMoHzjup6PFGiLqtYcv63f+JN9ZtW9Pw1s//N8/sK20z\nOeaIqdzxodc0ZBsqHSdv/fx/86nZf8orp08GGyf27ODpkeLPL8pgTFkpqm5m1QyiF7Zsp1n02gFl\nRhqrszgYOW/WQzj3tZLFZk7thodymfTlXbDotfvYsPU59h8cZebUbhbOm8ajO/YzNj75e9rV2cEb\nTzsKHvoRAHvufYoVs0dLXnvPvd3QtbD299AzGxb9Ue3PjyGJmpGzga3OuScBzOxm4BLAG4xcAlyT\n//ubwD+YmbmsVs/Wwp8ZOeLl0HtM0V1/8b1HGTw4q3i5MfiL7z3Poa6jfIVOr071h/7C3zimZJs+\numwRFwZsU+D78ujv6y3ZF0lIc6yWh/f24ig9iezZS13eq9+azYNctfZZhkd7gV5274WPrH2WQ11H\nHd4H73nTq/nlvQt4JZPByAlTdsKLxa9VKVWsMRDiKRyn/rFqIDzLEdYrr6oiRmVGGsuXGXnF1Id5\nxTEPBy/r6UBzGnBan+exUXjDvIDn7Mn/A97bF/B4wGtXbcbLmjoY6Qe2eW5vB14VtoxzbszMXgCO\n5PCubQHDvszI1KMP/+n9MQpSuNLM2pVn1PlUEkkpVyntq/W0h4qPEiAsH+jn0T0DsPu7h5d52dSd\nRc+J8vm0woB3aQWu/uPUweGApL+vl/NOncd167Zw5S0PFG1XIpMrKjPSWF0z096Cppap3jRmtgJY\nAbBgwYKUt6ZK/maaqbmrY/+PUZBOs6a+8kwkpVyltK/Wo4wnU0+VAoTCyXfAwT+cMPn4hSe8xBdf\n6q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UZj72KwYiZ/RdwTMBDn/DecM45Mwud6MbMjgW+ArzLOTcRsswKYAXAggULKm1a6lTQ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\nAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"HB0QCzkdMr71","colab_type":"text"},"source":["## Interactive visualization"]},{"cell_type":"code","metadata":{"id":"JsQ4HDZuMr72","colab_type":"code","colab":{}},"source":["def draw(M, learning_rate=1.0, tree_depth=1):\n"," pred_y = []\n"," for i in range(M):\n"," #if len(pred_y) < M:\n"," residuals = data_y - np.array(pred_y).sum(0)\n"," pred_y.append( weak_learner(data_x, residuals * learning_rate, max_depth = tree_depth) )\n"," \n"," connected_predicitons = np.array(pred_y[:M]).sum(0)\n"," plt.figure(figsize=(12,5))\n"," plt.plot(data_x, connected_predicitons, color='orange', linewidth=4);\n"," plt.scatter(data_x, data_y); plt.title(\"M value: \" + str(M)); plt.ylim(ylim);"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"lLqOPKc3Mr78","colab_type":"code","outputId":"35a5e09e-ce0b-4b8d-b76f-f24570c08d6e","executionInfo":{"status":"ok","timestamp":1574339901029,"user_tz":-60,"elapsed":832,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"resources":{"http://localhost:8080/nbextensions/google.colab/colabwidgets/controls.css":{"data":"/* Copyright (c) Jupyter Development Team.
 * Distributed under the terms of the Modified BSD License.
 */

 /* We import all of these together in a single css file because the Webpack
loader sees only one file at a time. This allows postcss to see the variable
definitions when they are used. */

 /*-----------------------------------------------------------------------------
| Copyright (c) Jupyter Development Team.
| Distributed under the terms of the Modified BSD License.
|----------------------------------------------------------------------------*/

 /*
This file is copied from the JupyterLab project to define default styling for
when the widget styling is compiled down to eliminate CSS variables. We make one
change - we comment out the font import below.
*/

 /**
 * The material design colors are adapted from google-material-color v1.2.6
 * https://github.com/danlevan/google-material-color
 * https://github.com/danlevan/google-material-color/blob/f67ca5f4028b2f1b34862f64b0ca67323f91b088/dist/palette.var.css
 *
 * The license for the material design color CSS variables is as follows (see
 * https://github.com/danlevan/google-material-color/blob/f67ca5f4028b2f1b34862f64b0ca67323f91b088/LICENSE)
 *
 * The MIT License (MIT)
 *
 * Copyright (c) 2014 Dan Le Van
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */

 /*
The following CSS variables define the main, public API for styling JupyterLab.
These variables should be used by all plugins wherever possible. In other
words, plugins should not define custom colors, sizes, etc unless absolutely
necessary. This enables users to change the visual theme of JupyterLab
by changing these variables.

Many variables appear in an ordered sequence (0,1,2,3). These sequences
are designed to work well together, so for example, `--jp-border-color1` should
be used with `--jp-layout-color1`. The numbers have the following meanings:

* 0: super-primary, reserved for special emphasis
* 1: primary, most important under normal situations
* 2: secondary, next most important under normal situations
* 3: tertiary, next most important under normal situations

Throughout JupyterLab, we are mostly following principles from Google's
Material Design when selecting colors. We are not, however, following
all of MD as it is not optimized for dense, information rich UIs.
*/

 /*
 * Optional monospace font for input/output prompt.
 */

 /* Commented out in ipywidgets since we don't need it. */

 /* @import url('https://fonts.googleapis.com/css?family=Roboto+Mono'); */

 /*
 * Added for compabitility with output area
 */

 :root {

  /* Borders

  The following variables, specify the visual styling of borders in JupyterLab.
   */

  /* UI Fonts

  The UI font CSS variables are used for the typography all of the JupyterLab
  user interface elements that are not directly user generated content.
  */ /* Base font size */ /* Ensures px perfect FontAwesome icons */

  /* Use these font colors against the corresponding main layout colors.
     In a light theme, these go from dark to light.
  */

  /* Use these against the brand/accent/warn/error colors.
     These will typically go from light to darker, in both a dark and light theme
   */

  /* Content Fonts

  Content font variables are used for typography of user generated content.
  */ /* Base font size */


  /* Layout

  The following are the main layout colors use in JupyterLab. In a light
  theme these would go from light to dark.
  */

  /* Brand/accent */

  /* State colors (warn, error, success, info) */

  /* Cell specific styles */
  /* A custom blend of MD grey and blue 600
   * See https://meyerweb.com/eric/tools/color-blend/#546E7A:1E88E5:5:hex */
  /* A custom blend of MD grey and orange 600
   * https://meyerweb.com/eric/tools/color-blend/#546E7A:F4511E:5:hex */

  /* Notebook specific styles */

  /* Console specific styles */

  /* Toolbar specific styles */
}

 /* Copyright (c) Jupyter Development Team.
 * Distributed under the terms of the Modified BSD License.
 */

 /*
 * We assume that the CSS variables in
 * https://github.com/jupyterlab/jupyterlab/blob/master/src/default-theme/variables.css
 * have been defined.
 */

 /* This file has code derived from PhosphorJS CSS files, as noted below. The license for this PhosphorJS code is:

Copyright (c) 2014-2017, PhosphorJS Contributors
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice,
  this list of conditions and the following disclaimer in the documentation
  and/or other materials provided with the distribution.

* Neither the name of the copyright holder nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*/

 /*
 * The following section is derived from https://github.com/phosphorjs/phosphor/blob/23b9d075ebc5b73ab148b6ebfc20af97f85714c4/packages/widgets/style/tabbar.css 
 * We've scoped the rules so that they are consistent with exactly our code.
 */

 .jupyter-widgets.widget-tab > .p-TabBar {
  display: -webkit-box;
  display: -ms-flexbox;
  display: flex;
  -webkit-user-select: none;
  -moz-user-select: none;
  -ms-user-select: none;
  user-select: none;
}

 .jupyter-widgets.widget-tab > .p-TabBar[data-orientation='horizontal'] {
  -webkit-box-orient: horizontal;
  -webkit-box-direction: normal;
      -ms-flex-direction: row;
          flex-direction: row;
}

 .jupyter-widgets.widget-tab > .p-TabBar[data-orientation='vertical'] {
  -webkit-box-orient: vertical;
  -webkit-box-direction: normal;
      -ms-flex-direction: column;
          flex-direction: column;
}

 .jupyter-widgets.widget-tab > .p-TabBar > .p-TabBar-content {
  margin: 0;
  padding: 0;
  display: -webkit-box;
  display: -ms-flexbox;
  display: flex;
  -webkit-box-flex: 1;
      -ms-flex: 1 1 auto;
          flex: 1 1 auto;
  list-style-type: none;
}

 .jupyter-widgets.widget-tab > .p-TabBar[data-orientation='horizontal'] > .p-TabBar-content {
  -webkit-box-orient: horizontal;
  -webkit-box-direction: normal;
      -ms-flex-direction: row;
          flex-direction: row;
}

 .jupyter-widgets.widget-tab > .p-TabBar[data-orientation='vertical'] > .p-TabBar-content {
  -webkit-box-orient: vertical;
  -webkit-box-direction: normal;
      -ms-flex-direction: column;
          flex-direction: column;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab {
  display: -webkit-box;
  display: -ms-flexbox;
  display: flex;
  -webkit-box-orient: horizontal;
  -webkit-box-direction: normal;
      -ms-flex-direction: row;
          flex-direction: row;
  -webkit-box-sizing: border-box;
          box-sizing: border-box;
  overflow: hidden;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabIcon,
.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabCloseIcon {
  -webkit-box-flex: 0;
      -ms-flex: 0 0 auto;
          flex: 0 0 auto;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabLabel {
  -webkit-box-flex: 1;
      -ms-flex: 1 1 auto;
          flex: 1 1 auto;
  overflow: hidden;
  white-space: nowrap;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab.p-mod-hidden {
  display: none !important;
}

 .jupyter-widgets.widget-tab > .p-TabBar.p-mod-dragging .p-TabBar-tab {
  position: relative;
}

 .jupyter-widgets.widget-tab > .p-TabBar.p-mod-dragging[data-orientation='horizontal'] .p-TabBar-tab {
  left: 0;
  -webkit-transition: left 150ms ease;
  transition: left 150ms ease;
}

 .jupyter-widgets.widget-tab > .p-TabBar.p-mod-dragging[data-orientation='vertical'] .p-TabBar-tab {
  top: 0;
  -webkit-transition: top 150ms ease;
  transition: top 150ms ease;
}

 .jupyter-widgets.widget-tab > .p-TabBar.p-mod-dragging .p-TabBar-tab.p-mod-dragging {
  -webkit-transition: none;
  transition: none;
}

 /* End tabbar.css */

 :root { /* margin between inline elements */

    /* From Material Design Lite */
}

 .jupyter-widgets {
    margin: 2px;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    color: black;
    overflow: visible;
}

 .jupyter-widgets.jupyter-widgets-disconnected::before {
    line-height: 28px;
    height: 28px;
}

 .jp-Output-result > .jupyter-widgets {
    margin-left: 0;
    margin-right: 0;
}

 /* vbox and hbox */

 .widget-inline-hbox {
    /* Horizontal widgets */
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-orient: horizontal;
    -webkit-box-direction: normal;
        -ms-flex-direction: row;
            flex-direction: row;
    -webkit-box-align: baseline;
        -ms-flex-align: baseline;
            align-items: baseline;
}

 .widget-inline-vbox {
    /* Vertical Widgets */
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-orient: vertical;
    -webkit-box-direction: normal;
        -ms-flex-direction: column;
            flex-direction: column;
    -webkit-box-align: center;
        -ms-flex-align: center;
            align-items: center;
}

 .widget-box {
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    margin: 0;
    overflow: auto;
}

 .widget-gridbox {
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    display: grid;
    margin: 0;
    overflow: auto;
}

 .widget-hbox {
    -webkit-box-orient: horizontal;
    -webkit-box-direction: normal;
        -ms-flex-direction: row;
            flex-direction: row;
}

 .widget-vbox {
    -webkit-box-orient: vertical;
    -webkit-box-direction: normal;
        -ms-flex-direction: column;
            flex-direction: column;
}

 /* General Button Styling */

 .jupyter-button {
    padding-left: 10px;
    padding-right: 10px;
    padding-top: 0px;
    padding-bottom: 0px;
    display: inline-block;
    white-space: nowrap;
    overflow: hidden;
    text-overflow: ellipsis;
    text-align: center;
    font-size: 13px;
    cursor: pointer;

    height: 28px;
    border: 0px solid;
    line-height: 28px;
    -webkit-box-shadow: none;
            box-shadow: none;

    color: rgba(0, 0, 0, .8);
    background-color: #EEEEEE;
    border-color: #E0E0E0;
    border: none;
}

 .jupyter-button i.fa {
    margin-right: 4px;
    pointer-events: none;
}

 .jupyter-button:empty:before {
    content: "\200b"; /* zero-width space */
}

 .jupyter-widgets.jupyter-button:disabled {
    opacity: 0.6;
}

 .jupyter-button i.fa.center {
    margin-right: 0;
}

 .jupyter-button:hover:enabled, .jupyter-button:focus:enabled {
    /* MD Lite 2dp shadow */
    -webkit-box-shadow: 0 2px 2px 0 rgba(0, 0, 0, .14),
                0 3px 1px -2px rgba(0, 0, 0, .2),
                0 1px 5px 0 rgba(0, 0, 0, .12);
            box-shadow: 0 2px 2px 0 rgba(0, 0, 0, .14),
                0 3px 1px -2px rgba(0, 0, 0, .2),
                0 1px 5px 0 rgba(0, 0, 0, .12);
}

 .jupyter-button:active, .jupyter-button.mod-active {
    /* MD Lite 4dp shadow */
    -webkit-box-shadow: 0 4px 5px 0 rgba(0, 0, 0, .14),
                0 1px 10px 0 rgba(0, 0, 0, .12),
                0 2px 4px -1px rgba(0, 0, 0, .2);
            box-shadow: 0 4px 5px 0 rgba(0, 0, 0, .14),
                0 1px 10px 0 rgba(0, 0, 0, .12),
                0 2px 4px -1px rgba(0, 0, 0, .2);
    color: rgba(0, 0, 0, .8);
    background-color: #BDBDBD;
}

 .jupyter-button:focus:enabled {
    outline: 1px solid #64B5F6;
}

 /* Button "Primary" Styling */

 .jupyter-button.mod-primary {
    color: rgba(255, 255, 255, 1.0);
    background-color: #2196F3;
}

 .jupyter-button.mod-primary.mod-active {
    color: rgba(255, 255, 255, 1);
    background-color: #1976D2;
}

 .jupyter-button.mod-primary:active {
    color: rgba(255, 255, 255, 1);
    background-color: #1976D2;
}

 /* Button "Success" Styling */

 .jupyter-button.mod-success {
    color: rgba(255, 255, 255, 1.0);
    background-color: #4CAF50;
}

 .jupyter-button.mod-success.mod-active {
    color: rgba(255, 255, 255, 1);
    background-color: #388E3C;
 }

 .jupyter-button.mod-success:active {
    color: rgba(255, 255, 255, 1);
    background-color: #388E3C;
 }

 /* Button "Info" Styling */

 .jupyter-button.mod-info {
    color: rgba(255, 255, 255, 1.0);
    background-color: #00BCD4;
}

 .jupyter-button.mod-info.mod-active {
    color: rgba(255, 255, 255, 1);
    background-color: #0097A7;
}

 .jupyter-button.mod-info:active {
    color: rgba(255, 255, 255, 1);
    background-color: #0097A7;
}

 /* Button "Warning" Styling */

 .jupyter-button.mod-warning {
    color: rgba(255, 255, 255, 1.0);
    background-color: #FF9800;
}

 .jupyter-button.mod-warning.mod-active {
    color: rgba(255, 255, 255, 1);
    background-color: #F57C00;
}

 .jupyter-button.mod-warning:active {
    color: rgba(255, 255, 255, 1);
    background-color: #F57C00;
}

 /* Button "Danger" Styling */

 .jupyter-button.mod-danger {
    color: rgba(255, 255, 255, 1.0);
    background-color: #F44336;
}

 .jupyter-button.mod-danger.mod-active {
    color: rgba(255, 255, 255, 1);
    background-color: #D32F2F;
}

 .jupyter-button.mod-danger:active {
    color: rgba(255, 255, 255, 1);
    background-color: #D32F2F;
}

 /* Widget Button*/

 .widget-button, .widget-toggle-button {
    width: 148px;
}

 /* Widget Label Styling */

 /* Override Bootstrap label css */

 .jupyter-widgets label {
    margin-bottom: 0;
    margin-bottom: initial;
}

 .widget-label-basic {
    /* Basic Label */
    color: black;
    font-size: 13px;
    overflow: hidden;
    text-overflow: ellipsis;
    white-space: nowrap;
    line-height: 28px;
}

 .widget-label {
    /* Label */
    color: black;
    font-size: 13px;
    overflow: hidden;
    text-overflow: ellipsis;
    white-space: nowrap;
    line-height: 28px;
}

 .widget-inline-hbox .widget-label {
    /* Horizontal Widget Label */
    color: black;
    text-align: right;
    margin-right: 8px;
    width: 80px;
    -ms-flex-negative: 0;
        flex-shrink: 0;
}

 .widget-inline-vbox .widget-label {
    /* Vertical Widget Label */
    color: black;
    text-align: center;
    line-height: 28px;
}

 /* Widget Readout Styling */

 .widget-readout {
    color: black;
    font-size: 13px;
    height: 28px;
    line-height: 28px;
    overflow: hidden;
    white-space: nowrap;
    text-align: center;
}

 .widget-readout.overflow {
    /* Overflowing Readout */

    /* From Material Design Lite
        shadow-key-umbra-opacity: 0.2;
        shadow-key-penumbra-opacity: 0.14;
        shadow-ambient-shadow-opacity: 0.12;
     */
    -webkit-box-shadow: 0 2px 2px 0 rgba(0, 0, 0, .2),
                        0 3px 1px -2px rgba(0, 0, 0, .14),
                        0 1px 5px 0 rgba(0, 0, 0, .12);

    box-shadow: 0 2px 2px 0 rgba(0, 0, 0, .2),
                0 3px 1px -2px rgba(0, 0, 0, .14),
                0 1px 5px 0 rgba(0, 0, 0, .12);
}

 .widget-inline-hbox .widget-readout {
    /* Horizontal Readout */
    text-align: center;
    max-width: 148px;
    min-width: 72px;
    margin-left: 4px;
}

 .widget-inline-vbox .widget-readout {
    /* Vertical Readout */
    margin-top: 4px;
    /* as wide as the widget */
    width: inherit;
}

 /* Widget Checkbox Styling */

 .widget-checkbox {
    width: 300px;
    height: 28px;
    line-height: 28px;
}

 .widget-checkbox input[type="checkbox"] {
    margin: 0px 8px 0px 0px;
    line-height: 28px;
    font-size: large;
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    -ms-flex-negative: 0;
        flex-shrink: 0;
    -ms-flex-item-align: center;
        align-self: center;
}

 /* Widget Valid Styling */

 .widget-valid {
    height: 28px;
    line-height: 28px;
    width: 148px;
    font-size: 13px;
}

 .widget-valid i:before {
    line-height: 28px;
    margin-right: 4px;
    margin-left: 4px;

    /* from the fa class in FontAwesome: https://github.com/FortAwesome/Font-Awesome/blob/49100c7c3a7b58d50baa71efef11af41a66b03d3/css/font-awesome.css#L14 */
    display: inline-block;
    font: normal normal normal 14px/1 FontAwesome;
    font-size: inherit;
    text-rendering: auto;
    -webkit-font-smoothing: antialiased;
    -moz-osx-font-smoothing: grayscale;
}

 .widget-valid.mod-valid i:before {
    content: "\f00c";
    color: green;
}

 .widget-valid.mod-invalid i:before {
    content: "\f00d";
    color: red;
}

 .widget-valid.mod-valid .widget-valid-readout {
    display: none;
}

 /* Widget Text and TextArea Stying */

 .widget-textarea, .widget-text {
    width: 300px;
}

 .widget-text input[type="text"], .widget-text input[type="number"]{
    height: 28px;
    line-height: 28px;
}

 .widget-text input[type="text"]:disabled, .widget-text input[type="number"]:disabled, .widget-textarea textarea:disabled {
    opacity: 0.6;
}

 .widget-text input[type="text"], .widget-text input[type="number"], .widget-textarea textarea {
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    border: 1px solid #9E9E9E;
    background-color: white;
    color: rgba(0, 0, 0, .8);
    font-size: 13px;
    padding: 4px 8px;
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    min-width: 0; /* This makes it possible for the flexbox to shrink this input */
    -ms-flex-negative: 1;
        flex-shrink: 1;
    outline: none !important;
}

 .widget-textarea textarea {
    height: inherit;
    width: inherit;
}

 .widget-text input:focus, .widget-textarea textarea:focus {
    border-color: #64B5F6;
}

 /* Widget Slider */

 .widget-slider .ui-slider {
    /* Slider Track */
    border: 1px solid #BDBDBD;
    background: #BDBDBD;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    position: relative;
    border-radius: 0px;
}

 .widget-slider .ui-slider .ui-slider-handle {
    /* Slider Handle */
    outline: none !important; /* focused slider handles are colored - see below */
    position: absolute;
    background-color: white;
    border: 1px solid #9E9E9E;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    z-index: 1;
    background-image: none; /* Override jquery-ui */
}

 /* Override jquery-ui */

 .widget-slider .ui-slider .ui-slider-handle:hover, .widget-slider .ui-slider .ui-slider-handle:focus {
    background-color: #2196F3;
    border: 1px solid #2196F3;
}

 .widget-slider .ui-slider .ui-slider-handle:active {
    background-color: #2196F3;
    border-color: #2196F3;
    z-index: 2;
    -webkit-transform: scale(1.2);
            transform: scale(1.2);
}

 .widget-slider  .ui-slider .ui-slider-range {
    /* Interval between the two specified value of a double slider */
    position: absolute;
    background: #2196F3;
    z-index: 0;
}

 /* Shapes of Slider Handles */

 .widget-hslider .ui-slider .ui-slider-handle {
    width: 16px;
    height: 16px;
    margin-top: -7px;
    margin-left: -7px;
    border-radius: 50%;
    top: 0;
}

 .widget-vslider .ui-slider .ui-slider-handle {
    width: 16px;
    height: 16px;
    margin-bottom: -7px;
    margin-left: -7px;
    border-radius: 50%;
    left: 0;
}

 .widget-hslider .ui-slider .ui-slider-range {
    height: 8px;
    margin-top: -3px;
}

 .widget-vslider .ui-slider .ui-slider-range {
    width: 8px;
    margin-left: -3px;
}

 /* Horizontal Slider */

 .widget-hslider {
    width: 300px;
    height: 28px;
    line-height: 28px;

    /* Override the align-items baseline. This way, the description and readout
    still seem to align their baseline properly, and we don't have to have
    align-self: stretch in the .slider-container. */
    -webkit-box-align: center;
        -ms-flex-align: center;
            align-items: center;
}

 .widgets-slider .slider-container {
    overflow: visible;
}

 .widget-hslider .slider-container {
    height: 28px;
    margin-left: 6px;
    margin-right: 6px;
    -webkit-box-flex: 1;
        -ms-flex: 1 1 148px;
            flex: 1 1 148px;
}

 .widget-hslider .ui-slider {
    /* Inner, invisible slide div */
    height: 4px;
    margin-top: 12px;
    width: 100%;
}

 /* Vertical Slider */

 .widget-vbox .widget-label {
    height: 28px;
    line-height: 28px;
}

 .widget-vslider {
    /* Vertical Slider */
    height: 200px;
    width: 72px;
}

 .widget-vslider .slider-container {
    -webkit-box-flex: 1;
        -ms-flex: 1 1 148px;
            flex: 1 1 148px;
    margin-left: auto;
    margin-right: auto;
    margin-bottom: 6px;
    margin-top: 6px;
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-orient: vertical;
    -webkit-box-direction: normal;
        -ms-flex-direction: column;
            flex-direction: column;
}

 .widget-vslider .ui-slider-vertical {
    /* Inner, invisible slide div */
    width: 4px;
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    margin-left: auto;
    margin-right: auto;
}

 /* Widget Progress Styling */

 .progress-bar {
    -webkit-transition: none;
    transition: none;
}

 .progress-bar {
    height: 28px;
}

 .progress-bar {
    background-color: #2196F3;
}

 .progress-bar-success {
    background-color: #4CAF50;
}

 .progress-bar-info {
    background-color: #00BCD4;
}

 .progress-bar-warning {
    background-color: #FF9800;
}

 .progress-bar-danger {
    background-color: #F44336;
}

 .progress {
    background-color: #EEEEEE;
    border: none;
    -webkit-box-shadow: none;
            box-shadow: none;
}

 /* Horisontal Progress */

 .widget-hprogress {
    /* Progress Bar */
    height: 28px;
    line-height: 28px;
    width: 300px;
    -webkit-box-align: center;
        -ms-flex-align: center;
            align-items: center;

}

 .widget-hprogress .progress {
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    margin-top: 4px;
    margin-bottom: 4px;
    -ms-flex-item-align: stretch;
        align-self: stretch;
    /* Override bootstrap style */
    height: auto;
    height: initial;
}

 /* Vertical Progress */

 .widget-vprogress {
    height: 200px;
    width: 72px;
}

 .widget-vprogress .progress {
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    width: 20px;
    margin-left: auto;
    margin-right: auto;
    margin-bottom: 0;
}

 /* Select Widget Styling */

 .widget-dropdown {
    height: 28px;
    width: 300px;
    line-height: 28px;
}

 .widget-dropdown > select {
    padding-right: 20px;
    border: 1px solid #9E9E9E;
    border-radius: 0;
    height: inherit;
    -webkit-box-flex: 1;
        -ms-flex: 1 1 148px;
            flex: 1 1 148px;
    min-width: 0; /* This makes it possible for the flexbox to shrink this input */
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    outline: none !important;
    -webkit-box-shadow: none;
            box-shadow: none;
    background-color: white;
    color: rgba(0, 0, 0, .8);
    font-size: 13px;
    vertical-align: top;
    padding-left: 8px;
	appearance: none;
	-webkit-appearance: none;
	-moz-appearance: none;
    background-repeat: no-repeat;
	background-size: 20px;
	background-position: right center;
    background-image: url("data:image/svg+xml;base64,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");
}

 .widget-dropdown > select:focus {
    border-color: #64B5F6;
}

 .widget-dropdown > select:disabled {
    opacity: 0.6;
}

 /* To disable the dotted border in Firefox around select controls.
   See http://stackoverflow.com/a/18853002 */

 .widget-dropdown > select:-moz-focusring {
    color: transparent;
    text-shadow: 0 0 0 #000;
}

 /* Select and SelectMultiple */

 .widget-select {
    width: 300px;
    line-height: 28px;

    /* Because Firefox defines the baseline of a select as the bottom of the
    control, we align the entire control to the top and add padding to the
    select to get an approximate first line baseline alignment. */
    -webkit-box-align: start;
        -ms-flex-align: start;
            align-items: flex-start;
}

 .widget-select > select {
    border: 1px solid #9E9E9E;
    background-color: white;
    color: rgba(0, 0, 0, .8);
    font-size: 13px;
    -webkit-box-flex: 1;
        -ms-flex: 1 1 148px;
            flex: 1 1 148px;
    outline: none !important;
    overflow: auto;
    height: inherit;

    /* Because Firefox defines the baseline of a select as the bottom of the
    control, we align the entire control to the top and add padding to the
    select to get an approximate first line baseline alignment. */
    padding-top: 5px;
}

 .widget-select > select:focus {
    border-color: #64B5F6;
}

 .wiget-select > select > option {
    padding-left: 4px;
    line-height: 28px;
    /* line-height doesn't work on some browsers for select options */
    padding-top: calc(28px - var(--jp-widgets-font-size) / 2);
    padding-bottom: calc(28px - var(--jp-widgets-font-size) / 2);
}

 /* Toggle Buttons Styling */

 .widget-toggle-buttons {
    line-height: 28px;
}

 .widget-toggle-buttons .widget-toggle-button {
    margin-left: 2px;
    margin-right: 2px;
}

 .widget-toggle-buttons .jupyter-button:disabled {
    opacity: 0.6;
}

 /* Radio Buttons Styling */

 .widget-radio {
    width: 300px;
    line-height: 28px;
}

 .widget-radio-box {
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-orient: vertical;
    -webkit-box-direction: normal;
        -ms-flex-direction: column;
            flex-direction: column;
    -webkit-box-align: stretch;
        -ms-flex-align: stretch;
            align-items: stretch;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    margin-bottom: 8px;
}

 .widget-radio-box label {
    height: 20px;
    line-height: 20px;
    font-size: 13px;
}

 .widget-radio-box input {
    height: 20px;
    line-height: 20px;
    margin: 0 8px 0 1px;
    float: left;
}

 /* Color Picker Styling */

 .widget-colorpicker {
    width: 300px;
    height: 28px;
    line-height: 28px;
}

 .widget-colorpicker > .widget-colorpicker-input {
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    -ms-flex-negative: 1;
        flex-shrink: 1;
    min-width: 72px;
}

 .widget-colorpicker input[type="color"] {
    width: 28px;
    height: 28px;
    padding: 0 2px; /* make the color square actually square on Chrome on OS X */
    background: white;
    color: rgba(0, 0, 0, .8);
    border: 1px solid #9E9E9E;
    border-left: none;
    -webkit-box-flex: 0;
        -ms-flex-positive: 0;
            flex-grow: 0;
    -ms-flex-negative: 0;
        flex-shrink: 0;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    -ms-flex-item-align: stretch;
        align-self: stretch;
    outline: none !important;
}

 .widget-colorpicker.concise input[type="color"] {
    border-left: 1px solid #9E9E9E;
}

 .widget-colorpicker input[type="color"]:focus, .widget-colorpicker input[type="text"]:focus {
    border-color: #64B5F6;
}

 .widget-colorpicker input[type="text"] {
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    outline: none !important;
    height: 28px;
    line-height: 28px;
    background: white;
    color: rgba(0, 0, 0, .8);
    border: 1px solid #9E9E9E;
    font-size: 13px;
    padding: 4px 8px;
    min-width: 0; /* This makes it possible for the flexbox to shrink this input */
    -ms-flex-negative: 1;
        flex-shrink: 1;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
}

 .widget-colorpicker input[type="text"]:disabled {
    opacity: 0.6;
}

 /* Date Picker Styling */

 .widget-datepicker {
    width: 300px;
    height: 28px;
    line-height: 28px;
}

 .widget-datepicker input[type="date"] {
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    -ms-flex-negative: 1;
        flex-shrink: 1;
    min-width: 0; /* This makes it possible for the flexbox to shrink this input */
    outline: none !important;
    height: 28px;
    border: 1px solid #9E9E9E;
    background-color: white;
    color: rgba(0, 0, 0, .8);
    font-size: 13px;
    padding: 4px 8px;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
}

 .widget-datepicker input[type="date"]:focus {
    border-color: #64B5F6;
}

 .widget-datepicker input[type="date"]:invalid {
    border-color: #FF9800;
}

 .widget-datepicker input[type="date"]:disabled {
    opacity: 0.6;
}

 /* Play Widget */

 .widget-play {
    width: 148px;
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-align: stretch;
        -ms-flex-align: stretch;
            align-items: stretch;
}

 .widget-play .jupyter-button {
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    height: auto;
}

 .widget-play .jupyter-button:disabled {
    opacity: 0.6;
}

 /* Tab Widget */

 .jupyter-widgets.widget-tab {
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-orient: vertical;
    -webkit-box-direction: normal;
        -ms-flex-direction: column;
            flex-direction: column;
}

 .jupyter-widgets.widget-tab > .p-TabBar {
    /* Necessary so that a tab can be shifted down to overlay the border of the box below. */
    overflow-x: visible;
    overflow-y: visible;
}

 .jupyter-widgets.widget-tab > .p-TabBar > .p-TabBar-content {
    /* Make sure that the tab grows from bottom up */
    -webkit-box-align: end;
        -ms-flex-align: end;
            align-items: flex-end;
    min-width: 0;
    min-height: 0;
}

 .jupyter-widgets.widget-tab > .widget-tab-contents {
    width: 100%;
    -webkit-box-sizing: border-box;
            box-sizing: border-box;
    margin: 0;
    background: white;
    color: rgba(0, 0, 0, .8);
    border: 1px solid #9E9E9E;
    padding: 15px;
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    overflow: auto;
}

 .jupyter-widgets.widget-tab > .p-TabBar {
    font: 13px Helvetica, Arial, sans-serif;
    min-height: 25px;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab {
    -webkit-box-flex: 0;
        -ms-flex: 0 1 144px;
            flex: 0 1 144px;
    min-width: 35px;
    min-height: 25px;
    line-height: 24px;
    margin-left: -1px;
    padding: 0px 10px;
    background: #EEEEEE;
    color: rgba(0, 0, 0, .5);
    border: 1px solid #9E9E9E;
    border-bottom: none;
    position: relative;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab.p-mod-current {
    color: rgba(0, 0, 0, 1.0);
    /* We want the background to match the tab content background */
    background: white;
    min-height: 26px;
    -webkit-transform: translateY(1px);
            transform: translateY(1px);
    overflow: visible;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab.p-mod-current:before {
    position: absolute;
    top: -1px;
    left: -1px;
    content: '';
    height: 2px;
    width: calc(100% + 2px);
    background: #2196F3;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab:first-child {
    margin-left: 0;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tab:hover:not(.p-mod-current) {
    background: white;
    color: rgba(0, 0, 0, .8);
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-mod-closable > .p-TabBar-tabCloseIcon {
    margin-left: 4px;
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-mod-closable > .p-TabBar-tabCloseIcon:before {
    font-family: FontAwesome;
    content: '\f00d'; /* close */
}

 .jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabIcon,
.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabLabel,
.jupyter-widgets.widget-tab > .p-TabBar .p-TabBar-tabCloseIcon {
    line-height: 24px;
}

 /* Accordion Widget */

 .p-Collapse {
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-orient: vertical;
    -webkit-box-direction: normal;
        -ms-flex-direction: column;
            flex-direction: column;
    -webkit-box-align: stretch;
        -ms-flex-align: stretch;
            align-items: stretch;
}

 .p-Collapse-header {
    padding: 4px;
    cursor: pointer;
    color: rgba(0, 0, 0, .5);
    background-color: #EEEEEE;
    border: 1px solid #9E9E9E;
    padding: 10px 15px;
    font-weight: bold;
}

 .p-Collapse-header:hover {
    background-color: white;
    color: rgba(0, 0, 0, .8);
}

 .p-Collapse-open > .p-Collapse-header {
    background-color: white;
    color: rgba(0, 0, 0, 1.0);
    cursor: default;
    border-bottom: none;
}

 .p-Collapse .p-Collapse-header::before {
    content: '\f0da\00A0';  /* caret-right, non-breaking space */
    display: inline-block;
    font: normal normal normal 14px/1 FontAwesome;
    font-size: inherit;
    text-rendering: auto;
    -webkit-font-smoothing: antialiased;
    -moz-osx-font-smoothing: grayscale;
}

 .p-Collapse-open > .p-Collapse-header::before {
    content: '\f0d7\00A0'; /* caret-down, non-breaking space */
}

 .p-Collapse-contents {
    padding: 15px;
    background-color: white;
    color: rgba(0, 0, 0, .8);
    border-left: 1px solid #9E9E9E;
    border-right: 1px solid #9E9E9E;
    border-bottom: 1px solid #9E9E9E;
    overflow: auto;
}

 .p-Accordion {
    display: -webkit-box;
    display: -ms-flexbox;
    display: flex;
    -webkit-box-orient: vertical;
    -webkit-box-direction: normal;
        -ms-flex-direction: column;
            flex-direction: column;
    -webkit-box-align: stretch;
        -ms-flex-align: stretch;
            align-items: stretch;
}

 .p-Accordion .p-Collapse {
    margin-bottom: 0;
}

 .p-Accordion .p-Collapse + .p-Collapse {
    margin-top: 4px;
}

 /* HTML widget */

 .widget-html, .widget-htmlmath {
    font-size: 13px;
}

 .widget-html > .widget-html-content, .widget-htmlmath > .widget-html-content {
    /* Fill out the area in the HTML widget */
    -ms-flex-item-align: stretch;
        align-self: stretch;
    -webkit-box-flex: 1;
        -ms-flex-positive: 1;
            flex-grow: 1;
    -ms-flex-negative: 1;
        flex-shrink: 1;
    /* Makes sure the baseline is still aligned with other elements */
    line-height: 28px;
    /* Make it possible to have absolutely-positioned elements in the html */
    position: relative;
}

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 */","ok":true,"headers":[["content-type","text/css"]],"status":200,"status_text":""}},"base_uri":"https://localhost:8080/","height":432}},"source":["interactive_plot = interactive( draw,\n"," M=widgets.IntSlider(min=1,max=200,step=1,value=1, continuous_update=False),\n"," learning_rate=widgets.FloatText(step=0.1,value=1,continuous_update=True),\n"," tree_depth=widgets.IntText(step=1,value=1, continuous_update=True))\n","\n","output = interactive_plot.children[-1]\n","output.layout.height = '350px'\n","interactive_plot"],"execution_count":27,"outputs":[{"output_type":"display_data","data":{"application/vnd.jupyter.widget-view+json":{"model_id":"b204c64272814c0e918630c7e019e8ae","version_minor":0,"version_major":2},"text/plain":["interactive(children=(IntSlider(value=1, continuous_update=False, description='M', max=200, min=1), FloatText(…"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"vZsRLgUrMr7_","colab_type":"text"},"source":["# Binary Classification with Gradient Boosting"]},{"cell_type":"markdown","metadata":{"id":"NhWVEL5aMr8A","colab_type":"text"},"source":["## Loading explanatory data"]},{"cell_type":"code","metadata":{"id":"YYhMIr3QMr8C","colab_type":"code","outputId":"2f3af248-a9ba-4bab-8a4c-4b6947475443","executionInfo":{"status":"ok","timestamp":1574339834590,"user_tz":-60,"elapsed":4948,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":408}},"source":["from sklearn import datasets\n","dataset = datasets.load_breast_cancer()\n","\n","data = dataset['data']\n","data -= np.mean(data)\n","\n","targ = dataset['target']\n","\n","train_x = data[:400]\n","train_y = targ[:400]\n","test_x = data[400:]\n","test_y = targ[400:]\n","\n","print('training shape: ', train_x.shape)\n","print('test set shape: ', test_x.shape)\n","\n","plt.figure(figsize=(10,6))\n","plt.scatter(data[:, 0], data[:, 1], c=targ, alpha=0.5, cmap='jet', s=50);"],"execution_count":10,"outputs":[{"output_type":"stream","text":["training shape: (400, 30)\n","test set shape: (169, 30)\n"],"name":"stdout"},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAlgAAAFlCAYAAAA3apYyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nZA2WmLCCra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YNBpNpMFxBekTMU15Oy+bNzLn11jNaV3QuecrLueqBBwj39JCIRnEUFmK0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7nnbIVo5Hl//qv7PnVr2jfvj076Lfq+uuZ/uEPI4Sg7pZb6HjnHWKBQPZ1JcJh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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"mHejgB6eMr8G","colab_type":"text"},"source":["## We will treat classification similarly as regression\n","\n","**We round predicted float value to the closest integer**"]},{"cell_type":"code","metadata":{"id":"_WuGBrhQMr8H","colab_type":"code","colab":{}},"source":["from sklearn.tree import DecisionTreeRegressor\n","\n","def weak_classify(data, target):\n"," tree = DecisionTreeRegressor(criterion='mse', max_depth=1)\n"," tree.fit(data, target)\n"," pred = tree.predict(data);\n"," return pred, tree\n","\n","def predict(trees, data, learning_rate=1):\n"," pred = trees[0].predict(test_x)\n"," for tree in trees[1:]:\n"," pred += tree.predict(test_x) * learning_rate\n"," return np.round( pred )"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"4qiWRDg6Mr8M","colab_type":"text"},"source":["## Create first learner"]},{"cell_type":"code","metadata":{"scrolled":true,"id":"vnBYQiAyMr8O","colab_type":"code","outputId":"b2118ad0-337b-4fb6-d69c-09aa8c4b9b98","executionInfo":{"status":"ok","timestamp":1574339834592,"user_tz":-60,"elapsed":4904,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["prediction = []\n","trees = []\n","tr_errors = []\n","ts_errors = []\n","\n","pred, tree = weak_classify(train_x, train_y)\n","prediction.append(pred)\n","trees.append(tree)\n","\n","resi = train_y - prediction[-1]\n","\n","tr_errors.append( np.sum( np.round(np.array(prediction).sum(0)) == train_y) / train_y.shape[0] )\n","ts_errors.append( np.sum(predict(trees, test_x) == test_y)/test_y.shape[0] )\n","print( 'training accuracy: ', tr_errors[-1] )\n","print( 'test accuracy: ', ts_errors[-1] )"],"execution_count":12,"outputs":[{"output_type":"stream","text":["training accuracy: 0.925\n","test accuracy: 0.893491124260355\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"4GfyXyA7Mr8U","colab_type":"text"},"source":["# Create next M learners\n","\n","**The same way as before - fit the next learner to the residuals of the previous one!**"]},{"cell_type":"code","metadata":{"scrolled":true,"id":"PPP3Vo4xMr8W","colab_type":"code","outputId":"4ba168e8-8af9-41e1-b133-9eba8a5708ec","executionInfo":{"status":"ok","timestamp":1574339835813,"user_tz":-60,"elapsed":6106,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["learning_rate = 0.5\n","\n","for i in range(100): # M = 100 here\n"," pred, tree = weak_classify(train_x, resi)\n"," prediction.append(pred * learning_rate)\n"," trees.append(tree)\n"," \n"," resi = (resi - prediction[-1]) # calculate new residuals\n"," \n"," # save errors to history array\n"," tr_errors.append( np.sum(np.round( np.array(prediction).sum(0) ) == train_y) / train_y.shape[0] )\n"," ts_errors.append( np.sum(predict(trees, test_x) == test_y)/test_y.shape[0] )\n"," \n","print( 'training error: ', np.max(np.array(tr_errors)) )\n","print( 'test error: ', np.max(np.array(ts_errors)) )"],"execution_count":13,"outputs":[{"output_type":"stream","text":["training error: 0.9825\n","test error: 0.9644970414201184\n"],"name":"stdout"}]},{"cell_type":"code","metadata":{"id":"E-gIkJWsMr8c","colab_type":"code","outputId":"310e1187-7d92-453b-dfa8-4750e2f7e7c1","executionInfo":{"status":"ok","timestamp":1574339835815,"user_tz":-60,"elapsed":6083,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":296}},"source":["plt.figure(figsize=(15,4))\n","plt.plot(tr_errors, linewidth=5, label='training')\n","plt.plot(ts_errors, linewidth=5, label='validation')\n","plt.xlabel('M value')\n","plt.ylabel('accuracy')\n","plt.legend(loc=4)"],"execution_count":14,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{"tags":[]},"execution_count":14},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA34AAAEGCAYAAAA6x0eRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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7r46lBTDv0c4xbK99LgQLnsj8K/ZzHvgK48tf+D8ev/ys/Kro75yJsHEq72vJaTA9Z9A8x7e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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"URDB2TnIMr8i","colab_type":"text"},"source":["### It can be compared with Random Forest Classifier"]},{"cell_type":"code","metadata":{"id":"KhhaPBvqMr8l","colab_type":"code","outputId":"7045591a-493d-4ff0-c019-23d6387f2ddd","executionInfo":{"status":"ok","timestamp":1574339835816,"user_tz":-60,"elapsed":6069,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["from sklearn.ensemble import RandomForestClassifier as RFC\n","forest = RFC(n_estimators=100)\n","forest.fit(train_x, train_y)\n","forest.score(test_x, test_y)"],"execution_count":15,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0.9763313609467456"]},"metadata":{"tags":[]},"execution_count":15}]},{"cell_type":"markdown","metadata":{"id":"lBiG1czjMr8r","colab_type":"text"},"source":["# Binary Classification with Adaptive Boosting"]},{"cell_type":"markdown","metadata":{"id":"mE_YgczDMr8u","colab_type":"text"},"source":["## 0) We introduce a probability distribution"]},{"cell_type":"code","metadata":{"scrolled":true,"id":"z3xwsC2_Mr8x","colab_type":"code","outputId":"e74f66b8-0fe0-4b9a-e18d-acd68a7eaa6d","executionInfo":{"status":"ok","timestamp":1574339835817,"user_tz":-60,"elapsed":6035,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["distrib = np.ones(train_x.shape[0]) / train_x.shape[0]\n","print(\"Probability distribution:\", distrib[:10], \"...\")\n","\n","idx = np.random.choice(range(train_x.shape[0]), size=train_x.shape[0], replace=True, p=distrib)\n","idx = np.unique(idx)\n","\n","temporal_train_x = train_x [ idx ]\n","temporal_train_y = train_y [ idx ]\n","\n","print(\"Uniques in sampled set:\", idx.shape[0])"],"execution_count":16,"outputs":[{"output_type":"stream","text":["Probability distribution: [0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025 0.0025] ...\n","Uniques in sampled set: 250\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"yoUt3vjZMr85","colab_type":"text"},"source":["## 1) Create first classifier on it\n","**Decision Tree stomp**"]},{"cell_type":"code","metadata":{"id":"313sOaZhMr87","colab_type":"code","outputId":"91d3c483-c58e-4b24-c583-78ac0a835200","executionInfo":{"status":"ok","timestamp":1574339835822,"user_tz":-60,"elapsed":6026,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["pred, tree = weak_classify(temporal_train_x, temporal_train_y)\n","pred = np.round(tree.predict(train_x)) \n","accuracy = np.sum(pred==train_y) / pred.shape[0]\n","\n","print( 'training accuracy: ', accuracy )\n","print( 'test accuracy: ', np.sum( np.round(tree.predict(test_x)) == test_y) / test_y.shape[0] )"],"execution_count":17,"outputs":[{"output_type":"stream","text":["training accuracy: 0.9125\n","test accuracy: 0.893491124260355\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"r1VYtYQSMr9A","colab_type":"text"},"source":["## 2) Compute classifier weight\n","\n","### $\\alpha_t = \\frac12 \\ln(\\frac{1-\\epsilon_t}{\\epsilon_t})$"]},{"cell_type":"code","metadata":{"id":"mRs3FHQWMr9B","colab_type":"code","outputId":"ff6697e2-b403-4438-9e6f-b84aa8237c69","executionInfo":{"status":"ok","timestamp":1574339835828,"user_tz":-60,"elapsed":6009,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["def classifier_weight(accuracy):\n"," return 1/2 * np.log((accuracy)/(1-accuracy))\n","\n","weight = classifier_weight(accuracy)\n","print(weight)"],"execution_count":18,"outputs":[{"output_type":"stream","text":["1.1722746460465387\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"JpJKSaZTMr9H","colab_type":"text"},"source":["## 3) Compute new data distribution\n","\n","### $D_{t+1}(i) = \\frac{D_{t} \\exp(-\\alpha_t y_i h_t (x_i)) }{Z_t}$"]},{"cell_type":"code","metadata":{"scrolled":true,"id":"3ukKu46tMr9I","colab_type":"code","outputId":"ac290c78-96f7-4428-bbfa-0839c4262eda","executionInfo":{"status":"ok","timestamp":1574339835833,"user_tz":-60,"elapsed":6001,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":265}},"source":["YtimesH = np.array([-1,1])[(pred == train_y)*1] # swap from [0,1] to [-1,1]!\n","distrib = distrib * np.exp( -weight * YtimesH )\n","distrib /= np.sum(distrib)\n","\n","plt.hist(distrib);"],"execution_count":19,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXcAAAD4CAYAAAAXUaZHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"mLb34oXuMr9L","colab_type":"text"},"source":["## 4) Sample training dataset"]},{"cell_type":"code","metadata":{"id":"wDnD87GpMr9M","colab_type":"code","outputId":"d450dfe3-e36b-49d1-cdcd-862ed61c7435","executionInfo":{"status":"ok","timestamp":1574339836148,"user_tz":-60,"elapsed":6306,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["idx = np.random.choice(range(train_x.shape[0]), size=train_x.shape[0], replace=True, p=distrib)\n","idx = np.unique(idx)\n","\n","temporal_train_x = train_x [ idx ]\n","temporal_train_y = train_y [ idx ]\n","\n","print(\"Uniques in sampled set:\", idx.shape[0])"],"execution_count":20,"outputs":[{"output_type":"stream","text":["Uniques in sampled set: 185\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"aykPwna-Mr9P","colab_type":"text"},"source":["## 5) Repeat!"]},{"cell_type":"code","metadata":{"id":"JcoG4tKBMr9P","colab_type":"code","colab":{}},"source":["def AdaBoost_step(forest, weights, distribution):\n","\n"," # Sample from distribution\n"," idx = np.random.choice(range(train_x.shape[0]),\n"," size=int(train_x.shape[0]/6), replace=False, p=distribution)\n"," \n"," # A little tweak - add some easy examples to stabilize the training\n"," idx2 = np.random.choice(range(train_x.shape[0]), size=int(train_x.shape[0]/6),\n"," replace=False, p=(1/distribution)/np.sum(1/distribution))\n"," idx = np.append(idx, idx2)\n"," idx = np.unique(idx)\n"," \n"," temporal_train_x = train_x [ idx ]\n"," temporal_train_y = train_y [ idx ]\n"," \n"," # Classify with new classifier\n"," pred, tree = weak_classify(temporal_train_x, temporal_train_y)\n"," forest.append(tree)\n"," \n"," pred = np.round(tree.predict(train_x))\n"," accuracy = np.sum(pred==train_y) / pred.shape[0] \n","\n"," # Compute classifier weight\n"," weight = classifier_weight(accuracy)\n"," weights.append(weight)\n"," \n"," train_acc = np.sum(forest_predict(forest, weights, train_x)==train_y)/train_y.shape[0]\n"," test_acc = np.sum(forest_predict(forest, weights, test_x)==test_y)/test_y.shape[0]\n"," \n"," # Compute data distribution\n"," YtimesH = np.array([-1,1])[(pred == train_y)*1]\n"," distribution = distribution * np.exp( -weight * YtimesH )\n"," distribution /= np.sum(distribution)\n"," \n"," return forest, weights, distribution, train_acc, test_acc"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"x-0B5VyhMr9S","colab_type":"code","colab":{}},"source":["def forest_predict(forest, weights, data):\n"," prediction = np.zeros(data.shape[0])\n"," #weights = np.array(weights) / sum(weights)\n"," \n"," for tree, weight in zip(forest, weights):\n"," prediction += (tree.predict(data) * 2 - 1) * weight\n"," \n"," return (prediction>=0)*1"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"pArBb-FWMr9V","colab_type":"text"},"source":["### we reset the distribution"]},{"cell_type":"code","metadata":{"id":"0MIP5QtzMr9W","colab_type":"code","colab":{}},"source":["forest = []\n","weights = []\n","tr_acc = []\n","ts_acc = []\n","distribution = distribution = np.ones(train_x.shape[0]) / train_x.shape[0]"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"dwua04tDMr9Z","colab_type":"text"},"source":["### and make M iterations"]},{"cell_type":"code","metadata":{"id":"E-3ApRQdMr9a","colab_type":"code","outputId":"85c8c42e-2ba2-455d-8605-d4e82b780d4c","executionInfo":{"status":"ok","timestamp":1574339839668,"user_tz":-60,"elapsed":9789,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":51}},"source":["for i in range(200):\n"," forest, weights, distribution, acc, ts = AdaBoost_step(forest, weights, distribution)\n"," tr_acc.append(acc)\n"," ts_acc.append(ts)\n"," \n","print('training accuracy:', max(tr_acc))\n","print('test accuracy:', max(ts_acc))"],"execution_count":24,"outputs":[{"output_type":"stream","text":["training accuracy: 0.985\n","test accuracy: 0.9704142011834319\n"],"name":"stdout"}]},{"cell_type":"markdown","metadata":{"id":"0ApF-EinMr9g","colab_type":"text"},"source":["### and plot the training curves"]},{"cell_type":"code","metadata":{"id":"XjRtAx3MMr9h","colab_type":"code","outputId":"8cc341e7-2388-4df9-feb9-703c429ef2ec","executionInfo":{"status":"ok","timestamp":1574339839677,"user_tz":-60,"elapsed":9721,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":296}},"source":["plt.figure(figsize=(15,4))\n","plt.plot(tr_acc, linewidth=5, label='training')\n","plt.plot(ts_acc, linewidth=5, label='validation')\n","plt.xlabel('M value')\n","plt.ylabel('accuracy')\n","plt.legend(loc=4)"],"execution_count":25,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{"tags":[]},"execution_count":25},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA4UAAAEGCAYAAADSazD/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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xFNMkmLXGldAJbin/e3fJlZps7wcXvtxRUAILlj68vHqtyvwWUgkIAR3g2HyDVCw2T3/4O7I\nES4AZz0Qfchy07aR006c8WfXa1xZGU1gzN3R1xvjeiLTovSqnv6nyCGqwYZfDW0HRS5/786gc3BX\nzQeEJi1yWfiNn4N73OcmWQFhPaOgsIErL7e8Njdy6OiEozpz5sB2IT9jB7bjn1ccyT3nDyI7M/TD\nluYz3Hhab165bgRnDWp/aJ/hXVuS5lPxGJa8GblsqccycdZ/FfrHG1yi+JSbQoe0BUQrDuG1zeoP\noThsiEhpofedWmkYivZ5///vWVv9UuYHdrqKe/EsecMNw6yOtV9UreT7lJtcOxP5DHzzkStS8cXf\nYZvHTZp3fueOVd8sn45ngYpgS9+KzI8C+Oofbjj6278NDZID3rrR3egKtnlhzQQkwQ5sh/eqOUtX\n8X6Y6tGzuWedm9OuLk271X1XB7Nl7vx6/V0INuffkVONgAvI9lQtfeaQLx+v3I0YcH+D3v6NG2rs\ndYO49xjoM9ZN+N6sc+T6M+6s6J0OyG3veqYra+TNFXMgRtOqB5zwi8jlnY+LP8omLd0NcyXsWrC4\nAKbf5oL6mr5J3rglnP7HyOVL3wp9r7x/l/dQ2gZKQWEDN3vtLtbvCv2S9Rn4zmDvYUzGGC48qhNT\nbziJ84Z2oHVOFqf1a8OrPzqOn43uVScTzqe8on1ufp5wmxfA7nW13576IFpuz7cfw4KXQ5ft3+7y\nS+Iec6r7YxDt2Mveij18TA5fH/4F9ka5MPz0YZdvUlUz/gCFCQZJU25yPdlVUVbq8nSqYsdK+Ocp\n0c9BuGm3uotpL4U73e9c38TKJwwoL/Vebsth4uUw/0Xv9ZvnuyIYh45T7g9kyry3r46ZT7lJwqvq\nw3tg73rvdZ/91Q3BrAvLprrvaC9rP4d5/42+7/4d8O7t3uuK93kXXUnUng0usKiKBS/Di5dGvg/S\nG8GZf3E9dJlN4LzHID2oGN+gCdELphxzrRvqmahuI+HYBIffnvALFwQGZLd2VUQTqRrfcTgc6ZGX\nuHASvHhJzX4WfOlwzt9g0EVuqG6w3WsqbmZtmu9u6Mghyils4F79OvIi4IRe+bTOaRRzv86tmvDg\nhCHJatbhZdV70SuKLZ8WPU+uIYsVnE2/zRUIaNzcPfe6w5/THvZvDb2I27seNs1z5zyaqTe7P5KZ\nTarcdKlntix2vV7RlJe4IWtXvJ7YxU+waHNmdTkeWnZ3vRfBdn0LnzwEJ1fhbv9X/4CtiyKXD5oA\nzcN6GpZPczelQl7bY/h1hyNdMY+ZT4Yu3781dltm/wuGXAadjorf7lRQctC7yEeLbrGHpQfzmlsu\n2Ht/crlZOW1dOoHXjax+50Be78ReD9xNri8fd4FNxUIXcP5ghismVBlbl8Yu1hH4LFz5RuU/C9VR\nfCAyJy3c2791hZC8hjG+e3vsYbWLX3NDSXueWvm2Tb8VSsKG1Rqfy9UNL2Iz86nIG0Re76+TbnIF\nWgK6ngDXfeza2Lyz60WMdv7TMuDi/7qbHFsWE7P3u3U/1xuZnhl9m2AZjeCyV9yxD+52++a2T2xf\ngNG3uxERB3aELvc6B33ProhJlpwAACAASURBVFrhpMym7v8xUMin07Fueo5gy6ZAXh//jZny0HUZ\nTeDYH9fs+zuQg10PKCisD4r2uUTk7PwarexWVFrGW/Mj8wnPG1qJD3ldObjXTSicLDntvL/srHV3\nmrLzITM7sWPFCnCWTal6UFi4y5WLzs6Lv621rqJXs46JVVsr3O3ySKKdg13fVC53pXFL90cukS/a\n7Stcz0U0+7fC+3e6HAfwvsM/YLy76A3voX3/z7GHiuxe63o5Bl3onsd6H+zb6irJhQ/hAdfbs315\n9J6FVJLe2P3x9bqALNwdWea8rqRlQf4R3t+BRQXufMeS1zuySmSgDHy8/6dvPnQX35WtdOg1Z1ZW\nLlzwtKvmuetb1/sd7JMHXDAVK0cnXPGBiry2YO2HwrmPRf7f9j8PHj8x9t35tCxXDKNld1exMVov\njSd/oZLvPOyeZmS78+9VgObATnfTLKetx2H831sHd1fitatg4xz3fRescQuXs/VqDd20K9rr8hFH\n/MR7OHGrXjD+ycQv0A+1s7kbhhhs4xz4+AHoeUrljvX2b+N/Fr792A3163xM7O1q0vyJ7rs5lgPb\nYdr/wdE/CF2+a03kzRcvU37lzn9lYoGtS2Dx65HLh1/tPXSxeWeYHGdak1Y94bifRS7P6+V+EpGe\n5T7j/c9LbPvKyGwCAy+o2r5NWsKpf4DJ18ferlVP991TE5Vh+5wZGRQufh0wrvp4uJE3ew+TbSCM\njTcO+zAwfPhwO2uWx1jy+mDpWy4J9uAeV+XswuegRZdqHbKwuIyS8nLeX7qVG16cG7KucUYas35z\nKtlZKXy/4JOHYMYdyRl6E6zPWFdJL8Pfa3pgJ7zwXZeX4MuAcfd7D4cIVl4G9/aMPnzMlwE3r/YO\nLGL57G/uznNpoSsD/91nIStKgvmuNa5U9Y6V7uLsgqfcF6UXa93F5cf3uTtoXufgPxd6f5nG0+kY\nV+ktXun9Tx+On4NlfPDD9yC/L9zTLfKC7qopLiic9uvKtzNc7zPhu8+4ABBcMPzfi92QpcwcGPNn\nGHZFxfYr3nHVB8NLcKeypm3hsknQdqB7Hv4+SBWNW8IlE0N7oD77K7xze/zvA5MGp/0htHDDvBfh\nf9dGbutLT15AP+YvcOx17vG2ZfDYcUl6LQM/nOF6+7xMvy12r9Co/4NR/s/P7rXwt6Mj87kCEjlf\nzTrD5a9WXNha64KZzx8FLPQf7+ZICwRF+7a6763wHs3aMugiN4Tv3h7ev5tJi/2ei7c+3BWvu8qm\nlVVWAv84CbYmUGylKir7e9SW6rQrmb9Tdj5cP6tiJEuw8nJ4+gyXMx/N5f9z1bIPV+Xl8MyY2Ckf\nNXkOtq+Ev8WZziogrw9c90nlb8zUM8aY2dba4V7rlACWyspKXFXEQEWrTXPho3urfLjPVm3nu49/\nRr/bpzHo929HBIQAZ/Rvk9oB4Yp33VCQ2vgjtWwKvBd0t+/16ysS1ctL4I0b4lfLWvdV7Hyi8pLo\nZZ6j2brUBU2BC7SV70RW6jx0/DKYeEVFz1vJfnj5e9ErbS5+DT66pyIQCD8Hk39atYAQ3B+BN26I\nv10ieX223A1jWv2B9x3+Tse4SXtrwvKpMCPsfbD2c/e4uMDdYd7jz8EpLXbl0utTQAiwbzP895KK\nSpuLXw99H6SKwp3w4sWuBxNcKfG3f5PY94Etc9sGhgkW7orsYQFo2cPdCEmGtgPhqKCejPw+yZsQ\nffj3oweE4KZJyIkyKqRldzg+6LPavLO7gx7N2X+ruKEQzZ61Ln+q1D+Ufs7z/qDUf2N60avuJgS4\ngPGVH9RdQAj+oYjN3VBfL8f9FAZe6L3O+NxNlsYJzj054IKqBYTghguOe6Bq+8bTopu74ZhqfBku\ncKhKpU1wlTaDc+Nq0ul3egeE4HrKz3ogMs8toP/4wzsgBHcOxj3gXRkUav4c5PV0vfCJGHf/YR8Q\nxqOgMJVtXRKZu1HZyU2BgyVl/PHNxVzyzy+Z+e2umEW6zhvWsdLHrzUlB91Qr9r0xWOuSpxnkrt1\nhR3KY1yQJlK8oLLFTRa+EnkRPOffsNbjztusp93NhGClhd5BZLS5kg6dg2nVr5i6ZLIL7KOJVjRm\n6GWRyzbM9pcnD9PrDDfEsEVXaN0/fpuGeBw73JePuwtUr3NQetDlSQCs+aT+VjLbs9ZdlEd7H6SK\n/dtcL3lVvw/euglKi9wxwivcghuW3O9sN29XTRv3YOTw15N+Bc3iVP6rrFjzhgVk5bhJqb2Mva9i\ndEDAiOu98926nuiqD457MH67ti+DLx6NXpH1kwdhxyr3HedVnKu2pGW6ed/AjZYIl9vRBcmn/8kN\nBw531A/dhe1pCRTcycypmCeyqrqMgCGXVu8YXsbel7zPQnUcfwN0Hxk5JUMi2g2Go652AYCvhm+A\ndzmhIvUgmrYD4ZjrIpdn5rgpJRqCtgNq9xxEGxkVbNAE6HZizb92PaOgMJV5XbAUbHI9iFHsPlDM\nW/M38fwXa3j+izU89/m3nP23T3jqk/jJ8nlNszi+R6tqNDjJPn0o8aT/mmLL3CTn0ZLcN811gVc0\niQR8y6dHliuPJdoxw8ue79sa2sMVcowpsDQsYI02V9Khc1BD86hNucld0HtZ8XZk71SLbnDWQ26o\naDivKnnBfwDi/TFoNxjG3edy1WKJ9z4IBP/1vXrpp4+4ns6CyFzjlDLzSXj9xy7frLJ2rnJD8mc+\nFbmu/3kVwcCYuxLv6UnE0dd6F17JzPbfOa/BP8dj70ksJ7HfOZEX/IMuqjgHwdIz3efQFzTRd2aO\nv+3G/W5eF3rhPrzH9bZ7jaAoK3ajCabfFv84yTT44or808EXudziAJPmensysyGnjQsMgzXvDKf4\n2z/kssiJssOd/kfvfMrKOu2O0HZW16AJ0MtfeGXM3TX7WaiOvD5wov9m4NHXQgfPUXDe0hv538Np\n0KZfxXFqQmZTF2gmkjc/6tbQQjLgbiDk1uD/X6o7+Vb3tz1Yss7BkVeFfm+Fy24Np0W5VmpglFOY\nyqLlu9wwL/ILBVi38wDfffxzNu+NcsEdx61nHsG1I3tUad+k27EK/j4icoLRpm0qV/0qnqJ9lS9g\nk9UMfjoLmrYOXe45lt24P0zhuTlXveUqjMWzey08FGOY1hl3wYgfu8evXhu9RDq4HJ+ffOkSx7cs\nil94wkubAW74UjSlxd4VEUfd6oavhXvpsopet4Bjf+Ly9r79FJ71uGsfLC3T5WgGLujWz4InY5Tn\nDrRj31YXFG+a64LSyr4PTBrcvMqdwz1h04y06hU937OubV7ohjDHk9PeXQDXla1LXI9sPF7fB3s3\nJtZ7m9kUrp8Zuv/WJS6HeXs1yvBnZEOv01zxCK9CKwHLp7sJw71uzCQqO9/1GPU/N/F9Sg66tIQN\ns6HzCDjxxtif6dUfuKA8LQuOu94VswkoL4fPHnF5tYGKjJvm1cww5LaDKl9Ns7LSslxvwYk3hfaU\nbl3icp1LD7pAr1dYlcp5L7npBXLbu57f4Dnfive7ibnXfhn6WWvc0vUqxZvjrTJ2rHKFiuJVnYwl\nvbHrhTvxl6Hvg61L3Y1Zr7kpa4PxuboKo24J/VtbuNt9d2+YFTuvtXkXd9Oiy4iKZdbCV0+40R9F\nBdH3jadlD1dAqMOwxPfZs8EN0d+zwRVGG3JJ1V+/vtq70U0HVBvnYM3nbrh6+LQ7rfvBCTe6YaYN\nRKycQgWFKWzpq3dyxPx7IpaXX/EGvu6Rdx9/89oCnv8iToUuvyaZaaT572i1bJrJdwa158bTeuNL\nxYnmrYUXLnDlmIP50uG6T6F1nF6eyigtgseOr3xgOPhiOC9sIuLP/hqZs9TxaHdxHR74jLg+sSFE\nXz4Ru8cuM8dd2O5cBc+Oi3+8E2+Ck2+DZ86EdV/E3z5Y91Fw+Wux74xaC//6TmSFxbQs+MkXLncp\noOQg3NM9srz3lW9WDOv433Wx56PqMdoVswgoL4f7+0QvoX/tR663MFxpMTx+fPyKlsFO+IUb/hbM\nlw6/Wlm5SpK16b073YVJLOmN3M0DjxtRteazv8HbcXqPfOlw7ceuByDYlsXw+Anxb3ic8Wd3YSc1\na9qtsaf8SMQRZ8FFL9RMe0REGrBYQWEKVxRp2DbtKeTz+cvwCncWL1nEgEBQuPh1+Ph+wMDOMcCg\nmMfNTPNx0xm9ufqE7qSlYgDoZckbkQEhuAu4mgwIwZVAHncfPHdO5fab91//fHlBQuaO8uszxg3x\nCQ8Kv3wc5v7Huz1djndtatwifo5icQH89cjEqxl+8oC761/Zku++DJdvEm+ojDFuu8ePD21TmT/4\nTg+6G2/LIgPCRs2h87EVz0+7wz9H0h7v1wsfLurzuXP+9XOR2+Z2cL0PXtIzXbufOzv67xbus79G\nLus8InUDQnC9QvNfctOsRBM+Z1ZdOOZamPtC7AqLx/4oMiAEt+zYH8WutNm6vxuKJjVv1K2w8FVX\nzKgqMppEz30UEZEao5zCFFRWbvnFS3NpWuo9D9z8RQuw1ro74BOvcMNzNs3lDwf/QncTPRfoiLY5\nvH798VxzUo/6ExCWlXrnl+R2hJPiTGZbVd1HwYDzo68ffrX3hX7hztAfrwnr+4x1E6+H5w+Vl0bu\nX7jTDSVbOAn+M8FVS/z2k/jtL9kfOcwW3PC1tLDKWrbcOyBs1cvlG0Vz/A2Jz5nU+gjXExrRzgOh\nv6tXoNfr9NAhTE1bw+gY01V45RB6FYoIbBsrqO0+0lUFTJRXIB7ttVNFRmM4M0ZPYbQ5s2pbvAqL\nOe1hZJQKvBC70ia4XKAanANWgjTKjT0Kou1AVxwqmpE3uzw9ERFJqqQGhcaYMcaYZcaYlcaYiL/Y\nxpguxpgZxpj5xpgPjDEdg9aVGWPm+n8mBy3vZoz50n/Ml4wxh1392Mc/XMUXq3eSZ7x7Q9L3rueT\nldthwcSQ5WnGcn7aR4eet8nN4pJjOnPliC48ftkwXr/+ePq2q+R8eHVt3ReuKmK4M+9Obp7W6Xe6\noZjhmnd2hQVO/X3lj9miqytokp3npkyojHVfwqSrI/O/mrZxlQbj6XCkmzT2+ASmhADXM3nmPdHP\nQWUT9Efe7AL5yvIK8o78XmgeU0DbQdDM4zW6jXR5MokcO9wZUd4HzTp7Vx2MeI0amhYjmfqMiV5d\ncOx9NTOBcE2IVWEx3vdBrEqbQy4LzTOSmjfgfPc59DLuQVcYJ3jUQEBeH5dTLCIiSZe0oNAYkwY8\nCpwJ9AMuNsaEj+25D3jOWjsIuAMI/qtdaK0d4v8JHsP1F+BBa21PYBdwdbJ+h7owZ+0uHnjH5TG1\nMt5znXUw2/nbeythe2Te20BTUZ3zzAHt+PN5A/nDOQMYM6AdWelJTtJPBq9qjt1GJr9Edm47OMVj\nDrMz73WFWYZeAR09KgnGMuiiip6pQRMq3yav+QyPGBdZ/S6cSXO9LD6fC+biDQUMzJmV09a7rH3g\nHFRGZrabCLoyGrd0BTrC+dL8Vd7Cvr6CJ5APee0mkT2/zTq7UvrxRDsHY+/xrtAYLL9vaM5kKhtz\ntyuIEqz/eOhxct20J5rT7ojspe95KvRNYJhvv3PctsEat0hs2gCpHmP8vbFh93CHXemqlrbo6gq0\nhBt3X4OfN0xEpLYks6fwaGCltXa1tbYYeBEIH4/WDwhMvPe+x/oQxhgDnAJM8i/6F1CJMmup7+EZ\nKygrd8V/YgWFX36zk8JNkVXABvq+IVB17JhuKVJCuqqshaXhcwPiqrUlUva5uo651lWlysxxAcrY\n+yp6fnw+uOg/bl4i4uXVpblS98cHDcMbernr8Qq/SKqsPmPd+Tjlt64KaricdnDB09B+iHue0Rgu\ne9U7l86X4S6uz36kYtnR10Q/B5XV9ywY85fEcuxyO8AFT1VUEQ3X4Ui48N/u90vLchN1D/9+9OOd\n9gc3FBXckMjzn0y8Byz8HJx5r+tljDc0NJGeyFTRvBNcOtFV6PNlQN/vwDkxcvDqSnYeXPaK+z80\naS7IO/+pxL4PjHHb9jzV7duqp/ssZCfQ0y7Vl9fLfWfmdnTfewO/Gzp0+YQb4dgfuxzCJnlwzqPx\np3MQEZEak7Tqo8aYC4Ax1tof+J9fDhxjrb0+aJv/AF9aax82xowHXgHyrLU7jDGlwFygFLjbWvua\nMSYP+MLfS4gxphMw1Vo7wOP1rwGuAejcufORa9bEKKSQIsrLLb1/M5XScgtYlmVdRZaJLBdfZNPp\nX/Q0Sxt9n3Qi85hOKHqI9bY1M287lfycFBn6VRXblsGjR4cuMz64aUXtXsiVlbiLyGjl5Iv2uaql\n0WQ2ccGYl9Iit7+X6be6IiDRZGS76RcCpdPLSkPz8oxxAVi0C+aDe0PnvIzVznjnoDLKy11+ZDTx\n2h3RttLayQcLPwcHdsK9PaNXtbz6Xe956VJdaXH96J2pTjvry+94OLLWfZainf+a/K4REZEQqVx9\n9Cbgb8aYq4CPgA1A4Aqri7V2gzGmO/CeMWYBEKXkYCRr7RPAE+CmpKjRVifJ/uJSf0AIORR6BoQA\nWaaUYWaFZ0AIMMisJjOvW/UDwm3LXEXMvUmcyDq/Nwy7CprmR67zqrTZ6Zjav7Mfa84ucLlMVc1v\nTM+K3mN1+p9g+bTolTZ7nhI6l1ZaOmS3Svy1G1UivzTeOagMn69y7YyntgqEhJ+DJi1dddE1HsV/\nsvNdb2Z9VF+Cpeq0s778jocjY2Kf/5r8rhERkYQl82pqAxA0gysd/csOsdZuBMYDGGOaAudba3f7\n123w/7vaGPMBMBTXk9jcGJNurS31OmZ9VnCwIshrFaXITMCJaQuirhvk+4bcrtUcOrplMTwzJnpA\nUpPmvQQ/eBcaNw9d7pVPWJ+G5FVXoNLmW1GKuqR6ZcuGoM+Z3kFh7zHq6RAREZF6I5lXLTOBXv5q\noZnARcDk4A2MMXnGHKoWcSvwtH95C2NMVmAb4HhgsXVjXd8HAnXirwReT+LvUKv2HqzoGWyFdz5h\nwIm++VHXDTSrObo6+YTl5fDGDbUTEIKbKP69sGIp+7bBuq8it21ogVC0SpvGV5EjJ3Un2k2KhvY+\nFRERkXotaUGhvyfvemA6sASYaK1dZIy5wxgTKBU3ClhmjFkOtAECkxn1BWYZY+bhgsC7rbWBWYt/\nDdxojFkJtAKeStbvUNuCewqjTUcRMCioymi4gb5vOKpL86jr45r7PKz3CMiSaeaTsHFOxfMV0wkU\nzDmkVc/E58Y7XPj8lUPDi9l0PVEFMlJBqx7QZmDosqxmrnqriIiISD2R1GQca+0UYErYst8FPZ5E\nRSXR4G0+AwaGL/evW42rbHrYKQjqKcyLUnk0wGeip0nmmgPk2M1Az8o3Yv8OeCfG5OBJY+HNG90w\nUl+aho4G6zAMxt4LU34FWGjUPPaE41K7xt4D/5kARXtd5c4z7678lB0iIiIidaiuC81IkL2FQTmF\ncYaPxmM2zYW8KgSFM37vXRnytD+6idJryvqZMPOfocs2fg2zn4Uhl8Cq9yL3achD8o7+oSulv2OV\nm2g7Mzv+PlI7uhwHP5sDm+a63ux480CKiIiIpBgFhSkkuKcwXqGZuDbOgYEXxN8u2Lqv4OvnIpcP\nvDB0jr2aMGA8rPkUti4OXT7jD7B3A5QcCF3euCV0PCw7iBPXspv7kdSTnRc5MbqIiIhIPaHyeClk\nbyVyCuMKzs9LRFmpG74ZLivXTY1Q09Iy/LlyYQ7ugY/vj1ze+4zam3pARERERKQBUVCYQvZWIqcw\nrk3zoDzKpNpeZj4JWzymuTjlt5BTg8NGg3UZAUMuTWzbhppPKCIiIiKSZAoKU0jIPIXVzCmkeB/s\nWJngC2+OnBICoO0gOOrq6rUjntPucIVTYknLhB6nJLcdIiIiIiINlILCFLK3MDinsJpBISQ+hHT6\nbVBcELbQwFkPukqgyZSdB+PuJ2LKhWDHXAtZOclth4iIiIhIA6UkrRQS6ClMp5QWZl+l9p1T3pOh\nvrCewY1zYPBFsXdc/QEsjJgVBI68EjoOr1QbqmzgBS44XPKmyykMSMt0lR0HX1w77RARERERaYAU\nFKaQQPXRloT32sVnB34XFt0VunD9LDfvYDTlpfDWTZHLm7SC0bdXug3V0n2UJvwWEREREakDCgpT\nSKD6aKUrj2blMmz0hMigcMMsuLd75Rty2h3QpGXl9xMRERERkXpHOYUpJNBT6BkUpjeOvmNgwuzG\nLarfiE7HwuBLqn8cERERERGpFxQUppBATqFn5dF2g6LvmNcLjIH2Q6vXAJPmir749LYQEREREWko\ndPWfIkrKyjlQ7OYV9Kw82nYg+KKM9m3Vy/074ILqNWLET6DtgOodQ0RERERE6hXlFKaIfUFzFHpO\nXN+0LeR2gN1rItfl9XT/Dr4Y9m2Guf+BAzsTf/HGzaH/eXDybyrZahERERERqe8UFKaIvQcr5ij0\nzCnMzoPmnb2DwkBPoc8HJ/7S/YiIiIiIiCRAw0dTREFQT2ErvILCfGjWyXvnVj2S1CoRERERETnc\nKShMEcE9hZ45hdn50NwjKGzWCTJiVCYVERERERGJQUFhithbGNRT6JlTGKWnsFXPJLZKREREREQO\ndwoKU0TBoZ5CS1604aPdR4IJ+y/rdVrS2yYiIiIiIoevpAaFxpgxxphlxpiVxphbPNZ3McbMMMbM\nN8Z8YIzp6F8+xBjzuTFmkX/dhKB9njXGfGOMmev/GZLM36G2BHIKcygky5SGrkxvBJlNXaGZ0/4I\nvgy3vPcYGHZlLbdUREREREQOJ0mrPmqMSQMeBU4D1gMzjTGTrbWLgza7D3jOWvsvY8wpwF3A5cAB\n4Apr7QpjTHtgtjFmurV2t3+/X1lrJyWr7XUhkFPYyrPyaGs3OT3AcdfD0Euh5CDktK1YLiIiIiIi\nUgXJ7Ck8GlhprV1trS0GXgTOCdumH/Ce//H7gfXW2uXW2hX+xxuBrUB+Etta5wI9hd5DR/NCnzdu\nAbntFBCKiIiIiEi1JTMo7ACsC3q+3r8s2DxgvP/xeUCOMaZV8AbGmKOBTGBV0OI7/cNKHzTGZHm9\nuDHmGmPMLGPMrG3btlXn96gVewsDPYVRKo+KiIiIiIgkQV0XmrkJGGmMmQOMBDYAZYGVxph2wL+B\n71lry/2LbwWOAI4CWgK/9jqwtfYJa+1wa+3w/PzUD6oO9RQqKBQRERERkVqUtJxCXIAXPIdCR/+y\nQ/xDQ8cDGGOaAucH8gaNMbnAW8Bt1tovgvbZ5H9YZIx5BhdY1nsFRf6eQqJMRyEiIiIiIpIEyewp\nnAn0MsZ0M8ZkAhcBk4M3MMbkGXNojoVbgaf9yzOB/+GK0EwK26ed/18DnAssTOLvUGsC8xTmeRaa\nUVAoIiIiIiLJkbSg0FpbClwPTAeWABOttYuMMXcYY872bzYKWGaMWQ60Ae70L78QOAm4ymPqiReM\nMQuABUAe8Kdk/Q61qSBm9VEFhSIiIiIikhzJHD6KtXYKMCVs2e+CHk8CIqaWsNY+Dzwf5Zin1HAz\nU0LsnMK8yGUiIiIiIiI1oK4LzQhgra2Yp9ArpzC7dS23SEREREREGgoFhSmgqLSckjILKKdQRERE\nRERql4LCFBDoJQRLLgciN2jSslbbIyIiIiIiDYeCwhQQqDyaQRk+Y0NX+tIhLaMOWiUiIiIiIg2B\ngsIUEKg8mkVx5Mr0RrXcGhERERERaUgUFKaAvf7Ko1mURK5My6zl1oiIiIiISEOioDAFVPQUegSF\n6ikUEREREZEkUlCYAgJzFGYar6Awq5ZbIyIiIiIiDYmCwhSwt1A9hSIiIiIiUjcSCgqNMa8aY8YZ\nYxREJkFBrJxC9RSKiIiIiEgSJRrk/R24BFhhjLnbGNMniW1qcGLnFCooFBERERGR5EkoKLTWvmut\nvRQYBnwLvGuM+cwY8z1jjCbRq6ZD1UeVUygiIiIiIrUs4eGgxphWwFXAD4A5wMO4IPGdpLSsAQn0\nFGYqp1BERERERGpZeiIbGWP+B/QB/g18x1q7yb/qJWPMrGQ1rqGIOU+hegpFRERERCSJEgoKgUes\nte97rbDWDq/B9jRIqj4qIiIiIiJ1JdHho/2MMc0DT4wxLYwxP05Smxqcglg5hWnqKRQRERERkeRJ\nNCj8obV2d+CJtXYX8MPkNKnh2Xuo+mhx5EoNHxURERERkSRKNChMM8aYwBNjTBqQGW8nY8wYY8wy\nY8xKY8wtHuu7GGNmGGPmG2M+MMZ0DFp3pTFmhf/nyqDlRxpjFviP+Uhwu+qj8nLLviLXU5hJaeQG\nGj4qIiIiIiJJlGhQOA1XVGa0MWY08F//sqj8geOjwJlAP+BiY0y/sM3uA56z1g4C7gDu8u/bErgd\nOAY4GrjdGNPCv89juF7KXv6fMQn+Dilpf3Ep1rrHKjQjIiIiIiK1LdGg8NfA+8CP/D8zgJvj7HM0\nsNJau9paWwy8CJwTtk0/4D3/4/eD1p8BvGOt3ekfqvoOMMYY0w7ItdZ+Ya21wHPAuQn+DikpUHkU\nIMt4DR9VT6GIiIiIiCRPQtVHrbXluB66xypx7A7AuqDn63E9f8HmAeNxcx6eB+T450P02reD/2e9\nx/IIxphrgGsAOnfuXIlm167AHIUQracw7ihdERERERGRKkuop9AY08sYM8kYs9gYszrwUwOvfxMw\n0hgzBxgJbADKauC4WGufsNYOt9YOz8/Pr4lDJkVBUE+hcgpFRERERKS2JTp89BlcL2EpcDJu2Obz\ncfbZAHQKet7Rv+wQa+1Ga+14a+1Q4Db/st0x9t3gfxz1mPVNYI5CUPVRERERERGpfYkGhY2ttTMA\nY61dY639PTAuzj4zgV7GmG7GmEzgImBy8AbGmDxjTKANtwJP+x9PB073z4fYAjgdmG6t3QTsNcYc\n6686egXweoK/Q0oqCMkp1OT1IiIiIiJSuxLKKQSK/MHbCmPM9bjeuaaxdrDWlvq3nQ6kAU9baxcZ\nY+4AZllrJwOjgLuMR+254wAAHmRJREFUMRb4CPiJf9+dxpg/4gJLgDustTv9j38MPAs0Bqb6f+qt\nvXFzCtVTKCIiIiIiyZNoUHgD0AT4GfBH3BDSK2PuAVhrpwBTwpb9LujxJGBSlH2fpqLnMHj5LGBA\ngu1OeSE9hV5BYZqCQhERERERSZ64QaF/vsEJ1tqbgH3A95LeqgYkfk+hho+KiIiIiEjyxM0ptNaW\nASfUQlsapL2F8XIK1VMoIiIiIiLJk+jw0TnGmMnAy8D+wEJr7atJaVUDEn+eQvUUioiIiIhI8iQa\nFDYCdgCnBC2zgILCaoqbU6ieQhERERERSaKEgkJrrfIIkyQ4pzBTQaGIiIiIiNSyhIJCY8wzuJ7B\nENba79d4ixqY9bsKDz1WTqGIiIiIiNS2RIePvhn0uBFwHrCx5pvTsOwpLGFbQdGh58opFBERERGR\n2pbo8NFXgp8bY/4LfJKUFjUgK7fuC3munEIREREREaltcaekiKIX0LomG9IQrUooKFRPoYiIiIiI\nJE+iOYUFhOYUbgZ+nZQWNSArtwUHhdY7pzBNPYUiIiIiIpI8iQ4fzUl2Qxqi4OGjmZRGbuDLAF9V\nO3NFRERERETiSyjiMMacZ4xpFvS8uTHm3OQ1q2EIDgo1dFREREREROpCot1Qt1tr9wSeWGt3A7cn\np0kNw8GSMtbtOnDouYrMiIiIiIhIXUg0KPTaLtHpLMTD6m37sUFZmlkUR26koFBERERERJIs0aBw\nljHmAWNMD//PA8DsZDbscBdaZAYyjUdOoYJCERERERFJskSDwp8CxcBLwIvAQeAnyWpUQ5DYHIXK\nKRQRERERkeRKtProfuCWJLelQYmco1DDR0VEREREpPYlWn30HWNM86DnLYwx05PXrMOfegpFRERE\nRCQVJDp8NM9fcRQAa+0uoHW8nYwxY4wxy4wxK40xET2NxpjOxpj3jTFzjDHzjTFj/csvNcbMDfop\nN8YM8a/7wH/MwLq47Ug1pWXlfLN9f8gy74nrM2upRSIiIiIi0lAlWkG03BjT2Vq7FsAY0xWwsXYw\nxqQBjwKnAeuBmcaYydbaxUGb/QaYaK19zBjTD5gCdLXWvgC84D/OQOA1a+3coP0utdbOSrDtKWfd\nrkKKy8pDlrXMspFnVD2FIiIiIiKSZIkGhbcBnxhjPgQMcCJwTZx9jgZWWmtXAxhjXgTOAYKDQgvk\n+h83AzZ6HOdiXHGbw0b40FGAzs3SYHfYQuUUioiIiIhIkiU0fNRaOw0YDiwD/gv8EiiMs1sHYF3Q\n8/X+ZcF+D1xmjFmP6yX8qcdxJvhfM9gz/qGjvzXGGK8XN8ZcY4yZZYyZtW3btjhNrV1eQWGnHI9f\nQz2FIiIiIiKSZIkWmvkBMAMXDN4E/BsX0FXXxcCz1tqOwFjg38aYQ20yxhwDHLDWLgza51Jr7UBc\nb+WJwOVeB7bWPmGtHW6tHZ6fn18DTa05XkFhu2yP/wr1FIqIiIiISJIlWmjmBuAoYI219mRgKJGD\nHcNtADoFPe/oXxbsamAigLX2c6ARkBe0/iLCegmttRv8/xYA/8ENU61XwieuB2ib7bGhgkIRERER\nEUmyRIPCg9bagwDGmCxr7VKgT5x9ZgK9jDHdjDGZuABvctg2a4HR/uP2xQWF2/zPfcCFBOUTGmPS\njTF5/scZwFnAQuoRa23EHIUA+Y01fFRERERERGpfooVm1vvnKXwNeMcYswtYE2sHa22pMeZ6YDqQ\nBjxtrV1kjLkDmGWtnYwbjvpPY8wvcEVnrrLWBmpwngSsCxSq8csCpvsDwjTgXeCfCf4OKWHL3iL2\nFZWGLGuckUZuelnkxuopFBERERGRJEsoKLTWnud/+HtjzPu4SqHTEthvCq6ATPCy3wU9XgwcH2Xf\nD4Bjw5btB45MpM2pyiufsHt+Nr6yosiN1VMoIiIiIiJJlmhP4SHW2g+T0ZCGYuXWgohlPVs3hdKD\nkRurp1BERERERJIs0ZxCqSFeRWZ65jeFsuLIjdMUFIqIiIiISHIpKKxlXsNH1VMoIiIiIiJ1RUFh\nLVu5dX/EMhcUKqdQRERERERqX6VzCqV6Xr5uBCu37mPl1n2s2FrA6m376dIqWz2FIiIiIiJSJxQU\n1rJuedl0y8vmtH5tQleop1BEREREROqAho+mCs+gMLP22yEiIiIiIg2KgsJUoZ5CERERERGpAwoK\nU4VnTqGCQhERERERSS4FhanCs6dQhWZERERERCS5FBSmCvUUioiIiIhIHVBQmCrKiiOXpanQjIiI\niIiIJJeCwlShnkIREREREakDCgpThXIKRURERESkDigoTBXqKRQRERERkTqgoDAVWOudU6ieQhER\nERERSTIFhanAa+hoWiYYU/ttERERERGRBiWpQaExZowxZpkxZqUx5haP9Z2NMe8bY+YYY+YbY8b6\nl3c1xhQaY+b6fx4P2udIY8wC/zEfMeYwiJw0dFREREREROpI0oJCY0wa8ChwJtAPuNgY0y9ss98A\nE621Q4GLgL8HrVtlrR3i/7kuaPljwA+BXv6fMcn6HWqNisyIiIiIiEgdSWZP4dHASmvtamttMfAi\ncE7YNhbI9T9uBmyMdUBjTDsg11r7hbXWAs8B59Zss+uAegpFRERERKSOJDMo7ACsC3q+3r8s2O+B\ny4wx64EpwE+D1nXzDyv90BhzYtAx18c5Zv2jIjMiIiIiIlJH6rrQzMXAs9bajsBY4N/GGB+wCejs\nH1Z6I/AfY0xujONEMMZcY4yZZYyZtW3bthpveI3y6ilMU1AoIiIiIiLJl8ygcAPQKeh5R/+yYFcD\nEwGstZ8DjYA8a22RtXaHf/lsYBXQ279/xzjHxL/fE9ba4dba4fn5+TXw6ySRcgpFRERERKSOJDMo\nnAn0MsZ0M8Zk4grJTA7bZi0wGsAY0xcXFG4zxuT7C9VgjOmOKyiz2lq7CdhrjDnWX3X0CuD1JP4O\ntUM5hSIiIiIiUkfSk3Vga23p/7d378FWVXeCx7+/vqAIEiDYvkCFcYxeLyKvGC1aC58hdkejYxRK\nu8WJOiGadKft6mAmJeqYbjsxKUOVmtZpk7SjMbehrVAdHI0zaGKPGB4S4hUUH6gXjAKJiu0jor/5\n42zwgufw8p6zL/d8P1XUPXvttff5ncVic353rb12RFwO3Ae0ALdnZkdEXAssysy5wBXAbRHxVSqL\nzkzLzIyIE4BrI+Jd4H3gi5n5u+LUXwJ+COwF3Fv82b1VTQodKZQkSZJUf3VLCgEycx6VBWS6ll3V\n5fUTwMQqx80B5tQ45yJgVPdGWrKN1RaacaRQkiRJUv2VvdCMoMZI4R6Nj0OSJElS0zEp7AmqLjTj\nSKEkSZKk+jMp7Am8p1CSJElSSUwKewJHCiVJkiSVxKSwJ3jP5xRKkiRJKodJYU9QbaSwxaRQkiRJ\nUv2ZFPYEPrxekiRJUklMCnuCqvcUOlIoSZIkqf5MCnsCF5qRJEmSVBKTwp7AR1JIkiRJKolJYU/g\n9FFJkiRJJTEp7AkcKZQkSZJUEpPCnsB7CiVJkiSVxKSwJ/Dh9ZIkSZJK0qfsAJpWJrzxCrz2Irzz\nxof3+/B6SZIkSQ1gUthocy6G1Uvgtc4PRgj3HPThek4flSRJktQAJoWN9vvn4XfPbFn2zmsfruf0\nUUmSJEkN4D2FjTb4oB2r50ihJEmSpAaoa1IYEZMj4smIeDoiZlTZf3BEzI+IxyJiWUScXpSfGhGL\nI+I3xc+TuhzzYHHOpcWffev5GbrdoB1NCh0plCRJklR/dZs+GhEtwE3AqUAnsDAi5mbmE12qfQNo\nz8xbIuJIYB4wAlgHfDYz10TEKOA+YFiX487PzEX1ir2udnik0KRQkiRJUv3Vc6TwGODpzHw2M/8A\n3A2cuVWdBD5WvB4ErAHIzMcyc01R3gHsFRG9I0sadPCO1TMplCRJktQA9VxoZhjwYpftTuBTW9W5\nGrg/Ir4MDABOqXKe/wIsycyuD/P7QUS8B8wBrsvM3PqgiLgUuBTg4IN3MBFrBO8plCRJkgB49913\n6ezs5O233y47lF6jX79+DB8+nL59++7wMWWvPjoV+GFmficijgPuiIhRmfk+QES0Af8AnNblmPMz\nc3VEDKSSFP458M9bnzgzbwVuBZgwYcKHksbS7Og9hS171DcOSZIkqWSdnZ0MHDiQESNGEBFlh7Pb\ny0zWr19PZ2cnI0eO3OHj6jl9dDXQNQMaXpR19QWgHSAzHwH6AfsARMRw4B7gLzJz8zMcMnN18XMD\ncBeVaaq7jz33hr0+vu06ffqB/ygkSZLUy7399tsMHTrUhLCbRARDhw7d6ZHXeiaFC4HDImJkROwB\nTAHmblXnBeBkgIhopZIUro2IwcDPgBmZ+e+bKkdEn4jYlDT2Bf4MeLyOn6E+tjeFtMX7CSVJktQc\nTAi71660Z92SwszcCFxOZeXQ5VRWGe2IiGsj4oyi2hXAJRHxa+DHwLTi/sDLgf8MXLXVoyf2BO6L\niGXAUiojj7fV6zPUzfamkLrIjCRJkqQGqetzCjNzXmZ+IjMPzcxvFmVXZebc4vUTmTkxM4/OzDGZ\neX9Rfl1mDijKNv15JTP/IzPHZ+bozGzLzL/MzPfq+RnqYvB2Fr5xkRlJkiSpIV599VVuvvnmnT7u\n9NNP59VXX91mnauuuooHHnhgV0NrmLIXmmlOjhRKkiRJm42Y8bO6v8eq6/+0avmmpPBLX/rSFuUb\nN26kT5/a6dK8efO2+57XXnvtzgVZkrqOFKoGRwolSZKkHmHGjBk888wzjBkzhk9+8pMcf/zxnHHG\nGRx55JEAfO5zn2P8+PG0tbVx6623bj5uxIgRrFu3jlWrVtHa2soll1xCW1sbp512Gm+99RYA06ZN\nY/bs2Zvrz5w5k3HjxnHUUUexYsUKANauXcupp55KW1sbF198MYcccgjr1q1raBuYFJZhewvN9PFx\nFJIkSVIjXH/99Rx66KEsXbqUb3/72yxZsoTvfe97PPXUUwDcfvvtLF68mEWLFjFr1izWr1//oXOs\nXLmSyy67jI6ODgYPHsycOXOqvtc+++zDkiVLmD59OjfccAMA11xzDSeddBIdHR2cc845vPDCC/X7\nsDWYFJZhu9NHHSmUJEmSynDMMcds8Yy/WbNmcfTRR3Psscfy4osvsnLlyg8dM3LkSMaMGQPA+PHj\nWbVqVdVzn3322R+q8/DDDzNlyhQAJk+ezJAhQ7rx0+wY7yksw15DYI+94Q9vVN/vPYWSJElSKQYM\nGLD59YMPPsgDDzzAI488Qv/+/Zk0aVLVZwDuuecH399bWlo2Tx+tVa+lpYWNGzd2c+S7zqSwDBGV\n0cK1y6vvd6RQkiRJTaTWIjCNMHDgQDZs2FB132uvvcaQIUPo378/K1asYMGCBd3+/hMnTqS9vZ2v\nfe1r3H///fz+97/v9vfYHpPCsgzeVlLoSKEkSZLUCEOHDmXixImMGjWKvfbai/3222/zvsmTJ/P9\n73+f1tZWDj/8cI499thuf/+ZM2cydepU7rjjDo477jj2339/Bg4c2O3vsy1ReVZ87zZhwoRctGhR\n2WFs6WdXwML/WX3f6Clw9j82Nh5JkiSpwZYvX05ra2vZYZTqnXfeoaWlhT59+vDII48wffp0li5d\n+pHOWa1dI2JxZk6oVt+RwrJsa7EZRwolSZKkpvDCCy9w7rnn8v7777PHHntw2223NTwGk8KybOux\nFN5TKEmSJDWFww47jMcee6zUGHwkRVkGbeMB9o4USpIkSWoQk8KyOFIoSZIkqQcwKSzLgH2hZY/q\n+/rUKJckSZKkbmZSWJY/+iMYNLz6PkcKJUmSJDWISWGZBte4r9CkUJIkSeqR9t57bwDWrFnDOeec\nU7XOpEmT2N4j8W688UbefPPNzdunn346r776avcFuhNcfbRMtR5L4UIzkiRJaiZXD2rAe7zWrac7\n8MADmT179i4ff+ONN3LBBRfQv39/AObNm9ddoe00RwrL5EihJEmSVKoZM2Zw0003bd6++uqrue66\n6zj55JMZN24cRx11FD/96U8/dNyqVasYNWoUAG+99RZTpkyhtbWVs846i7feemtzvenTpzNhwgTa\n2tqYOXMmALNmzWLNmjWceOKJnHjiiQCMGDGCdevWAfDd736XUaNGMWrUKG688cbN79fa2soll1xC\nW1sbp5122hbv81HUNSmMiMkR8WREPB0RM6rsPzgi5kfEYxGxLCJO77LvyuK4JyPi0zt6zt1KrZHC\nWgvQSJIkSepW5513Hu3t7Zu329vbufDCC7nnnntYsmQJ8+fP54orriAza57jlltuoX///ixfvpxr\nrrmGxYsXb973zW9+k0WLFrFs2TIeeughli1bxle+8hUOPPBA5s+fz/z587c41+LFi/nBD37Ao48+\nyoIFC7jttts2P8dw5cqVXHbZZXR0dDB48GDmzJnTLW1Qt6QwIlqAm4DPAEcCUyPiyK2qfQNoz8yx\nwBTg5uLYI4vtNmAycHNEtOzgOXcftR5L4UihJEmS1BBjx47llVdeYc2aNfz6179myJAh7L///nz9\n619n9OjRnHLKKaxevZqXX3655jl+8YtfcMEFFwAwevRoRo8evXlfe3s748aNY+zYsXR0dPDEE09s\nM56HH36Ys846iwEDBrD33ntz9tln88tf/hKAkSNHMmbMGADGjx/PqlWrPuKnr6jnPYXHAE9n5rMA\nEXE3cCbQtRUS+FjxehCwpnh9JnB3Zr4DPBcRTxfnYwfOufvwnkJJkiSpdJ///OeZPXs2v/3tbznv\nvPO48847Wbt2LYsXL6Zv376MGDGCt99+e6fP+9xzz3HDDTewcOFChgwZwrRp03bpPJvsuecHeUJL\nS0u3TR+tZ1I4DHixy3Yn8Kmt6lwN3B8RXwYGAKd0OXbBVscOK15v75y7j48Nq16e7zU2DkmSJKlM\n3bwIzM4677zzuOSSS1i3bh0PPfQQ7e3t7LvvvvTt25f58+fz/PPPb/P4E044gbvuuouTTjqJxx9/\nnGXLlgHw+uuvM2DAAAYNGsTLL7/Mvffey6RJkwAYOHAgGzZsYJ999tniXMcffzzTpk1jxowZZCb3\n3HMPd9xxR10+9yZlrz46FfhhZn4nIo4D7oiIUd1x4oi4FLgU4OCDayzoUraWGs3/vkmhJEmS1Cht\nbW1s2LCBYcOGccABB3D++efz2c9+lqOOOooJEyZwxBFHbPP46dOnc9FFF9Ha2kprayvjx48H4Oij\nj2bs2LEcccQRHHTQQUycOHHzMZdeeimTJ0/efG/hJuPGjWPatGkcc0xlouTFF1/M2LFju22qaDWx\nrRsmP9KJK0ne1Zn56WL7SoDM/PsudTqAyZn5YrH9LHAs8IWudSPiPiqjimzvnNVMmDAht/eckNL8\ny0XQ8a8fbPfpB3+zEvp9rPYxkiRJUi+wfPlyWltbyw6j16nWrhGxODMnVKtfz9VHFwKHRcTIiNiD\nysIxc7eq8wJwchFkK9APWFvUmxIRe0bESOAw4Fc7eM7dy598FfoP7bL91yaEkiRJkhqmbtNHM3Nj\nRFwO3Ae0ALdnZkdEXAssysy5wBXAbRHxVSqLzkzLytBlR0S0U1lAZiNwWWblRrtq56zXZ2iIA0bD\n5Yvg+X+v3GM4bFzZEUmSJElqInWbPtqT9Ojpo5IkSVKTWr58OUcccQQRUXYovUZmsmLFih4zfVSS\nJEmSaurXrx/r16/f5oPhteMyk/Xr19Ov384997zs1UclSZIkNanhw4fT2dnJ2rVryw6l1+jXrx/D\nhw/fqWNMCiVJkiSVom/fvowcObLsMJqe00clSZIkqYmZFEqSJElSEzMplCRJkqQm1hSPpIiItcDz\nZcdRxT7AurKDaFK2fbls/3LZ/uWx7ctl+5fHti+X7V+untL+h2TmH1fb0RRJYU8VEYtqPStE9WXb\nl8v2L5ftXx7bvly2f3ls+3LZ/uXaHdrf6aOSJEmS1MRMCiVJkiSpiZkUluvWsgNoYrZ9uWz/ctn+\n5bHty2X7l8e2L5ftX64e3/7eUyhJkiRJTcyRQkmSJElqYiaFkiRJktTETApLEBGTI+LJiHg6ImaU\nHU9vFxEHRcT8iHgiIjoi4i+L8qsjYnVELC3+nF52rL1VRKyKiN8U7byoKPt4RPw8IlYWP4eUHWdv\nExGHd+nfSyPi9Yj4K/t+/UTE7RHxSkQ83qWsal+PilnF/wXLImJceZHv/mq0/bcjYkXRvvdExOCi\nfEREvNXl38D3y4u8d6jR/jWvNRFxZdH3n4yIT5cTde9Ro/1/0qXtV0XE0qLc/t+NtvE9c7e69ntP\nYYNFRAvwFHAq0AksBKZm5hOlBtaLRcQBwAGZuSQiBgKLgc8B5wJvZOYNpQbYBCJiFTAhM9d1KfsW\n8LvMvL745ciQzPxaWTH2dsW1ZzXwKeAi7Pt1EREnAG8A/5yZo4qyqn29+IL8ZeB0Kn8v38vMT5UV\n++6uRtufBvzfzNwYEf8AULT9CODfNtXTR1ej/a+myrUmIo4EfgwcAxwIPAB8IjPfa2jQvUi19t9q\n/3eA1zLzWvt/99rG98xp7EbXfkcKG+8Y4OnMfDYz/wDcDZxZcky9Wma+lJlLitcbgOXAsHKjEpV+\n/6Pi9Y+oXEBVPycDz2Tm82UH0ptl5i+A321VXKuvn0nlC1xm5gJgcPHlQrugWttn5v2ZubHYXAAM\nb3hgTaJG36/lTODuzHwnM58Dnqby/Ui7aFvtHxFB5RfhP25oUE1iG98zd6trv0lh4w0DXuyy3YkJ\nSsMUvx0bCzxaFF1eDN3f7vTFukrg/ohYHBGXFmX7ZeZLxevfAvuVE1rTmMKWXwjs+41Tq6/7/0Fj\n/Vfg3i7bIyPisYh4KCKOLyuoJlDtWmPfb6zjgZczc2WXMvt/HWz1PXO3uvabFKppRMTewBzgrzLz\ndeAW4FBgDPAS8J0Sw+vt/iQzxwGfAS4rprlslpV57M5lr5OI2AM4A/iXosi+XxL7ejki4r8DG4E7\ni6KXgIMzcyzw18BdEfGxsuLrxbzW9AxT2fKXgvb/OqjyPXOz3eHab1LYeKuBg7psDy/KVEcR0ZfK\nP9Q7M/NfATLz5cx8LzPfB27DqSt1k5mri5+vAPdQaeuXN02XKH6+Ul6Evd5ngCWZ+TLY90tQq6/7\n/0EDRMQ04M+A84svZhTTFtcXrxcDzwCfKC3IXmob1xr7foNERB/gbOAnm8rs/92v2vdMdrNrv0lh\n4y0EDouIkcVv76cAc0uOqVcr5tL/E7A8M7/bpbzr/O2zgMe3PlYfXUQMKG68JiIGAKdRaeu5wIVF\ntQuBn5YTYVPY4rfE9v2Gq9XX5wJ/UaxEdyyVRSBeqnYC7ZqImAz8LXBGZr7ZpfyPi8WXiIj/BBwG\nPFtOlL3XNq41c4EpEbFnRIyk0v6/anR8TeIUYEVmdm4qsP93r1rfM9nNrv19yg6g2RQroF0O3Ae0\nALdnZkfJYfV2E4E/B36zaTlm4OvA1IgYQ2U4fxXw38oJr9fbD7incs2kD3BXZv7viFgItEfEF4Dn\nqdwEr25WJOKnsmX//pZ9vz4i4sfAJGCfiOgEZgLXU72vz6Oy+tzTwJtUVoXVLqrR9lcCewI/L65B\nCzLzi8AJwLUR8S7wPvDFzNzRRVJURY32n1TtWpOZHRHRDjxBZVrvZa48+tFUa//M/Cc+fD852P+7\nW63vmbvVtd9HUkiSJElSE3P6qCRJkiQ1MZNCSZIkSWpiJoWSJEmS1MRMCiVJkiSpiZkUSpIkSVIT\nMymUJKmGiMiI+F9dtvtExNqI+LduOPek7jiPJEkflUmhJEm1/QcwKiL2KrZPBVaXGI8kSd3OpFCS\npG2bB/xp8XoqH34QNAARsSAi2rpsPxgREyLimIh4JCIei4j/FxGHVzn26oj4my7bj0fEiOL1BRHx\nq4hYGhH/GBEt3fjZJEkyKZQkaTvuBqZERD9gNPBojXo/Ac4FiIgDgAMycxGwAjg+M8cCVwF/t6Nv\nHBGtwHnAxMwcA7wHnL+rH0SSpGr6lB2AJEk9WWYuK0btplIZNaylHbgfmEklOZxdlA8CfhQRhwEJ\n9N2Jtz8ZGA8sjAiAvYBXduJ4SZK2y6RQkqTtmwvcAEwChlarkJmrI2J9RIymMrr3xWLX/wDmZ+ZZ\nRXL5YJXDN7Ll7J1+xc8AfpSZV37E+CVJqsnpo5Ikbd/twDWZ+Zvt1PsJ8LfAoMxcVpQN4oPFaabV\nOG4VMA4gIsYBI4vy/wOcExH7Fvs+HhGH7MoHkCSpFpNCSZK2IzM7M3PWDlSdDUyhMpV0k28Bfx8R\nj1F7hs4c4OMR0QFcDjxVvO8TwDeA+yNiGfBz4IBd+xSSJFUXmVl2DJIkSZKkkjhSKEmSJElNzKRQ\nkiRJkpqYSaEkSZIkNTGTQkmSJElqYiaFkiRJktTETAolSZIkqYmZFEqSJElSE/v/mfYOUYEv5jIA\nAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"c_7fXcEbMr9m","colab_type":"text"},"source":["### It can be compared with stable, sklearn AdaBoost"]},{"cell_type":"code","metadata":{"id":"FjWZoYrjMr9n","colab_type":"code","outputId":"c1b70bc5-64a0-4fd7-f686-4c6990c3cc66","executionInfo":{"status":"ok","timestamp":1574339842263,"user_tz":-60,"elapsed":12288,"user":{"displayName":"Jan Chorowski","photoUrl":"","userId":"18100051538790809279"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["from sklearn.ensemble import AdaBoostClassifier as ABC\n","forest = ABC(n_estimators=1000)\n","forest.fit(train_x, train_y)\n","forest.score(test_x, test_y)"],"execution_count":26,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0.9822485207100592"]},"metadata":{"tags":[]},"execution_count":26}]},{"cell_type":"code","metadata":{"id":"x3T9FVXAvtSa","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]}]} \ No newline at end of file