Roko_Ch_4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "07cd0f67",
   "metadata": {},
   "outputs": [],
   "source": [
    "#In this equation:\n",
    "#ˆ\n",
    "#𝛉 is the value of θ that minimizes the cost function.\n",
    "#y is the vector of target values containing y(1) to y(m).\n",
    "#Let’s generate some linear-looking data to test this equation on (Figure 4-1):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b2d6f969",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 2 * np.random.rand(m, 1) # column vector\n",
    "y = 4 + 3 * X + np.random.randn(m, 1) # column vector\n",
    "\n",
    "plt.plot(X, y, 'bo')\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"X1\")\n",
    "plt.ylabel('y')\n",
    "plt.title('Randomly generated linear dataset')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "de8ba3e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.74908024],\n",
       "       [1.        , 1.90142861],\n",
       "       [1.        , 1.46398788],\n",
       "       [1.        , 1.19731697],\n",
       "       [1.        , 0.31203728]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Now lets compute theta using Normal equation. We will use the inv() function from NumPy’s linear algebra module (np.linalg) to compute the inverse of a \n",
    "#matrix, and the dot() method for matrix multiplication:\n",
    "\n",
    "from sklearn.preprocessing import add_dummy_feature\n",
    "\n",
    "X_b = add_dummy_feature(X) #adds x0 = 1 to each instance\n",
    "X_b[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "299e365b",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_best = np.linalg.inv(X_b.T @ X_b) @ X_b.T @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3fb2a951",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The function that we used to generate the data is y = 4 + 3x1 + Gaussian noise. Let’s see what the equation found:\n",
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0c45f7e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [1., 2.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#We would have hoped for θ0 = 4 and θ1 = 3 instead of θ0 = 4.215 and θ1 = 2.770. Close enough, \n",
    "#but the noise made it impossible to recover the exact parameters of \n",
    "#the original function. The smaller and noisier the dataset, the harder it gets.\n",
    "\n",
    "\n",
    "#Now we can make predictions using 𝛉:\n",
    "\n",
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = add_dummy_feature(X_new) ## add x0 = 1 to each instance\n",
    "X_new_b[:2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d4e89b4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predict = X_new_b @ theta_best\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c2dbbd71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r.\", label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6cecfb43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [2]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "07961a80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5a3b462a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Performing linear regression using Scikit-Learn is \n",
    "#relatively straightforward:\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7ed70eb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new) #the same results as in cell [9] above.\n",
    "#tells you that doing predictions manually with the formula from cell\n",
    "#[6] gives you same results as just running stuff with scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b71d1f1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Notice that Scikit-Learn separates the bias term (intercept_) from \n",
    "#the feature weights (coef_). The LinearRegression class is based on the\n",
    "#scipy.linalg.lstsq() function (the name stands for “least squares”), \n",
    "#which you could call directly:\n",
    "\n",
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "85669396",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1.        , 0.74908024],\n",
       "        [1.        , 1.90142861],\n",
       "        [1.        , 1.46398788],\n",
       "        [1.        , 1.19731697],\n",
       "        [1.        , 0.31203728]]),\n",
       " array([[6.33428778],\n",
       "        [9.40527849],\n",
       "        [8.48372443],\n",
       "        [5.60438199],\n",
       "        [4.71643995]]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_b[:5], y[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "baf68057",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "71c317a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#This function computes 𝛉 , where is the pseudoinverse of X \n",
    "#(specifically, the Moore–Penrose inverse). You can use np.linalg.pinv() \n",
    "#to compute the pseudoinverse directly:\n",
    "\n",
    "np.linalg.pinv(X_b) @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "daf65fdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Computational Complexity\n",
    "#The Normal equation computes the inverse of X⊺ X, which is an (n + 1) × \n",
    "#(n + 1) matrix (where n is the number of features). The computational \n",
    "#complexity of inverting such a matrix is typically about O(n2.4) to O(n3)\n",
    "#, depending on the implementation. In other words, if you double the \n",
    "#number of features, you multiply the computation time by roughly \n",
    "#22.4 = 5.3 to 23 = 8. The SVD approach used by Scikit-Learn’s \n",
    "#LinearRegression class is about O(n2). If you double the number of \n",
    "#features, you multiply the computation time by roughly 4.\n",
    "\n",
    "#Also, once you have trained your linear regression model (using the \n",
    "#Normal equation or any other algorithm), predictions are very fast:\n",
    "#the computational complexity is linear with regard to both the number\n",
    "#of instances you want to make predictions on and the number of \n",
    "#features. In other words, making predictions on twice as many \n",
    "#instances (or twice as many features) will take roughly twice as \n",
    "#much time.\n",
    "\n",
    "#Now we will look at a very different way to train a linear \n",
    "#regression model, which is better suited for cases where there are \n",
    "#a large number of features or too many training instances to fit \n",
    "#in memory.\n",
    "\n",
    "#Gradient Descent\n",
    "#Gradient descent is a generic optimization algorithm capable of \n",
    "#finding optimal solutions to a wide range of problems. The general \n",
    "#idea of gradient descent is to tweak parameters iteratively in order\n",
    "#to minimize a cost function. Suppose you are lost in the mountains in a \n",
    "#dense fog, and you can only feel the slope of the ground below your \n",
    "#feet. A good strategy to get to the bottom of the valley quickly is \n",
    "#to go downhill in the direction of the steepest slope. This is exactly\n",
    "#what gradient descent does: it measures the local gradient of the error\n",
    "#function with regard to the parameter vector θ, and it goes in the \n",
    "#direction of descending gradient. Once the gradient is zero, you \n",
    "#have reached a minimum!\n",
    "#In practice, you start by filling θ with random values (this is \n",
    "#called random initialization). Then you improve it gradually, \n",
    "#taking one baby step at a time, each step attempting to decrease\n",
    "#the cost function (e.g., the MSE), until the algorithm converges to \n",
    "#a minimum (see Figure 4-3).\n",
    "\n",
    "#Fortunately, the MSE cost function for a linear regression model \n",
    "#happens to be a convex function, which means that if you pick any \n",
    "#two points on the curve, the line segment joining them is never \n",
    "#below the curve. This implies that there are no local minima, \n",
    "#just one global minimum. It is also a continuous function with\n",
    "#a slope that never changes abruptly.2 These two facts have a great\n",
    "#consequence: gradient descent is guaranteed to approach arbitrarily \n",
    "#closely the global minimum (if you wait long enough and if the \n",
    "#learning rate is not too high).\n",
    "\n",
    "\n",
    "#nice explanation on the page 208 with figures!!!\n",
    "\n",
    "#Let’s look at a quick implementation of this algorithm:\n",
    "\n",
    "eta = 0.1 #learning rate\n",
    "n_epochs = 1000\n",
    "m = len(X_b) #number of instances\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1) #random initialized model parameters\n",
    "for epoch in range(n_epochs):\n",
    "    gradients = 2 / m * X_b.T @ (X_b @ theta - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e8aa6466",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#That wasn’t too hard! Each iteration over the training set is called \n",
    "#an epoch. Let’s look at the resulting theta:\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4363c151",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 1000)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(n_epochs)\n",
    "#nice visual explanation of epochs in figures on pagew 213"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0a247d23",
   "metadata": {},
   "outputs": [],
   "source": [
    "#You may wonder how to set the number of epochs. If it is too low, \n",
    "#you will still be far away from the optimal solution when the \n",
    "#algorithm stops; but if it is too high, you will waste time while \n",
    "#the model parameters do not change anymore. A simple solution is \n",
    "#to set a very large number of epochs but to interrupt the algorithm\n",
    "#when the gradient vector becomes tiny—that is, when its norm becomes\n",
    "#smaller than a tiny number ε (called the tolerance)—because this \n",
    "#happens when gradient descent has (almost) reached the minimum.\n",
    "\n",
    "#Stochastic Gradient Descent\n",
    "#The main problem with batch gradient descent is the fact that it uses \n",
    "#the whole training set to compute the gradients at every step, which\n",
    "#makes it very slow when the training set is large. At the opposite \n",
    "#extreme, stochastic gradient descent picks a random instance in the \n",
    "#training set at every step and computes the gradients based only on\n",
    "#that single instance. Obviously, working on a single instance at a \n",
    "#time makes the algorithm much faster because it has very little data\n",
    "#to manipulate at every iteration. It also makes it possible to train \n",
    "#on huge training sets, since only one instance needs to be in memory \n",
    "#at each iteration (stochastic GD can be implemented as an out-of-core \n",
    "#algorithm.\n",
    "\n",
    "#On the other hand, due to its stochastic (i.e., random) nature, \n",
    "#this algorithm is much less regular than batch gradient descent: \n",
    "#instead of gently decreasing until it reaches the minimum, the cost\n",
    "#function will bounce up and down, decreasing only on average. Over \n",
    "#time it will end up very close to the minimum, but once it gets there \n",
    "#it will continue to bounce around, never settling down (see Figure 4-9).\n",
    "#Once the algorithm stops, the final parameter values will be good, \n",
    "#but not optimal.\n",
    "\n",
    "#When the cost function is very irregular (as in Figure 4-6), this \n",
    "#can actually help the algorithm jump out of local minima, so \n",
    "#stochastic gradient descent has a better chance of finding the global \n",
    "#minimum than batch gradient descent does. Therefore, randomness is \n",
    "#good to escape from local optima, but bad because it means that \n",
    "#the algorithm can never settle at the minimum. One solution to\n",
    "#this dilemma is to gradually reduce the learning rate. The steps \n",
    "#start out large (which helps make quick progress and escape local \n",
    "#minima), then get smaller and smaller, allowing the algorithm to \n",
    "#settle at the global minimum. This process is akin to simulated \n",
    "#annealing, an algorithm inspired by the process in metallurgy of \n",
    "#annealing, where molten metal is slowly cooled down. The function \n",
    "#that determines the learning rate at each iteration is called the\n",
    "#learning schedule. If the learning rate is reduced too quickly, \n",
    "#you may get stuck in a local minimum, or even end up frozen halfway\n",
    "#to the minimum. If the learning rate is reduced too slowly, you may\n",
    "#jump around the minimum for a long time and end up with a suboptimal\n",
    "#solution if you halt training too early.\n",
    "\n",
    "\n",
    "#This code implements stochastic gradient descent using a simple \n",
    "#learning schedule.\n",
    "\n",
    "n_epochs = 50\n",
    "t0, t1 = 5, 50\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2, 1) # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for iteration in range(m):\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index : random_index + 1]\n",
    "        yi = y[random_index : random_index +1]\n",
    "        gradients = 2 * xi.T @ (xi @ theta - yi) #for SGD, do not divide by m\n",
    "        eta = learning_schedule(epoch * m + iteration)\n",
    "        theta = theta - eta * gradients\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "bccad69d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "73dc6b86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SGDRegressor</label><div class=\"sk-toggleable__content\"><pre>SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "SGDRegressor(n_iter_no_change=100, penalty=None, random_state=42, tol=1e-05)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#To perform linear regression using stochastic GD with Scikit-Learn, \n",
    "#you can use the SGDRegressor class, which defaults to optimizing the\n",
    "#MSE cost function. The following code runs for maximum 1,000 epochs \n",
    "#(max_iter) or until the loss drops by less than 10–5 (tol) during 100 \n",
    "#epochs (n_iter_no_change). It starts with a learning rate of 0.01 \n",
    "#(eta0), using the default learning schedule (different from the one \n",
    "#we used). Lastly, it does not use any regularization (penalty=None; \n",
    "#more details on this shortly):\n",
    "\n",
    "\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-5, penalty=None,\n",
    "                      eta0=0.01, n_iter_no_change=100, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel()) #y.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "08046e30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.ravel().shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "17f5bf4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9d490947",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21278812]), array([2.77270267]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "463619d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Polynomial Regression\n",
    "\n",
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X ** 2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "97988191",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13b30a5c0>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c80a8c82",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Clearly, a straight line will never fit this data properly. So let’s \n",
    "#use Scikit-Learn’s PolynomialFeatures class to transform our training \n",
    "#data, adding the square (second-degree polynomial) of each feature in \n",
    "#the training set as a new feature (in this case there is just one\n",
    "#feature):\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "31b81041",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.75275929],\n",
       "       [ 2.70428584],\n",
       "       [ 1.39196365],\n",
       "       [ 0.59195091],\n",
       "       [-2.06388816]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "88f5d3d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.75275929,  0.56664654],\n",
       "       [ 2.70428584,  7.3131619 ],\n",
       "       [ 1.39196365,  1.93756281],\n",
       "       [ 0.59195091,  0.35040587],\n",
       "       [-2.06388816,  4.25963433]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0318cd99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#X_poly now contains the original feature of X plus the square of \n",
    "#this feature. Now we can fit a LinearRegression model to this \n",
    "#extended training data\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "64718d10",
   "metadata": {},
   "outputs": [],
   "source": [
    "# original function had 0.5 for x1 ** 2, and 1 for x1 and 2 for intercept\n",
    "#here the linear reg captures the relationship with estimated:\n",
    "# 0.56 for x1 ** 2, 0.93 for x1 and 1.78 for intercept.\n",
    "\n",
    "#not bad!\n",
    "\n",
    "#PolynomialFeatures(degree=d) transforms an array containing n features \n",
    "#into an array containing (n + d)! / d!n! features, where n! is the \n",
    "#factorial of n, equal to 1 × 2 × 3 × × n. Beware of the combinatorial \n",
    "#explosion of the number of features!\n",
    " \n",
    "\n",
    "#If you perform high-degree polynomial regression, you will likely fit \n",
    "#the training data much better than with plain linear regression. For \n",
    "#example, Figure 4-14 applies a 300-degree polynomial model to the \n",
    "#preceding training data, and compares the result with a pure linear\n",
    "#model and a quadratic model (second- degree polynomial). Notice how\n",
    "#the 300-degree polynomial model wiggles around to get as close as \n",
    "#possible to the training instances.\n",
    "\n",
    "#This high-degree polynomial regression model is severely overfitting \n",
    "#the training data, while the linear model is underfitting it. The model\n",
    "#that will generalize best in this case is the quadratic model, which\n",
    "#makes sense because the data was generated using a quadratic model. But\n",
    "#in general you won’t know what function generated the data, so how can\n",
    "#you decide how complex your model should be? How can you tell that your\n",
    "#model is overfitting or underfitting the data?\n",
    "\n",
    "\n",
    "#In Chapter 2 you used cross-validation to get an estimate of a model’s\n",
    "#generalization performance. If a model performs well on the training \n",
    "#data but generalizes poorly according to the cross-validation metrics,\n",
    "#then your model is overfitting. If it performs poorly on both, then it\n",
    "#is underfitting. This is one way to tell when a model is too simple or \n",
    "#too complex.\n",
    "\n",
    "#Another way to tell is to look at the learning curves, which are \n",
    "#plots of the model’s training error and validation error as a \n",
    "#function of the training iteration: just evaluate the model at \n",
    "#regular intervals during training on both the training set and the \n",
    "#validation set, and plot the results. If the model cannot be trained \n",
    "#incrementally (i.e., if it does not support partial_fit() or warm_start),\n",
    "#then you must train it several times on gradually larger subsets of \n",
    "#the training set.\n",
    "\n",
    "#Scikit-Learn has a useful learning_curve() function to help with this:\n",
    "#it trains and evaluates the model using cross-validation. By default \n",
    "#it retrains the model on growing subsets of the training set, but if\n",
    "#the model supports incremental learning you can set \n",
    "#exploit_incremental_learning=True when calling learning_curve() and \n",
    "#it will train the model incrementally instead. The function returns\n",
    "#the training set sizes at which it evaluated the model, and the \n",
    "#training and validation scores it measured for each size and for \n",
    "#each cross-validation fold. Let’s use this function to look at the\n",
    "#learning curves of the plain linear regression model.\n",
    "\n",
    "from sklearn.model_selection import learning_curve\n",
    "\n",
    "train_sizes, train_scores, valid_scores = learning_curve(\n",
    "       LinearRegression(), X, y, train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
    "       scoring=\"neg_root_mean_squared_error\")\n",
    "\n",
    "train_errors = -train_scores.mean(axis=1)\n",
    "valid_errors = -valid_scores.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ce9eedc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01      , 0.03538462, 0.06076923, 0.08615385, 0.11153846,\n",
       "       0.13692308, 0.16230769, 0.18769231, 0.21307692, 0.23846154,\n",
       "       0.26384615, 0.28923077, 0.31461538, 0.34      , 0.36538462,\n",
       "       0.39076923, 0.41615385, 0.44153846, 0.46692308, 0.49230769,\n",
       "       0.51769231, 0.54307692, 0.56846154, 0.59384615, 0.61923077,\n",
       "       0.64461538, 0.67      , 0.69538462, 0.72076923, 0.74615385,\n",
       "       0.77153846, 0.79692308, 0.82230769, 0.84769231, 0.87307692,\n",
       "       0.89846154, 0.92384615, 0.94923077, 0.97461538, 1.        ])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(0.01, 1.0, 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8858152c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
    "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"Training Size\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.ylim(0, 2.5)\n",
    "plt.show()\n",
    "\n",
    "#training size is max 80 because there are 100 instances in the training\n",
    "#data, and with 5-fold CV it means that max number of training set size\n",
    "#is 80, given that validation set has to be 20\n",
    "\n",
    "#This model is underfitting. To see why, first let’s look at the training\n",
    "#error. When there are just one or two instances in the training set, \n",
    "#the model can fit them perfectly, which is why the curve starts at zero.\n",
    "#But as new instances are added to the training set, it becomes \n",
    "#impossible for the model to fit the training data perfectly, both \n",
    "#because the data is noisy and because it is not linear at all. So \n",
    "#the error on the training data goes up until it reaches a plateau, \n",
    "#at which point adding new instances to the training set doesn’t make\n",
    "#the average error much better or worse. Now let’s look at the validation\n",
    "#error. When the model is trained on very few training instances, it is\n",
    "#incapable of generalizing properly, which is why the validation error\n",
    "#is initially quite large. Then, as the model is shown more training \n",
    "#examples, it learns, and thus the validation error slowly goes down.\n",
    "#However, once again a straight line cannot do a good job of modeling \n",
    "#the data, so the error ends up at a plateau, very close to the other\n",
    "#curve.\n",
    "\n",
    "#These learning curves are typical of a model that’s underfitting. \n",
    "#Both curves have reached a plateau; they are close and fairly high.\n",
    "\n",
    "#If your model is underfitting the training data, adding more training\n",
    "#examples will not help. You need to use a better model or come up \n",
    "#with better features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2fd779cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now let’s look at the learning curves of a 10th-degree polynomial \n",
    "#model on the same data (Figure 4-16):\n",
    "\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "polynomial_regression = make_pipeline(\n",
    "    PolynomialFeatures(degree=10, include_bias=False), \n",
    "    LinearRegression())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "5f438fcb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;,\n",
       "                 PolynomialFeatures(degree=10, include_bias=False)),\n",
       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;,\n",
       "                 PolynomialFeatures(degree=10, include_bias=False)),\n",
       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PolynomialFeatures</label><div class=\"sk-toggleable__content\"><pre>PolynomialFeatures(degree=10, include_bias=False)</pre></div></div></div><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('polynomialfeatures',\n",
       "                 PolynomialFeatures(degree=10, include_bias=False)),\n",
       "                ('linearregression', LinearRegression())])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polynomial_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "50bf1f59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_sizes, train_scores, valid_scores = learning_curve(\n",
    "       polynomial_regression, X, y, \n",
    "       train_sizes=np.linspace(0.01, 1.0, 40), cv=5,\n",
    "       scoring=\"neg_root_mean_squared_error\")\n",
    "\n",
    "train_errors = -train_scores.mean(axis=1)\n",
    "valid_errors = -valid_scores.mean(axis=1)\n",
    "\n",
    "plt.plot(train_sizes, train_errors, \"r-+\", linewidth=2, label=\"train\")\n",
    "plt.plot(train_sizes, valid_errors, \"b-\", linewidth=3, label=\"valid\")\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"Training Size\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.ylim(0, 2.5)\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "6c22d16b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#These learning curves look a bit like the previous ones, but there \n",
    "#are two very important differences:\n",
    "#The error on the training data is much lower than before.\n",
    "#There is a gap between the curves. This means that the model \n",
    "#performs significantly better on the training data than on the \n",
    "#validation data, which is the hallmark of an overfitting model. \n",
    "#If you used a much larger training set, however, the two curves \n",
    "#would continue to get closer.\n",
    "\n",
    "#TIP\n",
    "#One way to improve an overfitting model is to feed it more training \n",
    "#data until the validation error reaches the training error.\n",
    "\n",
    "\n",
    "#THE BIAS/VARIANCE TRADE-OFF\n",
    "#An important theoretical result of statistics and machine learning is \n",
    "#the fact that a model’s generalization error can be expressed as the \n",
    "#sum of three very different errors:\n",
    "#Bias\n",
    "#This part of the generalization error is due to wrong assumptions, \n",
    "#such as assuming that the data is linear when it is actually quadratic.\n",
    "#A high-bias model is most likely to underfit the training data.\n",
    "\n",
    "#Variance\n",
    "#This part is due to the model’s excessive sensitivity to small \n",
    "#variations in the training data. A model with many degrees of \n",
    "#freedom (such as a high- degree polynomial model) is likely to have \n",
    "#high variance and thus overfit the training data.\n",
    "\n",
    "#Irreducible error\n",
    "#This part is due to the noisiness of the data itself. The only way to\n",
    "#reduce this part of the error is to clean up the data (e.g., fix the\n",
    "#data sources, such as broken sensors, or detect and remove outliers).\n",
    "#Increasing a model’s complexity will typically increase its variance\n",
    "#and reduce its bias. Conversely, reducing a model’s complexity \n",
    "#increases its bias and reduces its variance. This is why it is \n",
    "#called a trade-off.\n",
    "\n",
    "\n",
    "#Regularized Linear Models\n",
    "#As you saw in Chapters 1 and 2, a good way to reduce overfitting is\n",
    "#to regularize the model (i.e., to constrain it): the fewer degrees of \n",
    "#freedom it has, the harder it will be for it to overfit the data. A \n",
    "#simple way to regularize a polynomial model is to reduce the number \n",
    "#of polynomial degrees.\n",
    "\n",
    "#For a linear model, regularization is typically achieved by constraining\n",
    "#the weights of the model. We will now look at ridge regression, \n",
    "#lasso regression, and elastic net regression, which implement three \n",
    "#different ways to constrain the weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "1e39a995",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.82899748]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#As with linear regression, we can perform ridge regression either by \n",
    "#computing a closed-form equation or by performing gradient descent. \n",
    "#The pros and cons are the same. Equation 4-9 shows the closed-form \n",
    "#solution, where A is the (n + 1) × (n + 1) identity matrix,9 except \n",
    "#with a 0 in the top-left cell, corresponding to the bias term.\n",
    "#Here is how to perform ridge regression with Scikit-Learn using a \n",
    "#closed-form solution (a variant of Equation 4-9 that uses a matrix \n",
    "#factorization technique by André-Louis Cholesky):\n",
    "\n",
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=0.1, solver=\"cholesky\")\n",
    "ridge_reg.fit(X,y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3e91ee30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.82830117])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#And using stochastic gradient descent:\n",
    "sgd_reg = SGDRegressor(penalty=\"l2\", alpha=0.1 / m, tol=None,\n",
    "                      max_iter=1000, eta0=0.01, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel()) #y.ravel() because fit() expects 1D targets\n",
    "sgd_reg.predict([[1.5]])\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "7a0ab0c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.77621741])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The RidgeCV class also performs ridge regression, but it automatically\n",
    "#tunes hyperparameters using cross-validation. It’s roughly equivalent \n",
    "#to using GridSearchCV, but it’s optimized for ridge regression and runs\n",
    "#much faster. Several other estimators (mostly linear) also have \n",
    "#efficient CV variants, such as LassoCV and ElasticNetCV.\n",
    "\n",
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "92766a7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.78114505])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Elastic Net Regression\n",
    "#Elastic net regression is a middle ground between ridge regression \n",
    "#and lasso regression. The regularization term is a weighted sum of \n",
    "#both ridge and lasso’s regularization terms, and you can control\n",
    "#the mix ratio r. When r = 0, elastic net is equivalent to ridge \n",
    "#regression, and when r = 1, it is equivalent to lasso regression\n",
    "#(Equation 4-12).\n",
    "\n",
    "#So when should you use elastic net regression, or ridge, lasso, or \n",
    "#plain linear regression (i.e., without any regularization)? It is \n",
    "#almost always preferable to have at least a little bit of \n",
    "#regularization, so generally you should avoid plain linear regression. \n",
    "#Ridge is a good default, but if you suspect that only a few features\n",
    "#are useful, you should prefer lasso or elastic net because they tend \n",
    "#to reduce the useless features’ weights down to zero, as discussed \n",
    "#earlier. In general, elastic net is preferred over lasso because \n",
    "#lasso may behave erratically when the number of features is greater \n",
    "#than the number of training instances or when several features are \n",
    "#strongly correlated.\n",
    "\n",
    "#Here is a short example that uses Scikit-Learn’s ElasticNet \n",
    "#(l1_ratio corresponds to the mix ratio r):\n",
    "\n",
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "65a98c15",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Early Stopping\n",
    "#A very different way to regularize iterative learning algorithms such\n",
    "#as gradient descent is to stop training as soon as the validation \n",
    "#error reaches a minimum. This is called early stopping. Figure 4-20 \n",
    "#shows a complex model (in this case, a high- degree polynomial \n",
    "#regression model) being trained with batch gradient descent on the\n",
    "#quadratic dataset we used earlier. As the epochs go by, the algorithm\n",
    "#learns, and its prediction error (RMSE) on the training set goes down,\n",
    "#along with its prediction error on the validation set. After a while,\n",
    "#though, the validation error stops decreasing and starts to go back up.\n",
    "#This indicates that the model has started to overfit the training data.\n",
    "#With early stopping you just stop training as soon as the validation\n",
    "#error reaches the minimum. It is such a simple and efficient\n",
    "#regularization technique that Geoffrey Hinton called it a “beautiful\n",
    "#free lunch”.\n",
    "\n",
    "\n",
    "#Here is a basic implementation of early stopping:\n",
    "\n",
    "from copy import deepcopy\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "X_train, y_train, X_valid, y_valid = X[:80], y[:80], X[80:], y[80:]\n",
    "\n",
    "preprocessing = make_pipeline(PolynomialFeatures(degree=90,\n",
    "                                                include_bias=False),\n",
    "                             StandardScaler())\n",
    "X_train_prep = preprocessing.fit_transform(X_train)\n",
    "X_valid_prep = preprocessing.transform(X_valid)\n",
    "\n",
    "sgd_reg = SGDRegressor(penalty=None, eta0=0.002, random_state=42)\n",
    "n_epochs = 500\n",
    "best_valid_rmse = float('inf')\n",
    "\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.partial_fit(X_train_prep, y_train.ravel())\n",
    "    y_valid_predict = sgd_reg.predict(X_valid_prep)\n",
    "    val_error = mean_squared_error(y_valid, y_valid_predict, squared=False)\n",
    "    if val_error < best_valid_rmse:\n",
    "        best_valid_rmse = val_error\n",
    "        best_model = deepcopy(sgd_reg)\n",
    "        \n",
    "        \n",
    "        \n",
    "#This code first adds the polynomial features and scales all the input\n",
    "#features, both for the training set and for the validation set (the \n",
    "#code assumes that you have split the original training set into a \n",
    "#smaller training set and a validation set). Then it creates an \n",
    "#SGDRegressor model with no regularization and a small learning rate.\n",
    "#In the training loop, it calls partial_fit() instead of fit(), to \n",
    "#perform incremental learning. At each epoch, it measures the RMSE on\n",
    "#the validation set. If it is lower than the lowest RMSE seen so far,\n",
    "#it saves a copy of the model in the best_model variable. This \n",
    "#implementation does not actually sto p training, but it lets you \n",
    "#revert to the best model after training. Note that the model is \n",
    "#copied using copy.deepcopy(), because it copies both the model’s \n",
    "#hyperparameters and the learned parameters. In contrast, \n",
    "#sklearn.base.clone() only copies the model’s hyperparameters.\n",
    "\n",
    "#Logistic Regression\n",
    "\n",
    "#As discussed in Chapter 1, some regression algorithms can be used \n",
    "#for classification (and vice versa). Logistic regression (also called \n",
    "#logit regression) is commonly used to estimate the probability that\n",
    "#an instance belongs to a particular class (e.g., what is the \n",
    "#probability that this email is spam?). If the estimated probability\n",
    "#is greater than a given threshold (typically 50%), then the model\n",
    "#predicts that the instance belongs to that class (called the positive\n",
    "#class, labeled “1”), and otherwise it predicts that it does not\n",
    "#(i.e., it belongs to the negative class, labeled “0”). This makes\n",
    "#it a binary classifier.\n",
    "\n",
    "#Estimating Probabilities\n",
    "#So how does logistic regression work? Just like a linear regression \n",
    "#model, a logistic regression model computes a weighted sum of the \n",
    "#input features (plus a bias term), but instead of outputting the \n",
    "#result directly like the linear regression model does, it outputs \n",
    "#the logistic of this result (see Equation 4-13).\n",
    "    \n",
    "#The logistic—noted σ(·)—is a sigmoid function (i.e., S-shaped) \n",
    "#that outputs a number between 0 and 1. \n",
    "\n",
    "#Notice that σ(t) < 0.5 when t < 0, and σ(t) ≥ 0.5 when t ≥ 0, so \n",
    "#a logistic regression model using the default threshold of 50% \n",
    "#probability predicts 1 if θ⊺ x is positive and 0 if it is negative.\n",
    "\n",
    "\n",
    "\n",
    "#The cost function over the whole training set is the average cost over \n",
    "#all training instances. It can be written in a single expression \n",
    "#called the log loss, shown in Equation 4-17.\n",
    "\n",
    "#Decision Boundaries\n",
    "#We can use the iris dataset to illustrate logistic regression. This \n",
    "#is a famous dataset that contains the sepal and petal length and \n",
    "#width of 150 iris flowers of three different species: Iris setosa, \n",
    "#Iris versicolor, and Iris virginica (see Figure 4-22).\n",
    "\n",
    "#Let’s try to build a classifier to detect the Iris virginica type \n",
    "#based only on the petal width feature. The first step is to load the\n",
    "#data and take a quick peek:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "f4afb8ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename',\n",
       " 'data_module']"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "iris = load_iris(as_frame=True)\n",
    "list(iris)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "052f0277",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                5.1               3.5                1.4               0.2\n",
       "1                4.9               3.0                1.4               0.2\n",
       "2                4.7               3.2                1.3               0.2"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.data.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "25652f1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0\n",
       "1    0\n",
       "2    0\n",
       "Name: target, dtype: int64"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "5920c06c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'virginica'], dtype='<U10')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "ab5d4c61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" checked><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(random_state=42)"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Next we’ll split the data and train a logistic regression \n",
    "#model on the training set:\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X = iris.data[[\"petal width (cm)\"]].values\n",
    "X\n",
    "y = iris.target_names[iris.target] == 'virginica'\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "log_reg = LogisticRegression(random_state=42)\n",
    "log_reg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "ce7f3488",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let’s look at the model’s estimated probabilities for flowers with\n",
    "#petal widths varying from 0 cm to 3 cm\n",
    "\n",
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1) # reshape to get a column vector \n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0, 0] #first number where \n",
    "#probability is higher or equal to 0.5\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2,\n",
    "            label=\"Not Iris virginica proba\")\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica proba\")\n",
    "plt.plot([decision_boundary, decision_boundary], [0, 1], \"k:\", \n",
    "         linewidth=2, label=\"Decision boundary\")\n",
    "plt.grid(True)\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "4cd471f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6516516516516517"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "ef178d51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "72912d86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "LogisticRegression(C=30, random_state=42)"
      ]
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     "execution_count": 91,
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   "source": [
    "#Just like the other linear models, logistic regression models \n",
    "#can be regularized using l1 or l2 penalties. Scikit-Learn actually \n",
    "#adds an l2 penalty by default.\n",
    "\n",
    "#softmax regression\n",
    "#Now you can compute the gradient vector for every class, then use \n",
    "#gradient descent (or any other optimization algorithm) to find the \n",
    "#parameter matrix Θ that minimizes the cost function.\n",
    "\n",
    "#Let’s use softmax regression to classify the iris plants into all \n",
    "#three classes. Scikit-Learn’s LogisticRegression classifier uses \n",
    "#softmax regression automatically when you train it on more than \n",
    "#two classes (assuming you use solver=\"lbfgs\", which is the default).\n",
    "#It also applies l2 regularization by default, which you can control \n",
    "#using the hyperparameter C, as mentioned earlier:\n",
    "\n",
    "X = iris.data[[\"petal length (cm)\", \"petal width (cm)\"]].values\n",
    "y = iris.target\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "softmax_reg = LogisticRegression(C=30, random_state=42)\n",
    "softmax_reg.fit(X_train, y_train)\n"
   ]
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   "execution_count": 92,
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     "data": {
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       "array([2])"
      ]
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     "execution_count": 92,
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   "source": [
    "#So the next time you find an iris with petals that are 5 cm long \n",
    "#and 2 cm wide, you can ask your model to tell you what type of iris \n",
    "#it is, and it will answer Iris virginica (class 2) with 96% \n",
    "#probability (or Iris versicolor with 4% probability):\n",
    "\n",
    "softmax_reg.predict([[5, 2]])"
   ]
  },
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   "cell_type": "code",
   "execution_count": 93,
   "id": "72c8c87c",
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     "data": {
      "text/plain": [
       "array([[0.  , 0.04, 0.96]])"
      ]
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     "execution_count": 93,
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   "source": [
    "softmax_reg.predict_proba([[5, 2]]).round(2)"
   ]
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