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+{
+ "nbformat": 4,
+ "nbformat_minor": 0,
+ "metadata": {
+ "colab": {
+ "name": "Assignment4.ipynb",
+ "provenance": [],
+ "collapsed_sections": [],
+ "toc_visible": true,
+ "include_colab_link": true
+ },
+ "kernelspec": {
+ "name": "python3",
+ "display_name": "Python 3"
+ }
+ },
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "view-in-github",
+ "colab_type": "text"
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "wWKlAIeLj21v",
+ "colab_type": "text"
+ },
+ "source": [
+ "**Submission deadline:**\n",
+ "* **Regular problems: last lab session before or on Monday, 9.13.2020b**\n",
+ "* **Bonus problems: Last lab during semester**\n",
+ "\n",
+ "**Points: 5 + 9 bonus points**\n",
+ "\n",
+ "Please note: some of the assignments are tedious or boring if you are already a NumPy ninja. The bonus problems were designed to give you a more satisfying alternative.\n",
+ "\n",
+ "## Heads Up!\n",
+ "\n",
+ "This assignment comes with starter code, but you are not forced to use it, as long as you execute all analysis demanded in the problems.\n",
+ "\n",
+ "## A note about plots!\n",
+ "\n",
+ "Plots are a way of communication. Just lke text, they can be paraphrased. You do not have to exactly reproducy my plots, but you must try to make suer yourp plots tell a similar story:\n",
+ "- label axis\n",
+ "- add titles\n",
+ "- choose plot type properly\n",
+ "- choose a color scale, limits, ticks\n",
+ "\n",
+ "so that you can describe what is happening!\n",
+ "\n",
+ "## Bugs?!\n",
+ "\n",
+ "Please submit Github PRs or email us about any problems with the notebook - we will try to correct them quickly. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "fdbcvRkik-qM",
+ "colab_type": "code",
+ "colab": {}
+ },
+ "source": [
+ "# Standard IPython notebook imports\n",
+ "%matplotlib inline\n",
+ "\n",
+ "import os\n",
+ "\n",
+ "from io import StringIO\n",
+ "import itertools\n",
+ "import httpimport\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "from tqdm import tqdm_notebook\n",
+ "\n",
+ "import scipy.stats as sstats\n",
+ "import scipy.optimize as sopt\n",
+ "\n",
+ "import seaborn as sns\n",
+ "\n",
+ "import sklearn.datasets\n",
+ "import sklearn.ensemble\n",
+ "import sklearn.svm\n",
+ "import sklearn.tree\n",
+ "\n",
+ "import cvxopt\n",
+ "\n",
+ "\n",
+ "# In this way we can import functions straight from github\n",
+ "with httpimport.github_repo('janchorowski', 'nn_assignments', \n",
+ " module='common', branch='nn18'):\n",
+ " from common.plotting import plot_mat\n",
+ "\n",
+ "sns.set_style('whitegrid')"
+ ],
+ "execution_count": 0,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "tmhgKqnsIfx8",
+ "colab_type": "text"
+ },
+ "source": [
+ "\n",
+ "# SVM Theory\n",
+ "A linear SVM assigns points $x^{(i)}\\in\\mathbb{R}^n$ to one of two\n",
+ "classes, $y^{(i)}\\in\\{-1,1\\}$ using the decision rule:\n",
+ "\n",
+ "\\begin{equation}\n",
+ "y = \\text{signum}(w^T x + b).\n",
+ "\\end{equation}\n",
+ "\n",
+ "SVM training consists of finding weights $w\\in\\mathbb{R}^n$\n",
+ "and bias $b\\in\\mathbb{R}$ that maximize the separation margin. This\n",
+ "corresponds to solving the following quadratic optimization problem:\n",
+ "\n",
+ "\\begin{equation}\n",
+ "\\begin{split}\n",
+ " \\min_{w,b,\\xi} &\\frac{1}{2}w^Tw + C\\sum_{i=1}^m \\xi_i \\\\\n",
+ " \\text{s.t. } & y^{(i)}(w^T x^{(i)} + b) \\geq 1- \\xi_i\\;\\; \\forall_i \\\\\n",
+ " & \\xi_i \\geq 0 \\;\\; \\forall_i.\n",
+ "\\end{split}\n",
+ "\\end{equation}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "lE81O301Ol-A",
+ "colab_type": "text"
+ },
+ "source": [
+ "# Problem 1 [2p]\n",
+ "\n",
+ "Load the iris dataset. \n",
+ "\n",
+ "1. [1p] Using the `sklearn.svm.SVC` library train a linear SVM that\n",
+ "separates the Virginica from the Versicolor class using the\n",
+ "petal length and petal width features. Plot the obtained decision boundary and\n",
+ "the support vectors (their locations and weights - coefficients $\\alpha$).\n",
+ "\n",
+ "2. [.5p] Now train a nonlinear SVM using the Gaussian kernel. Tune the parameetrs `C` and `gamma` (for the kernel) to reach maximum training accurracy. Plot the decision boundary and supprt vectors.\n",
+ "\n",
+ "3. [.5p] Answer the following questions:\n",
+ " - When the SVM is forced to maximally accurate on the train set, roughly how many support vectors do we get ?\n",
+ " - what is the relationship between the regularization constant `C` and the support vector weights `alpha`?\n",
+ " \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "metadata": {
+ "id": "vM8N5kEdOq3c",
+ "colab_type": "code",
+ "outputId": "84ca3b92-fb16-427c-adaa-e6174e2e3318",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 331
+ }
+ },
+ "source": [
+ "# load iris, extract petal_length and petal_width of versicolors and virginicas\n",
+ "\n",
+ "iris = sklearn.datasets.load_iris()\n",
+ "print('Features: ', iris.feature_names)\n",
+ "print('Targets: ', iris.target_names)\n",
+ "petal_length = iris.data[:,iris.feature_names.index('petal length (cm)')]\n",
+ "petal_width = iris.data[:, iris.feature_names.index('petal width (cm)')]\n",
+ "\n",
+ "IrisX = np.array(iris.data.T)\n",
+ "IrisX = IrisX[:, iris.target!=0]\n",
+ "\n",
+ "IrisX2F = np.vstack([petal_length, petal_width])\n",
+ "IrisX2F = IrisX2F[:, iris.target!=0]\n",
+ "\n",
+ "# Set versicolor=0 and virginia=1\n",
+ "IrisY = (iris.target[iris.target!=0]-1).reshape(1,-1).astype(np.float64)\n",
+ "\n",
+ "plt.scatter(IrisX2F[0,:], IrisX2F[1,:], c=IrisY.ravel(),\n",
+ " cmap='spring', edgecolors='k')\n",
+ "plt.xlabel('petal_length')\n",
+ "plt.ylabel('petal_width')"
+ ],
+ "execution_count": 0,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "text": [
+ "Features: ['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
+ "Targets: ['setosa' 'versicolor' 'virginica']\n"
+ ],
+ "name": "stdout"
+ },
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'petal_width')"
+ ]
+ },
+ "metadata": {
+ "tags": []
+ },
+ "execution_count": 2
+ },
+ {
+ "output_type": "display_data",
+ "data": {
+ "image/png": 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IKTExEdOnT8T06WOwYMFn1RdN/Gfx4sXo1s0QnTtrY9SoAOTm5krdd15eHr75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\nEMaTyUAIIYRMBkIIIWQyEEIIgUwGQgghkMlACCEEMhkIAdx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+ "