492 lines
89 KiB
Text
492 lines
89 KiB
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"cells": [
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Coverage plots"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"from matplotlib import pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let us consider the following function which applies a linear model to the given data. \n",
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"Specifically, given a \"model\" vector containing the model coefficients $(a,b)$ and a $n \\times 2$ \"data\" matrix containing the data points to be classified, the function outputs a vector $\\mathbf{z}$, $|\\mathbf{z}| = n$ of booleans where $z_i$ is `True` if $a \\cdot x_{i,1} + b \\cdot x_{i,2} \\geq 0$, it is `False` otherwise."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"def apply_linear_model(model, data):\n",
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" return np.dot(data, np.transpose(model)) > 0"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Let us define `data` by generating $1000$ points drawn uniformly from $\\mathcal{X} = [-100,100]^2$."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"C:\\Users\\galat\\.conda\\envs\\aaut\\lib\\site-packages\\ipykernel_launcher.py:1: DeprecationWarning: This function is deprecated. Please call randint(-100, 100 + 1) instead\n",
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" \"\"\"Entry point for launching an IPython kernel.\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"array([[ -8, -49],\n",
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" [-39, 7],\n",
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" [ 48, 95],\n",
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" ...,\n",
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" [ -2, 7],\n",
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" [ 35, 72],\n",
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" [ 28, -5]])"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"data = np.random.random_integers(-100,100,[1000,2])\n",
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"data"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"and let target_labels be the labeling output by applying `apply_linear_model` with our target model: $4x -y > 0$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {},
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"outputs": [],
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"source": [
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"target_model = [4.,-1.]\n",
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"target_labels = apply_linear_model(target_model, data)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"By using matplotlib.pyplot module it is easy to plot the generated points onto a 2D plot:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.collections.PathCollection at 0x1f28b3e7788>"
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]
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},
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"execution_count": 10,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"colors = ['r' if l else 'b' for l in target_labels]\n",
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"plt.scatter(data[:,0], data[:,1], color=colors)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Finally let us now generate at random 100 linear models with coefficients in $[-5,5]$:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[-2.47471947, -3.5581708 ],\n",
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" [ 1.59686449, 1.71893864],\n",
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" [ 3.03294605, 4.57263288],\n",
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" [ 4.3603124 , -1.19540694],\n",
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" [ 1.21976183, 4.09720458],\n",
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" [ 0.42857121, 3.20268614],\n",
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" [-2.15226242, 2.96225011],\n",
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" [ 0.65773544, -2.54676899],\n",
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" [-2.79365386, -0.78924628],\n",
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" [ 2.90156232, -3.31703275],\n",
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" [-0.9849533 , 0.62170036],\n",
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" [-4.0396815 , 4.36277095],\n",
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" [ 1.34248188, 1.77758129],\n",
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" [ 0.38419206, 0.17314725],\n",
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" [-2.04665134, 2.10337995],\n",
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" [-2.50975771, 3.65315789],\n",
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" [ 2.004511 , 2.73918509],\n",
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" [ 4.15805913, -4.96182686],\n",
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" [ 4.51026319, -1.78429829],\n",
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" [-3.31973604, 3.43442154],\n",
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" [ 3.52497128, 0.85718807],\n",
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" [-3.06163513, -0.86712587],\n",
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" [-4.18156322, -2.21571818],\n",
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" [-4.59703113, 4.4801163 ],\n",
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" [-2.65368229, 4.37023623],\n",
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" [ 3.90990454, -2.1420455 ],\n",
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" [-3.24752094, -0.40639067],\n",
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" [ 0.10755654, 0.48649316],\n",
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" [ 2.26731088, 4.73364989],\n",
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" [-4.22292673, -0.21284274],\n",
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" [-4.66592874, -2.79620572],\n",
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" [ 4.63716865, 0.87182744],\n",
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" [-4.32406367, 1.10060443],\n",
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" [-0.45847 , 0.70180339],\n",
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" [ 3.22176576, -2.5364163 ],\n",
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" [ 3.80797501, 2.35293627],\n",
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" [ 3.36332162, -3.79299501],\n",
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" [ 3.99625756, 2.36135165],\n",
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" [ 1.20216525, -1.23827528],\n",
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" [-3.09694201, 3.9600678 ],\n",
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" [-0.64611333, 2.09501923],\n",
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" [ 0.99744202, 1.49993523],\n",
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" [-3.36391051, -3.90944487],\n",
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" [-3.58672509, -4.1088498 ],\n",
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" [ 3.46090243, 0.02661214],\n",
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" [-1.49631605, -2.28424324],\n",
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" [ 1.1089388 , -1.73806817],\n",
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" [ 3.30150146, -3.13759682],\n",
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" [-4.51293209, 4.08479726],\n",
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" [-4.09529163, 4.28334043],\n",
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" [-0.7227784 , 0.85683098],\n",
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" [-3.54236195, -4.37842609],\n",
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" [-1.67857772, 1.18420411],\n",
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" [-2.06131565, -3.81118901],\n",
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" [-0.94505145, -0.79410051],\n",
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" [-1.58100698, -4.40226088],\n",
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" [ 3.49623546, 0.98568917],\n",
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" [-4.7875311 , 2.46132599],\n",
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" [-0.90714606, -4.03370503],\n",
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" [-4.04974727, 1.89697029],\n",
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" [ 2.3912763 , 4.43535836],\n",
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" [ 1.91805621, 3.10706978],\n",
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" [ 2.7870542 , -4.76785357],\n",
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" [-4.83230806, 0.68706866],\n",
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" [ 4.21091682, 2.69235722],\n",
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" [ 4.92125435, 1.67552945],\n",
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|
|
" [-4.17809823, -3.0655279 ],\n",
|
||
|
|
" [ 1.34522792, -2.11218453],\n",
|
||
|
|
" [-2.82712946, -3.84431909],\n",
|
||
|
|
" [ 4.32983019, -0.67660343],\n",
|
||
|
|
" [ 3.69650316, -2.09533608],\n",
|
||
|
|
" [-2.46459767, -2.78730998],\n",
|
||
|
|
" [-0.12911643, 3.03464722],\n",
|
||
|
|
" [-0.54414414, -4.24446833],\n",
|
||
|
|
" [ 0.70841166, 0.82220448],\n",
|
||
|
|
" [-1.21624127, 2.67030582],\n",
|
||
|
|
" [-4.4511487 , -0.18157221],\n",
|
||
|
|
" [ 0.54850624, 3.80806515],\n",
|
||
|
|
" [ 0.41580003, 2.39770318],\n",
|
||
|
|
" [ 0.78040198, -2.27920522],\n",
|
||
|
|
" [-0.98993749, -4.66406869],\n",
|
||
|
|
" [ 2.67850165, 1.2013196 ],\n",
|
||
|
|
" [-0.85139301, -3.08916589],\n",
|
||
|
|
" [ 2.00142468, -3.62142984],\n",
|
||
|
|
" [-0.08136816, 1.76822154],\n",
|
||
|
|
" [-4.92951601, 0.11860089],\n",
|
||
|
|
" [-2.36011692, 2.25618495],\n",
|
||
|
|
" [ 1.60982063, -0.44192244],\n",
|
||
|
|
" [-2.54853258, -2.17737341],\n",
|
||
|
|
" [-1.31205757, 2.17528846],\n",
|
||
|
|
" [ 4.9863995 , -3.99442219],\n",
|
||
|
|
" [-1.87206871, -2.53218008],\n",
|
||
|
|
" [ 2.35107436, -4.08841325],\n",
|
||
|
|
" [ 3.5602568 , -2.39084033],\n",
|
||
|
|
" [-1.67264783, -2.78819786],\n",
|
||
|
|
" [ 2.14307079, -1.80908234],\n",
|
||
|
|
" [-2.47515458, 2.07939336],\n",
|
||
|
|
" [ 0.34640981, 0.10794752],\n",
|
||
|
|
" [ 1.0289358 , -1.10048266],\n",
|
||
|
|
" [-4.92276006, 0.74592667]])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"models = (np.random.rand(100,2) - 0.5) * 10\n",
|
||
|
|
"models"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Exercise"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"1. Write a function that, taken two list of labellings build the corresponding confusion matrix [[1](#hint1)];\n",
|
||
|
|
"1. For each model in `models` plot the [FP,TP] pairs on a scatter plot;\n",
|
||
|
|
"1. Just looking at the plot: which is the best model in the pool?\n",
|
||
|
|
"1. Find the model with the best accuracy [[2](#hint2)] and compare it with the target model, is it close? Is it the model you would have picked up visually from the scatter plot?\n",
|
||
|
|
"1. If everything is ok, you should have found a pretty good model for our data. It fits the data quite well and it is quite close to the target model. Did you expect this? If so, why? If not so, why not?\n",
|
||
|
|
"\n",
|
||
|
|
"<a name=\"hint1\">Hint 1:</a> it may be helpful to have a way to map TRUE to 0, FALSE to 1 and to use these values as indices in the confusion matrix. \n",
|
||
|
|
"\n",
|
||
|
|
"<a name=\"hint2\">Hint 2:</a> one way to proceed is to build a function `accuracy`, use the `map` function to calculate the accuracies of all the models, and then apply the `numpy.argmax` to retrieve the index of the best model."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Es. 1"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 28,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def build_confusion_matrix(labels1, labels2):\n",
|
||
|
|
" confusion_matrix = np.zeros((2,2))\n",
|
||
|
|
" for i in range(len(labels1)):\n",
|
||
|
|
" confusion_matrix[1 - labels1[i], 1 - labels2[i]] += 1\n",
|
||
|
|
" return confusion_matrix"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 31,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"[[202. 281.]\n",
|
||
|
|
" [310. 207.]]\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"print(build_confusion_matrix(apply_linear_model(target_model, data), apply_linear_model(models[0], data)))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Es. 2\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 43,
|
||
|
|
"metadata": {
|
||
|
|
"scrolled": true
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.collections.PathCollection at 0x1f28b4e2508>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 43,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fp = []\n",
|
||
|
|
"tp = []\n",
|
||
|
|
"\n",
|
||
|
|
"for model in models:\n",
|
||
|
|
" confusion = build_confusion_matrix(target_labels, apply_linear_model(model, data))\n",
|
||
|
|
" fp.append(confusion[1,0])\n",
|
||
|
|
" tp.append(confusion[0,0])\n",
|
||
|
|
"plt.scatter(fp, tp)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Es. 3"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Il modello migliore è quello in alto a sinistra (max TP/FP)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 51,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"array([ 4.3603124 , -1.19540694])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 51,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"models[np.argmax([t / f for t, f in zip(tp, fp)])]"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Es. 4\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 39,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def accuracy(tp, tn, total):\n",
|
||
|
|
" return (tp + tn) / total"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 53,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"model: [ 4.3603124 -1.19540694] accuracy: 0.995\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"accuracies = []\n",
|
||
|
|
"\n",
|
||
|
|
"for model in models:\n",
|
||
|
|
" confusion = build_confusion_matrix(target_labels, apply_linear_model(model, data))\n",
|
||
|
|
" accuracies.append(accuracy(confusion[0,0], confusion[1,1], 1000))\n",
|
||
|
|
"\n",
|
||
|
|
"print(\"model: \", models[np.argmax(accuracies)], \" accuracy: \", accuracies[np.argmax(accuracies)])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Il modello è lo stesso predetto dalla plot"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Es. 5"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Mi aspettavo di trovare un modello con un'accuracy alta ma non come quella trovata (0.995), perchè su 100 modelli, con due variabili comprese tra 5 e -5, generati con una funzione random uniforme mi aspetto dei valori vicini a quelli target."
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"anaconda-cloud": {},
|
||
|
|
"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": "3.7.7"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 1
|
||
|
|
}
|