UniTO/anno3/apprendimento_automatico/esercizi/1/.ipynb_checkpoints/coverage_plots-checkpoint.ipynb
Francesco Mecca 4af9518c85 teoria
2020-06-23 21:53:50 +02:00

317 lines
75 KiB
Text

{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Coverage plots"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us consider the following function which applies a linear model to the given data. \n",
"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."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def apply_linear_model(model, data):\n",
" return np.dot(data, np.transpose(model)) > 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us define `data` by generating $1000$ points drawn uniformly from $\\mathcal{X} = [-100,100]^2$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/user/.local/lib/python3.7/site-packages/ipykernel_launcher.py:1: DeprecationWarning: This function is deprecated. Please call randint(-100, 100 + 1) instead\n",
" \"\"\"Entry point for launching an IPython kernel.\n"
]
},
{
"data": {
"text/plain": [
"array([[-35, -99],\n",
" [ 46, -79],\n",
" [-42, -4],\n",
" ...,\n",
" [-15, 66],\n",
" [-79, -33],\n",
" [-61, 50]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = np.random.random_integers(-100,100,[1000,2])\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and let target_labels be the labeling output by applying `apply_linear_model` with our target model: $4x -y > 0$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"target_model = [4.,-1.]\n",
"target_labels = apply_linear_model(target_model, data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By using matplotlib.pyplot module it is easy to plot the generated points onto a 2D plot:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x7f756cd35510>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"colors = ['r' if l else 'b' for l in target_labels]\n",
"plt.scatter(data[:,0], data[:,1], color=colors)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally let us now generate at random 100 linear models with coefficients in $[-5,5]$:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-2.39430024, 4.82135902],\n",
" [ 1.05475945, 0.56506096],\n",
" [ 4.33381523, -2.79295785],\n",
" [ 1.40967652, 0.23582632],\n",
" [-1.86874245, -1.94575582],\n",
" [ 3.49504802, 4.46631455],\n",
" [ 3.73910681, -1.20697797],\n",
" [-0.03709135, -2.10326967],\n",
" [ 3.45305859, -4.34793504],\n",
" [ 3.03208277, 3.74285745],\n",
" [ 1.5465798 , 3.50062332],\n",
" [ 2.2422928 , 1.0046194 ],\n",
" [ 3.03217811, -0.82377688],\n",
" [-4.53947789, 3.70865422],\n",
" [-3.25118429, -1.72249205],\n",
" [ 2.26245853, -4.28364219],\n",
" [ 4.94378489, 4.28009147],\n",
" [-4.69232032, -0.58696177],\n",
" [-4.89189465, 0.39817474],\n",
" [ 3.76075994, 0.31297542],\n",
" [-3.16975246, 4.25281293],\n",
" [ 1.17872066, -1.09249838],\n",
" [-1.95646119, 2.20465081],\n",
" [ 4.27728295, 1.53512327],\n",
" [ 0.05835676, 1.70723529],\n",
" [ 2.60309217, -0.45217353],\n",
" [-0.17392586, -0.27012307],\n",
" [-2.05830803, -2.06266253],\n",
" [ 3.9529746 , 3.42138605],\n",
" [-3.79939733, -0.21979507],\n",
" [-2.29925996, -3.34504866],\n",
" [ 2.82327177, 3.36741078],\n",
" [-4.36398037, 4.90756469],\n",
" [ 0.42676851, -0.06020275],\n",
" [ 3.17293673, 4.77796787],\n",
" [-2.94774218, 3.9356928 ],\n",
" [ 2.59485714, -4.80307843],\n",
" [ 2.36994981, -0.95851792],\n",
" [ 4.88820476, -1.35503075],\n",
" [ 0.94150698, 3.12143851],\n",
" [ 0.33869197, -4.67364091],\n",
" [-2.72092697, -0.16985042],\n",
" [-1.95475038, 4.82283169],\n",
" [ 2.45764492, 4.77215002],\n",
" [ 0.05377156, -2.35640137],\n",
" [ 4.35117408, 1.90279533],\n",
" [ 4.51945998, -3.4003176 ],\n",
" [ 1.8446393 , -3.17348665],\n",
" [-3.39891706, -4.60282665],\n",
" [-2.73001814, -2.3755611 ],\n",
" [ 3.70599397, -4.46493656],\n",
" [ 2.21630505, 4.14085098],\n",
" [-3.41340833, 3.44627966],\n",
" [-4.60977981, 3.96608819],\n",
" [-3.12045006, -2.6109695 ],\n",
" [-1.09736041, -1.80670439],\n",
" [-0.01733633, -1.72932242],\n",
" [-3.8893666 , -0.23795606],\n",
" [ 4.32262985, -2.60558145],\n",
" [-4.94835985, 4.9499789 ],\n",
" [ 4.83372946, 3.18143365],\n",
" [-2.97234861, 3.43734029],\n",
" [ 4.13213153, -4.01988738],\n",
" [ 2.50430662, -3.55060295],\n",
" [-1.13021843, -2.66490227],\n",
" [-3.52868187, 3.08060977],\n",
" [-4.60059847, 0.07549374],\n",
" [ 3.02082047, 4.1033937 ],\n",
" [ 3.17455034, -3.3296469 ],\n",
" [ 1.5874334 , -3.8626682 ],\n",
" [-4.83005533, 1.64085882],\n",
" [-3.67705824, -3.7420375 ],\n",
" [ 3.37141151, 4.31804914],\n",
" [-2.32695571, -1.65021845],\n",
" [-4.93262416, 0.30335477],\n",
" [ 3.09178415, -3.5606033 ],\n",
" [-0.99362255, 4.12845851],\n",
" [-4.93026694, 2.8832776 ],\n",
" [ 4.76078721, 4.52391074],\n",
" [-4.02330413, -3.919773 ],\n",
" [-1.2605584 , 2.07658856],\n",
" [ 4.76819758, -1.74330259],\n",
" [-3.27001856, 0.52159983],\n",
" [ 4.28932043, -3.4243422 ],\n",
" [-0.29372312, -1.51538405],\n",
" [ 2.46437149, -3.73790856],\n",
" [ 3.25584766, 4.32526613],\n",
" [ 4.41084634, -2.65951582],\n",
" [ 2.05089111, -2.77049322],\n",
" [-4.64295989, 1.17909785],\n",
" [ 0.73985808, 1.09177819],\n",
" [-3.08619219, -2.23259432],\n",
" [-2.21523998, -4.29746264],\n",
" [ 2.93142476, -3.074807 ],\n",
" [-2.23827727, 4.12204265],\n",
" [-2.88171529, -0.87372322],\n",
" [ 1.48659654, 3.79868869],\n",
" [-2.57574569, 3.29476101],\n",
" [-2.86541983, 4.08032984],\n",
" [-0.36862476, 3.67346937]])"
]
},
"execution_count": 6,
"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": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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
}