ML_course/assignment 3/iml_assignment3_solved.ipynb
2023-05-16 15:02:37 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"source": [
"### Solution for Assignment 3 of the course \"Introduction to Machine Learning\" at the University of Leoben.\n",
"##### Author: Fotios Lygerakis\n",
"##### Semester: SS 2022/2023"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Create an abstract class “ContinuousDistribution”. The class must contain the following function definitions (not implementations)\n",
"* Data Import and Export using csv files.\n",
"* Computation of the mean based on the samples from the csv.\n",
"* Computation of the standard deviation based on the samples from the csv.\n",
"* Visualization of the distribution, the raw data or the generated samples.\n",
"* Generating/Drawing Samples from the distribution.\n"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 1,
"outputs": [],
"source": [
"import abc\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import multivariate_normal\n",
"from scipy.stats import beta"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class ContinuousDistribution(abc.ABC):\n",
" def __init__(self, name):\n",
" self.name = name\n",
"\n",
" @abc.abstractmethod\n",
" def import_data(self, filename):\n",
" pass\n",
"\n",
" @abc.abstractmethod\n",
" def export_data(self, filename):\n",
" pass\n",
"\n",
" @abc.abstractmethod\n",
" def compute_mean(self):\n",
" pass\n",
"\n",
" @abc.abstractmethod\n",
" def compute_std(self):\n",
" pass\n",
"\n",
" @abc.abstractmethod\n",
" def visualize(self):\n",
" pass\n",
"\n",
" @abc.abstractmethod\n",
" def generate_samples(self, n):\n",
" pass"
]
},
{
"cell_type": "markdown",
"source": [
"Implement a class “GaussDistribution”, which implements a multivariate Gaussian distribution (Equation 2.6 in the book).\n",
"* It is a child class of “ContinousDistribution”.\n",
"* Implement the functions defined in “ContinousDistribution”.\n",
"* Implement a constructor that optionally takes the dimension of the multivariate distribution.\n",
"* Implement a visualization for Multivariate Gaussians up to 3 dimensions.\n",
"* Find the empirical parameters of the distribution that created the samples in the MGD.csv file.\n",
"* Plot the samples of the MGD.csv file and the sample from the learned distribution in two subfigures.\n",
"* Generate visualizations of one- and two-dimensional Gaussians\n",
"\n",
"**The actual mean and covariance matrix of the MGD.csv file are [1, 0, 1] and [[1, 0.5, 0.5], [0.5, 1, 0.5], [0.5, 0.5, 1]] respectively.**\n"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 3,
"outputs": [],
"source": [
"class GaussDistribution(ContinuousDistribution):\n",
" def __init__(self, name, dim=1, mean=None, cov=None):\n",
" super().__init__(name)\n",
" self.dim = dim\n",
" self.mean = mean\n",
" self.cov = cov\n",
" self.data = None\n",
" self.sampled_data = None\n",
"\n",
" def import_data(self, filename):\n",
" self.data = pd.read_csv(filename)\n",
"\n",
" def export_data(self, filename):\n",
" self.data.to_csv(filename, index=False)\n",
"\n",
" def compute_mean(self):\n",
" return self.data.mean()\n",
"\n",
" def compute_std(self):\n",
" # return the covariance matrix if the distribution is multivariate\n",
" if self.dim > 1:\n",
" return self.data.cov()\n",
" return self.data.std()\n",
"\n",
" def visualize(self):\n",
" # Plot the samples of the MGD.csv file and the sample from the learned distribution in two separate sub-figures. add a title to each sub-figure.\n",
" if self.dim == 1:\n",
" data = self.sampled_data if self.sampled_data is not None else self.data\n",
" # plot the samples\n",
" plt.hist(data['x'], density=True, histtype='stepfilled', alpha=0.2)\n",
"\n",
" # create a grid of points\n",
" x = np.linspace(data['x'].min(), data['x'].max(), 100)\n",
"\n",
" # plot the pdf of the distribution\n",
" plt.plot(x, multivariate_normal.pdf(x, self.mean, self.cov))\n",
"\n",
" plt.show()\n",
" elif self.dim == 2:\n",
" data = self.sampled_data if self.sampled_data is not None else self.data\n",
" # create a grid of points\n",
" x = np.linspace(data['x'].min(), data['x'].max(), 100)\n",
" y = np.linspace(data['y'].min(), data['y'].max(), 100)\n",
"\n",
" # plot the pdf of the distribution\n",
" X, Y = np.meshgrid(x, y)\n",
" pos = np.empty(X.shape + (2,))\n",
" pos[:, :, 0] = X\n",
" pos[:, :, 1] = Y\n",
" rv = multivariate_normal(self.mean, self.cov)\n",
" plt.contourf(X, Y, rv.pdf(pos))\n",
" # plot the samples\n",
" plt.scatter(data['x'], data['y'], c='r', marker='o')\n",
" plt.show()\n",
" elif self.dim == 3:\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(121, projection='3d')\n",
" ax.set_title('Original Data')\n",
" ax.scatter(self.data['x'], self.data['y'], self.data['z'], c='r', marker='o')\n",
" ax.set_xlabel('X Label')\n",
" ax.set_ylabel('Y Label')\n",
" ax.set_zlabel('Z Label')\n",
" ax = fig.add_subplot(122, projection='3d')\n",
" ax.set_title('Sampled Data')\n",
" ax.scatter(self.sampled_data['x'], self.sampled_data['y'], self.sampled_data['z'], c='b', marker='o')\n",
" ax.set_xlabel('X Label')\n",
" ax.set_ylabel('Y Label')\n",
" ax.set_zlabel('Z Label')\n",
" plt.show()\n",
"\n",
" def generate_samples(self, n):\n",
" # generate samples from the distribution\n",
" if self.dim == 1:\n",
" self.sampled_data = pd.DataFrame(np.random.normal(self.mean, self.cov, n), columns=['x'])\n",
" elif self.dim == 2:\n",
" self.sampled_data = pd.DataFrame(np.random.multivariate_normal(self.mean, self.cov, n), columns=['x', 'y'])\n",
" elif self.dim == 3:\n",
" self.sampled_data = pd.DataFrame(np.random.multivariate_normal(self.mean, self.cov, n), columns=['x', 'y', 'z'])\n",
"\n",
" def fit(self):\n",
" self.mean = self.compute_mean()\n",
" self.cov = self.compute_std()"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Find the empirical parameters of the distribution that created the samples in the MGD.csv file."
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 4,
"outputs": [
{
"data": {
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"
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"x 0.984026\n",
"y 0.008833\n",
"z 0.860115\n",
"dtype: float64\n",
" x y z\n",
"x 0.957077 0.652484 0.563223\n",
"y 0.652484 1.420160 0.753830\n",
"z 0.563223 0.753830 1.255599\n"
]
}
],
"source": [
"gd = GaussDistribution('MGD', 3)\n",
"gd.import_data('MGD.csv')\n",
"gd.fit()\n",
"gd.generate_samples(100)\n",
"gd.visualize()\n",
"# print the mean and covariance matrix of the distribution\n",
"print(gd.mean)\n",
"print(gd.cov)"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Generate visualizations of one- and two-dimensional Gaussians using the above class."
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 5,
"outputs": [
{
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gd = GaussDistribution('1D', dim=1, mean=0, cov=1)\n",
"gd.generate_samples(100)\n",
"gd.visualize()\n",
"\n",
"gd = GaussDistribution('2D', dim=2, mean=[0, 0], cov=[[1, 0], [0, 1]])\n",
"gd.generate_samples(100)\n",
"gd.visualize()"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Implement a class “BetaDistribution” (Equation 2.5 in the book)\n",
"* It is also a child class of “ContinousDistribution”.\n",
"* Its purpose is to generate beta distributed samples and plot the distribution giving the parameters a and b.\n",
"* The contractor should take the parameters a and b as arguments.\n",
"* Implement a visualization for Beta distributions, including the mean and the standard deviation lines."
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 6,
"outputs": [],
"source": [
"class BetaDistribution(ContinuousDistribution):\n",
" def __init__(self, name, a, b):\n",
" super().__init__(name)\n",
" self.a = a\n",
" self.b = b\n",
" self.data = None\n",
" self.sampled_data = None\n",
"\n",
" def import_data(self, filename):\n",
" pass\n",
"\n",
" def export_data(self, filename):\n",
" self.sampled_data.to_csv(filename, index=False)\n",
"\n",
" def compute_mean(self):\n",
" pass\n",
"\n",
" def compute_std(self):\n",
" pass\n",
"\n",
" def visualize(self):\n",
" # Plot the distribution of the beta distribution\n",
" x = np.linspace(0, 1, 100)\n",
" y = beta.pdf(x, self.a, self.b)\n",
" plt.plot(x, y)\n",
" plt.title('Beta Distribution with a = ' + str(self.a) + ' and b = ' + str(self.b))\n",
" plt.xlabel('x')\n",
" plt.ylabel('y')\n",
" plt.show()\n",
"\n",
" def generate_samples(self, n):\n",
" self.sampled_data = pd.DataFrame(np.random.beta(self.a, self.b, n), columns=['x'])"
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "markdown",
"source": [
"Generate visualizations of Beta distributions using the above class."
],
"metadata": {
"collapsed": false
}
},
{
"cell_type": "code",
"execution_count": 7,
"outputs": [
{
"data": {
"text/plain": "<Figure size 640x480 with 1 Axes>",
"image/png": 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"
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bd = BetaDistribution('Beta', 2, 5)\n",
"bd.generate_samples(100)\n",
"bd.visualize()"
],
"metadata": {
"collapsed": false
}
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
}
},
"nbformat": 4,
"nbformat_minor": 0
}