572 lines
17 KiB
Plaintext
572 lines
17 KiB
Plaintext
{
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"cells": [
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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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"**Fundamentals of Machine Learning**"
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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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"collapsed": false,
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"slideshow": {
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"slide_type": "-"
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}
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},
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"outputs": [],
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"source": [
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"from __future__ import division, print_function, unicode_literals\n",
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"\n",
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"import os\n",
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"\n",
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"%matplotlib inline\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"plt.rcParams['axes.labelsize'] = 14\n",
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"plt.rcParams['xtick.labelsize'] = 12\n",
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"plt.rcParams['ytick.labelsize'] = 12\n",
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"\n",
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"PROJECT_ROOT_DIR = \".\"\n",
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"CHAPTER_ID = \"fundamentals\"\n",
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"\n",
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"def save_fig(fig_id):\n",
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" path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
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" print(\"Saving figure\", fig_id)\n",
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" plt.tight_layout()\n",
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" plt.savefig(path, format='png', dpi=300)"
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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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"## Load and prepare Life satisfaction data"
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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": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"\n",
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"# Download CSV from http://stats.oecd.org/index.aspx?DataSetCode=BLI\n",
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"datapath = \"datasets/lifesat/\"\n",
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"\n",
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"oecd_bli = pd.read_csv(datapath+\"oecd_bli_2015.csv\", thousands=',')\n",
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"oecd_bli = oecd_bli[oecd_bli[\"INEQUALITY\"]==\"TOT\"]\n",
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"oecd_bli = oecd_bli.pivot(index=\"Country\", columns=\"Indicator\", values=\"Value\")\n",
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"oecd_bli.head(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": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"oecd_bli[\"Life satisfaction\"].head()"
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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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"## Load and prepare GDP per capita data"
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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": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# Download data from http://goo.gl/j1MSKe (=> imf.org)\n",
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"gdp_per_capita = pd.read_csv(datapath+\"gdp_per_capita.csv\", thousands=',', delimiter='\\t',\n",
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" encoding='latin1', na_values=\"n/a\")\n",
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"gdp_per_capita.rename(columns={\"2015\": \"GDP per capita\"}, inplace=True)\n",
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"gdp_per_capita.set_index(\"Country\", inplace=True)\n",
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"gdp_per_capita.head(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": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"full_country_stats = pd.merge(left=oecd_bli, right=gdp_per_capita, left_index=True, right_index=True)\n",
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"full_country_stats.sort_values(by=\"GDP per capita\", inplace=\"True\")\n",
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"full_country_stats"
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"full_country_stats[[\"GDP per capita\", 'Life satisfaction']].loc[\"United States\"]"
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"remove_indices = [0, 1, 6, 8, 33, 34, 35]\n",
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"keep_indices = list(set(range(36)) - set(remove_indices))\n",
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"\n",
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"sample_data = full_country_stats[[\"GDP per capita\", 'Life satisfaction']].iloc[keep_indices]\n",
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"missing_data = full_country_stats[[\"GDP per capita\", 'Life satisfaction']].iloc[remove_indices]"
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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": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"sample_data.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction', figsize=(5,3))\n",
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"plt.axis([0, 60000, 0, 10])\n",
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"position_text = {\n",
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" \"Hungary\": (5000, 1),\n",
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" \"Korea\": (18000, 1.7),\n",
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" \"France\": (29000, 2.4),\n",
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" \"Australia\": (40000, 3.1),\n",
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" \"United States\": (52000, 3.8),\n",
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"}\n",
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"for country, pos_text in position_text.items():\n",
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" pos_data_x, pos_data_y = sample_data.loc[country]\n",
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" country = \"U.S.\" if country == \"United States\" else country\n",
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" plt.annotate(country, xy=(pos_data_x, pos_data_y), xytext=pos_text,\n",
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" arrowprops=dict(facecolor='black', width=0.5, shrink=0.1, headwidth=5))\n",
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" plt.plot(pos_data_x, pos_data_y, \"ro\")\n",
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"save_fig('money_happy_scatterplot')\n",
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"plt.show()"
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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": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"sample_data.loc[list(position_text.keys())]"
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"\n",
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"sample_data.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction', figsize=(5,3))\n",
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"plt.axis([0, 60000, 0, 10])\n",
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"X=np.linspace(0, 60000, 1000)\n",
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"plt.plot(X, 2*X/100000, \"r\")\n",
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"plt.text(40000, 2.7, r\"$\\theta_0 = 0$\", fontsize=14, color=\"r\")\n",
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"plt.text(40000, 1.8, r\"$\\theta_1 = 2 \\times 10^{-5}$\", fontsize=14, color=\"r\")\n",
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"plt.plot(X, 8 - 5*X/100000, \"g\")\n",
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"plt.text(5000, 9.1, r\"$\\theta_0 = 8$\", fontsize=14, color=\"g\")\n",
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"plt.text(5000, 8.2, r\"$\\theta_1 = -5 \\times 10^{-5}$\", fontsize=14, color=\"g\")\n",
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"plt.plot(X, 4 + 5*X/100000, \"b\")\n",
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"plt.text(5000, 3.5, r\"$\\theta_0 = 4$\", fontsize=14, color=\"b\")\n",
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"plt.text(5000, 2.6, r\"$\\theta_1 = 5 \\times 10^{-5}$\", fontsize=14, color=\"b\")\n",
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"save_fig('tweaking_model_params_plot')\n",
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"plt.show()"
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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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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from sklearn import linear_model\n",
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"lin1 = linear_model.LinearRegression()\n",
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"Xsample = np.c_[sample_data[\"GDP per capita\"]]\n",
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"ysample = np.c_[sample_data[\"Life satisfaction\"]]\n",
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"lin1.fit(Xsample, ysample)\n",
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"t0, t1 = lin1.intercept_[0], lin1.coef_[0][0]\n",
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"t0, t1"
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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": 12,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"sample_data.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction', figsize=(5,3))\n",
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"plt.axis([0, 60000, 0, 10])\n",
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"X=np.linspace(0, 60000, 1000)\n",
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"plt.plot(X, t0 + t1*X, \"b\")\n",
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"plt.text(5000, 3.1, r\"$\\theta_0 = 4.85$\", fontsize=14, color=\"b\")\n",
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"plt.text(5000, 2.2, r\"$\\theta_1 = 4.91 \\times 10^{-5}$\", fontsize=14, color=\"b\")\n",
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"save_fig('best_fit_model_plot')\n",
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"plt.show()\n"
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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": 13,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"cyprus_gdp_per_capita = gdp_per_capita.loc[\"Cyprus\"][\"GDP per capita\"]\n",
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"print(cyprus_gdp_per_capita)\n",
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"cyprus_predicted_life_satisfaction = lin1.predict(cyprus_gdp_per_capita)[0][0]\n",
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"cyprus_predicted_life_satisfaction"
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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": 14,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"sample_data.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction', figsize=(5,3), s=1)\n",
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"X=np.linspace(0, 60000, 1000)\n",
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"plt.plot(X, t0 + t1*X, \"b\")\n",
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"plt.axis([0, 60000, 0, 10])\n",
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"plt.text(5000, 7.5, r\"$\\theta_0 = 4.85$\", fontsize=14, color=\"b\")\n",
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"plt.text(5000, 6.6, r\"$\\theta_1 = 4.91 \\times 10^{-5}$\", fontsize=14, color=\"b\")\n",
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"plt.plot([cyprus_gdp_per_capita, cyprus_gdp_per_capita], [0, cyprus_predicted_life_satisfaction], \"r--\")\n",
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"plt.text(25000, 5.0, r\"Prediction = 5.96\", fontsize=14, color=\"b\")\n",
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"plt.plot(cyprus_gdp_per_capita, cyprus_predicted_life_satisfaction, \"ro\")\n",
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"save_fig('cyprus_prediction_plot')\n",
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"plt.show()"
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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": 15,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"sample_data[7:10]"
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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": 16,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"(5.1+5.7+6.5)/3"
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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": 17,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"backup = oecd_bli, gdp_per_capita\n",
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"\n",
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"def prepare_country_stats(oecd_bli, gdp_per_capita):\n",
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" return sample_data\n",
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"\n",
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"# Code example\n",
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"########################################################################\n",
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"import sklearn\n",
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"import numpy as np\n",
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"import pandas as pd\n",
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"\n",
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"# Load the data\n",
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"oecd_bli = pd.read_csv(datapath+\"oecd_bli_2015.csv\", thousands=',')\n",
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"gdp_per_capita = pd.read_csv(datapath+\"gdp_per_capita.csv\", thousands=',',delimiter='\\t',\n",
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" encoding='latin1', na_values=\"n/a\")\n",
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"\n",
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"# Prepare the data\n",
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"country_stats = prepare_country_stats(oecd_bli, gdp_per_capita)\n",
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"X = np.c_[country_stats[\"GDP per capita\"]]\n",
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"y = np.c_[country_stats[\"Life satisfaction\"]]\n",
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"\n",
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"# Visualize the data\n",
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"country_stats.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction')\n",
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"plt.show()\n",
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"\n",
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"# Select a linear model\n",
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"lin_reg_model = sklearn.linear_model.LinearRegression()\n",
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"\n",
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"# Train the model\n",
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"lin_reg_model.fit(X, y)\n",
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"\n",
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"# Make a prediction for Cyprus\n",
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"X_new = [[22587]] # Cyprus' GDP per capita\n",
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"print(lin_reg_model.predict(X_new)) # outputs [[ 5.96242338]]\n",
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"########################################################################\n",
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"\n",
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"oecd_bli, gdp_per_capita = backup"
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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": 18,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"missing_data"
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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": 19,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"position_text2 = {\n",
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" \"Brazil\": (1000, 9.0),\n",
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" \"Mexico\": (11000, 9.0),\n",
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" \"Chile\": (25000, 9.0),\n",
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" \"Czech Republic\": (35000, 9.0),\n",
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" \"Norway\": (60000, 3),\n",
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" \"Switzerland\": (72000, 3.0),\n",
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" \"Luxembourg\": (90000, 3.0),\n",
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"}"
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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": 20,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"sample_data.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction', figsize=(8,3))\n",
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"plt.axis([0, 110000, 0, 10])\n",
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"\n",
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"for country, pos_text in position_text2.items():\n",
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" pos_data_x, pos_data_y = missing_data.loc[country]\n",
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" plt.annotate(country, xy=(pos_data_x, pos_data_y), xytext=pos_text,\n",
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" arrowprops=dict(facecolor='black', width=0.5, shrink=0.1, headwidth=5))\n",
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" plt.plot(pos_data_x, pos_data_y, \"rs\")\n",
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"\n",
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"X=np.linspace(0, 110000, 1000)\n",
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"plt.plot(X, t0 + t1*X, \"b:\")\n",
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"\n",
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"lin_reg_full = linear_model.LinearRegression()\n",
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"Xfull = np.c_[full_country_stats[\"GDP per capita\"]]\n",
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"yfull = np.c_[full_country_stats[\"Life satisfaction\"]]\n",
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"lin_reg_full.fit(Xfull, yfull)\n",
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"\n",
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"t0full, t1full = lin_reg_full.intercept_[0], lin_reg_full.coef_[0][0]\n",
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"X = np.linspace(0, 110000, 1000)\n",
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"plt.plot(X, t0full + t1full * X, \"k\")\n",
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"\n",
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"save_fig('representative_training_data_scatterplot')\n",
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"plt.show()"
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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": 21,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"full_country_stats.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction', figsize=(8,3))\n",
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"plt.axis([0, 110000, 0, 10])\n",
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"\n",
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"from sklearn import preprocessing\n",
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"from sklearn import pipeline\n",
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"\n",
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"poly = preprocessing.PolynomialFeatures(degree=60, include_bias=False)\n",
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"scaler = preprocessing.StandardScaler()\n",
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"lin_reg2 = linear_model.LinearRegression()\n",
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"\n",
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"pipeline_reg = pipeline.Pipeline([('poly', poly), ('scal', scaler), ('lin', lin_reg2)])\n",
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"pipeline_reg.fit(Xfull, yfull)\n",
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"curve = pipeline_reg.predict(X[:, np.newaxis])\n",
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"plt.plot(X, curve)\n",
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"save_fig('overfitting_model_plot')\n",
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"plt.show()"
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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": 22,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"full_country_stats.loc[[c for c in full_country_stats.index if \"W\" in c.upper()]][\"Life satisfaction\"]"
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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": 23,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"gdp_per_capita.loc[[c for c in gdp_per_capita.index if \"W\" in c.upper()]].head()"
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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": 24,
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"metadata": {
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"collapsed": false
|
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},
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"outputs": [],
|
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"source": [
|
|
"plt.figure(figsize=(8,3))\n",
|
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"\n",
|
|
"plt.xlabel(\"GDP per capita\")\n",
|
|
"plt.ylabel('Life satisfaction')\n",
|
|
"\n",
|
|
"plt.plot(list(sample_data[\"GDP per capita\"]), list(sample_data[\"Life satisfaction\"]), \"bo\")\n",
|
|
"plt.plot(list(missing_data[\"GDP per capita\"]), list(missing_data[\"Life satisfaction\"]), \"rs\")\n",
|
|
"\n",
|
|
"X = np.linspace(0, 110000, 1000)\n",
|
|
"plt.plot(X, t0full + t1full * X, \"r--\", label=\"Linear model on all data\")\n",
|
|
"plt.plot(X, t0 + t1*X, \"b:\", label=\"Linear model on partial data\")\n",
|
|
"\n",
|
|
"ridge = linear_model.Ridge(alpha=10**9.5)\n",
|
|
"Xsample = np.c_[sample_data[\"GDP per capita\"]]\n",
|
|
"ysample = np.c_[sample_data[\"Life satisfaction\"]]\n",
|
|
"ridge.fit(Xsample, ysample)\n",
|
|
"t0ridge, t1ridge = ridge.intercept_[0], ridge.coef_[0][0]\n",
|
|
"plt.plot(X, t0ridge + t1ridge * X, \"b\", label=\"Regularized linear model on partial data\")\n",
|
|
"\n",
|
|
"plt.legend(loc=\"lower right\")\n",
|
|
"plt.axis([0, 110000, 0, 10])\n",
|
|
"save_fig('ridge_model_plot')\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"metadata": {
|
|
"collapsed": false
|
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},
|
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"outputs": [],
|
|
"source": [
|
|
"backup = oecd_bli, gdp_per_capita\n",
|
|
"\n",
|
|
"def prepare_country_stats(oecd_bli, gdp_per_capita):\n",
|
|
" return sample_data\n",
|
|
"\n",
|
|
"# Code example\n",
|
|
"########################################################################\n",
|
|
"from sklearn import neighbors\n",
|
|
"import numpy as np\n",
|
|
"import pandas as pd\n",
|
|
"\n",
|
|
"# Load the data\n",
|
|
"oecd_bli = pd.read_csv(datapath+\"oecd_bli_2015.csv\", thousands=',')\n",
|
|
"gdp_per_capita = pd.read_csv(datapath+\"gdp_per_capita.csv\", thousands=',',delimiter='\\t',\n",
|
|
" encoding='latin1', na_values=\"n/a\")\n",
|
|
"\n",
|
|
"# Prepare the data\n",
|
|
"country_stats = prepare_country_stats(oecd_bli, gdp_per_capita)\n",
|
|
"X = np.c_[country_stats[\"GDP per capita\"]]\n",
|
|
"y = np.c_[country_stats[\"Life satisfaction\"]]\n",
|
|
"\n",
|
|
"# Visualize the data\n",
|
|
"country_stats.plot(kind='scatter', x=\"GDP per capita\", y='Life satisfaction')\n",
|
|
"plt.show()\n",
|
|
"\n",
|
|
"# Select a k-neighboors regression model\n",
|
|
"k_neigh_reg_model = neighbors.KNeighborsRegressor(n_neighbors=3)\n",
|
|
"\n",
|
|
"# Train the model\n",
|
|
"k_neigh_reg_model.fit(X, y)\n",
|
|
"\n",
|
|
"# Make a prediction for Cyprus\n",
|
|
"X_new = [[22587]] # Cyprus' GDP per capita\n",
|
|
"print(lin_reg_model.predict(X_new)) # outputs [[ 5.96242338]]\n",
|
|
"########################################################################\n",
|
|
"\n",
|
|
"oecd_bli, gdp_per_capita = backup"
|
|
]
|
|
}
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|
],
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