mirror of
https://github.com/gsi-upm/sitc
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344 lines
56 KiB
Plaintext
344 lines
56 KiB
Plaintext
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{
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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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"![](images/EscUpmPolit_p.gif \"UPM\")"
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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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"# Course Notes for Learning Intelligent Systems"
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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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"Department of Telematic Engineering Systems, Universidad Politécnica de Madrid, © 2018 Óscar Araque"
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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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"## [Introduction to Machine Learning III](2_4_0_Intro_NN.ipynb)"
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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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"# MultiLayer Perceptron (MLP) applied to Regression"
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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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"In this notebook we are going to apply a MLP to a simple regression task: learning the Fresnel functions.\n",
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"\n",
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"\n",
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"Answer directly in your copy of the exercise and submit it as a moodle task."
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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 dataset"
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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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"ExecuteTime": {
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"end_time": "2017-03-27T19:44:45.989818",
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"start_time": "2017-03-27T19:44:45.624698"
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},
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"# Show plots in the notebooks\n",
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"%matplotlib inline"
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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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"ExecuteTime": {
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"end_time": "2017-03-27T19:44:47.582964",
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"start_time": "2017-03-27T19:44:46.844267"
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}
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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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"import matplotlib.pyplot as plt\n",
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"import seaborn as sns\n",
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"sns.set(color_codes=True)\n",
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"\n",
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"# function generator\n",
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"from scipy.special import fresnel"
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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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"Change this variables to change the train and test dataset."
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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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"ExecuteTime": {
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"end_time": "2017-03-27T19:44:49.811655",
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"start_time": "2017-03-27T19:44:49.805379"
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},
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"# variables to change\n",
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"\n",
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"n_examples = 500\n",
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"x_min = 0\n",
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"x_max = 3\n",
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"\n",
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"fresnel_func = 0 # can be 0,1"
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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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"ExecuteTime": {
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"end_time": "2017-03-27T19:45:21.738411",
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"start_time": "2017-03-27T19:45:21.489043"
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}
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},
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"outputs": [
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{
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"data": {
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAAegAAAFgCAYAAABws+q5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nz7+7wIJVE5G1DRnQgiD
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"text/plain": [
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"<matplotlib.figure.Figure at 0x7fad88a8aa58>"
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]
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},
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"metadata": {},
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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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"# Generate dataset (do not change)\n",
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"x = np.linspace(x_min, x_max, num=n_examples)\n",
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"y = fresnel(x)[fresnel_func]\n",
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"\n",
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"X = x.reshape(-1,1)\n",
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"\n",
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"plt.plot(x, y)\n",
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"plt.title('Fresnel S function')\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": "markdown",
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"metadata": {},
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"source": [
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"## Make the MLP learn"
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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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"ExecuteTime": {
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"end_time": "2017-03-27T19:45:33.201217",
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"start_time": "2017-03-27T19:45:33.184488"
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},
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"# do not change\n",
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"\n",
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"from sklearn.model_selection import train_test_split\n",
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"from sklearn.metrics import r2_score\n",
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"from sklearn.neural_network import MLPRegressor\n",
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"\n",
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"# split the dataset\n",
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"X_train, X_test, y_train, y_test = \\\n",
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" train_test_split(X, y, test_size=0.3, random_state=42)"
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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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"Change the parameters of the MLPRegressor to generate a network that learns the function."
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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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"ExecuteTime": {
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"end_time": "2017-03-27T19:44:57.970215",
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"start_time": "2017-03-27T19:44:57.916064"
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"MLPRegressor(activation='relu', alpha=0.0001, batch_size='auto', beta_1=0.9,\n",
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" beta_2=0.999, early_stopping=False, epsilon=1e-08,\n",
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" hidden_layer_sizes=(100,), learning_rate='constant',\n",
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" learning_rate_init=0.001, max_iter=200, momentum=0.9,\n",
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" nesterovs_momentum=True, power_t=0.5, random_state=None,\n",
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" shuffle=True, solver='adam', tol=0.0001, validation_fraction=0.1,\n",
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" verbose=False, warm_start=False)"
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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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"# CHANGE THIS CODE TO MAKE THE MLP LEARN\n",
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"\n",
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"# train the network\n",
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"mlp = MLPRegressor()\n",
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"mlp.fit(X_train, y_train)"
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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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"In this next cell, we can see how the network approximates the original function. \n",
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"\n",
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"The R score (a regression metric) must be between 0.95 and 1."
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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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"ExecuteTime": {
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|
"end_time": "2017-03-27T19:45:44.523305",
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"start_time": "2017-03-27T19:45:44.221047"
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}
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},
|
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|
"outputs": [
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||
|
{
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|
"data": {
|
||
|
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|
||
|
"text/plain": [
|
||
|
"<matplotlib.figure.Figure at 0x7fadb8f2ee80>"
|
||
|
]
|
||
|
},
|
||
|
"metadata": {},
|
||
|
"output_type": "display_data"
|
||
|
},
|
||
|
{
|
||
|
"name": "stdout",
|
||
|
"output_type": "stream",
|
||
|
"text": [
|
||
|
"R score: 0.226100740276\n"
|
||
|
]
|
||
|
}
|
||
|
],
|
||
|
"source": [
|
||
|
"# do not change\n",
|
||
|
"\n",
|
||
|
"# predict from test\n",
|
||
|
"preds = mlp.predict(X_test)\n",
|
||
|
"\n",
|
||
|
"plt.plot(x, y)\n",
|
||
|
"plt.scatter(X_test, preds, color='g')\n",
|
||
|
"plt.show()\n",
|
||
|
"\n",
|
||
|
"print('R score:',r2_score(y_test, preds))"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "markdown",
|
||
|
"metadata": {},
|
||
|
"source": [
|
||
|
"# References"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "markdown",
|
||
|
"metadata": {},
|
||
|
"source": [
|
||
|
"* [MLP documentation](http://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPClassifier.html)\n"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "markdown",
|
||
|
"metadata": {},
|
||
|
"source": [
|
||
|
"## Licence"
|
||
|
]
|
||
|
},
|
||
|
{
|
||
|
"cell_type": "markdown",
|
||
|
"metadata": {},
|
||
|
"source": [
|
||
|
"The notebook is freely licensed under under the [Creative Commons Attribution Share-Alike license](https://creativecommons.org/licenses/by/2.0/). \n",
|
||
|
"\n",
|
||
|
"© 2018 Óscar Araque, Universidad Politécnica de Madrid."
|
||
|
]
|
||
|
}
|
||
|
],
|
||
|
"metadata": {
|
||
|
"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": "3.5.5"
|
||
|
},
|
||
|
"latex_envs": {
|
||
|
"LaTeX_envs_menu_present": true,
|
||
|
"autocomplete": true,
|
||
|
"bibliofile": "biblio.bib",
|
||
|
"cite_by": "apalike",
|
||
|
"current_citInitial": 1,
|
||
|
"eqLabelWithNumbers": true,
|
||
|
"eqNumInitial": 1,
|
||
|
"hotkeys": {
|
||
|
"equation": "Ctrl-E",
|
||
|
"itemize": "Ctrl-I"
|
||
|
},
|
||
|
"labels_anchors": false,
|
||
|
"latex_user_defs": false,
|
||
|
"report_style_numbering": false,
|
||
|
"user_envs_cfg": false
|
||
|
}
|
||
|
},
|
||
|
"nbformat": 4,
|
||
|
"nbformat_minor": 1
|
||
|
}
|