Morten Hjorth-Jensen
3106 lines
767 KiB
Plaintext
3106 lines
767 KiB
Plaintext
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"<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
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"doconce format html week48.do.txt --no_mako -->\n",
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"<!-- dom:TITLE: Week 48: Gradient boosting and summary of course -->"
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"# Week 48: Gradient boosting and summary of course\n",
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"**Morten Hjorth-Jensen**, Department of Physics and Center for Computing in Science Education, University of Oslo, Norway\n",
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"\n",
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"Date: **Nov 24, 2024**\n",
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"\n",
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"Copyright 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license"
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"source": [
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"## Overview of week 48"
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"## Lecture Monday, November 25\n",
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"**Plans for the lecture Monday 25 November, with video suggestions etc.**\n",
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"\n",
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"1. Boosting and gradient boosting and ensemble models\n",
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"\n",
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"2. Summary of course\n",
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"\n",
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"3. Readings and Videos:\n",
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"\n",
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"a. These lecture notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/pub/week48/ipynb/week48.ipynb>\n",
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"\n",
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"b. See also lecture notes from week 47 at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/pub/week47/ipynb/week47.ipynb>. The lecture on Monday starts with a repetition on AdaBoost before we move over to gradient boosting with examples\n",
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"<!-- o Video of lecture at <https://youtu.be/RIHzmLv05DA> -->\n",
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"<!-- o Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesNovember25.pdf> -->\n",
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"\n",
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"c. Video on Decision trees <https://www.youtube.com/watch?v=RmajweUFKvM&ab_channel=Simplilearn>\n",
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"\n",
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"d. Video on boosting methods <https://www.youtube.com/watch?v=wPqtzj5VZus&ab_channel=H2O.ai>\n",
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"\n",
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"e. Video on AdaBoost <https://www.youtube.com/watch?v=LsK-xG1cLYA>\n",
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"\n",
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"f. Video on Gradient boost, part 1, parts 2-4 follow thereafter <https://www.youtube.com/watch?v=3CC4N4z3GJc>\n",
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"\n",
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"g. Decision Trees: Rashcka et al chapter 3 pages 86-98, and chapter 7 on Ensemble methods, Voting and Bagging and Gradient Boosting. See also lecture from STK-IN4300, lecture 7 at <https://www.uio.no/studier/emner/matnat/math/STK-IN4300/h20/slides/lecture_7.pdf>."
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"## Lab sessions\n",
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"**Lab sessions on Tuesday and Wednesday.**\n",
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"\n",
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" * Work and Discussion of project 3\n",
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"\n",
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" * Last weekly exercise\n",
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"\n",
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" * Lab sessions at usual times.\n",
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"\n",
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" * For the week of December 2-6, lab sessions start at 10am and end at 4pm, room FØ434, Tuesday and Wednesday"
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"## Random Forest Algorithm, reminder from last week\n",
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"\n",
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"The algorithm described here can be applied to both classification and regression problems.\n",
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"\n",
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"We will grow of forest of say $B$ trees.\n",
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"* For $b=1:B$\n",
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"\n",
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"a. Draw a bootstrap sample from the training data organized in our $\\boldsymbol{X}$ matrix.\n",
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"\n",
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"b. We grow then a random forest tree $T_b$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached\n",
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"\n",
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"1. we select $m \\le p$ variables at random from the $p$ predictors/features\n",
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"\n",
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"2. pick the best split point among the $m$ features using for example the CART algorithm and create a new node\n",
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"\n",
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"3. split the node into daughter nodes\n",
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"\n",
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"Finally we output then the ensemble of trees $\\{T_b\\}_1^{B}$ and make predictions for either a regression type of problem or a classification type of problem."
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"source": [
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"## Random Forests Compared with other Methods on the Cancer Data"
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"(426, 30)\n",
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"(143, 30)\n",
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"Test set accuracy Logistic Regression with scaled data: 0.96\n",
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"Test set accuracy SVM with scaled data: 0.96\n",
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"Test set accuracy with Decision Trees and scaled data: 0.91\n"
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"[1. 0.8 0.93333333 1. 1. 0.92857143\n",
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" 1. 0.92857143 0.92857143 0.92857143]\n",
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"Test set accuracy with Random Forests and scaled data: 0.98\n"
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.ensemble import BaggingClassifier\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"#define methods\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"# Support vector machine\n",
|
||
"svm = SVC(gamma='auto', C=100)\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
|
||
"#Scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Support Vector Machine\n",
|
||
"svm.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.ensemble import RandomForestClassifier\n",
|
||
"from sklearn.preprocessing import LabelEncoder\n",
|
||
"from sklearn.model_selection import cross_validate\n",
|
||
"# Data set not specificied\n",
|
||
"#Instantiate the model with 500 trees and entropy as splitting criteria\n",
|
||
"Random_Forest_model = RandomForestClassifier(n_estimators=500,criterion=\"entropy\")\n",
|
||
"Random_Forest_model.fit(X_train_scaled, y_train)\n",
|
||
"#Cross validation\n",
|
||
"accuracy = cross_validate(Random_Forest_model,X_test_scaled,y_test,cv=10)['test_score']\n",
|
||
"print(accuracy)\n",
|
||
"print(\"Test set accuracy with Random Forests and scaled data: {:.2f}\".format(Random_Forest_model.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"\n",
|
||
"import scikitplot as skplt\n",
|
||
"y_pred = Random_Forest_model.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = Random_Forest_model.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5cbe0e8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Recall that the cumulative gains curve shows the percentage of the\n",
|
||
"overall number of cases in a given category *gained* by targeting a\n",
|
||
"percentage of the total number of cases.\n",
|
||
"\n",
|
||
"Similarly, the receiver operating characteristic curve, or ROC curve,\n",
|
||
"displays the diagnostic ability of a binary classifier system as its\n",
|
||
"discrimination threshold is varied. It plots the true positive rate against the false positive rate."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "19bd77f2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Compare Bagging on Trees with Random Forests"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "84f1af2e",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"bag_clf = BaggingClassifier(\n",
|
||
" DecisionTreeClassifier(splitter=\"random\", max_leaf_nodes=16, random_state=42),\n",
|
||
" n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "6c01d900",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0.9790209790209791"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"bag_clf.fit(X_train, y_train)\n",
|
||
"y_pred = bag_clf.predict(X_test)\n",
|
||
"from sklearn.ensemble import RandomForestClassifier\n",
|
||
"rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)\n",
|
||
"rnd_clf.fit(X_train, y_train)\n",
|
||
"y_pred_rf = rnd_clf.predict(X_test)\n",
|
||
"np.sum(y_pred == y_pred_rf) / len(y_pred)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "896072f6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Boosting, a Bird's Eye View\n",
|
||
"\n",
|
||
"The basic idea is to combine weak classifiers in order to create a good\n",
|
||
"classifier. With a weak classifier we often intend a classifier which\n",
|
||
"produces results which are only slightly better than we would get by\n",
|
||
"random guesses.\n",
|
||
"\n",
|
||
"This is done by applying in an iterative way a weak (or a standard\n",
|
||
"classifier like decision trees) to modify the data. In each iteration\n",
|
||
"we emphasize those observations which are misclassified by weighting\n",
|
||
"them with a factor."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "babc9c9c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## What is boosting? Additive Modelling/Iterative Fitting\n",
|
||
"\n",
|
||
"Boosting is a way of fitting an additive expansion in a set of\n",
|
||
"elementary basis functions like for example some simple polynomials.\n",
|
||
"Assume for example that we have a function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2ed28584",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5b5b9631",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $\\beta_m$ are the expansion parameters to be determined in a\n",
|
||
"minimization process and $b(x;\\gamma_m)$ are some simple functions of\n",
|
||
"the multivariable parameter $x$ which is characterized by the\n",
|
||
"parameters $\\gamma_m$.\n",
|
||
"\n",
|
||
"As an example, consider the Sigmoid function we used in logistic\n",
|
||
"regression. In that case, we can translate the function\n",
|
||
"$b(x;\\gamma_m)$ into the Sigmoid function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7b6c43ec",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sigma(t) = \\frac{1}{1+\\exp{(-t)}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3962039f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $t=\\gamma_0+\\gamma_1 x$ and the parameters $\\gamma_0$ and\n",
|
||
"$\\gamma_1$ were determined by the Logistic Regression fitting\n",
|
||
"algorithm.\n",
|
||
"\n",
|
||
"As another example, consider the cost function we defined for linear regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ee5f259c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "079d8ee3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In this case the function $f(x)$ was replaced by the design matrix\n",
|
||
"$\\boldsymbol{X}$ and the unknown linear regression parameters $\\boldsymbol{\\beta}$,\n",
|
||
"that is $\\boldsymbol{f}=\\boldsymbol{X}\\boldsymbol{\\beta}$. In linear regression we can \n",
|
||
"simply invert a matrix and obtain the parameters $\\beta$ by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "11f821a2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "60990073",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters $\\beta_m$ and $\\gamma_m$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4d7195ab",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Iterative Fitting, Regression and Squared-error Cost Function\n",
|
||
"\n",
|
||
"The way we proceed is as follows (here we specialize to the squared-error cost function)\n",
|
||
"\n",
|
||
"1. Establish a cost function, here ${\\cal C}(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f_M(x_i))^2$ with $f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m)$.\n",
|
||
"\n",
|
||
"2. Initialize with a guess $f_0(x)$. It could be one or even zero or some random numbers.\n",
|
||
"\n",
|
||
"3. For $m=1:M$\n",
|
||
"\n",
|
||
"a. minimize $\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2$ wrt $\\gamma$ and $\\beta$\n",
|
||
"\n",
|
||
"b. This gives the optimal values $\\beta_m$ and $\\gamma_m$\n",
|
||
"\n",
|
||
"c. Determine then the new values $f_m(x)=f_{m-1}(x) +\\beta_m b(x;\\gamma_m)$\n",
|
||
"\n",
|
||
"We could use any of the algorithms we have discussed till now. If we\n",
|
||
"use trees, $\\gamma$ parameterizes the split variables and split points\n",
|
||
"at the internal nodes, and the predictions at the terminal nodes."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4bee726a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Squared-Error Example and Iterative Fitting\n",
|
||
"\n",
|
||
"To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.\n",
|
||
"\n",
|
||
"For simplicity we assume also that our functions $b(x;\\gamma)=1+\\gamma x$. \n",
|
||
"\n",
|
||
"This means that for every iteration $m$, we need to optimize"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1190b9a0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\beta_m,\\gamma_m) = \\mathrm{argmin}_{\\beta,\\lambda}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2=\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta(1+\\gamma x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2702211b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We start our iteration by simply setting $f_0(x)=0$. \n",
|
||
"Taking the derivatives with respect to $\\beta$ and $\\gamma$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1b1d9984",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial {\\cal C}}{\\partial \\beta} = -2\\sum_{i}(1+\\gamma x_i)(y_i-\\beta(1+\\gamma x_i))=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cdf7e56a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ac6f3b86",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial {\\cal C}}{\\partial \\gamma} =-2\\sum_{i}\\beta x_i(y_i-\\beta(1+\\gamma x_i))=0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "faf6fb5f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can then rewrite these equations as (defining $\\boldsymbol{w}=\\boldsymbol{e}+\\gamma \\boldsymbol{x})$ with $\\boldsymbol{e}$ being the unit vector)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "969f86ed",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\gamma \\boldsymbol{w}^T(\\boldsymbol{y}-\\beta\\gamma \\boldsymbol{w})=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a98a541c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives us $\\beta = \\boldsymbol{w}^T\\boldsymbol{y}/(\\boldsymbol{w}^T\\boldsymbol{w})$. Similarly we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d8be5438",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta\\gamma \\boldsymbol{x}^T(\\boldsymbol{y}-\\beta(1+\\gamma \\boldsymbol{x}))=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "932f43c5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which leads to $\\gamma =(\\boldsymbol{x}^T\\boldsymbol{y}-\\beta\\boldsymbol{x}^T\\boldsymbol{e})/(\\beta\\boldsymbol{x}^T\\boldsymbol{x})$. Inserting\n",
|
||
"for $\\beta$ gives us an equation for $\\gamma$. This is a non-linear equation in the unknown $\\gamma$ and has to be solved numerically. \n",
|
||
"\n",
|
||
"The solution to these two equations gives us in turn $\\beta_1$ and $\\gamma_1$ leading to the new expression for $f_1(x)$ as\n",
|
||
"$f_1(x) = \\beta_1(1+\\gamma_1x)$. Doing this $M$ times results in our final estimate for the function $f$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "24630eb9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Iterative Fitting, Classification and AdaBoost\n",
|
||
"\n",
|
||
"Let us consider a binary classification problem with two outcomes $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
|
||
"observations. We define a classification function $G(x)$ which produces a prediction taking one or the other of the two values \n",
|
||
"$\\{-1,1\\}$.\n",
|
||
"\n",
|
||
"The error rate of the training sample is then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9a7fa4b6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{\\overline{err}}=\\frac{1}{n} \\sum_{i=0}^{n-1} I(y_i\\ne G(x_i)).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7ead62b2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The iterative procedure starts with defining a weak classifier whose\n",
|
||
"error rate is barely better than random guessing. The iterative\n",
|
||
"procedure in boosting is to sequentially apply a weak\n",
|
||
"classification algorithm to repeatedly modified versions of the data\n",
|
||
"producing a sequence of weak classifiers $G_m(x)$.\n",
|
||
"\n",
|
||
"Here we will express our function $f(x)$ in terms of $G(x)$. That is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "91639c49",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e43865c2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"will be a function of"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1884c219",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"G_M(x) = \\mathrm{sign} \\sum_{i=1}^M \\alpha_m G_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bbb1cdbb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Adaptive Boosting, AdaBoost\n",
|
||
"\n",
|
||
"In our iterative procedure we define thus"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e3590f6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_m(x) = f_{m-1}(x)+\\beta_mG_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2eb8c86b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the\n",
|
||
"exponential cost/loss function defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e477d15a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{(-y_i(f_{m-1}(x_i)+\\beta G(x_i))}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b6f01e59",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We optimize $\\beta$ and $G$ for each value of $m=1:M$ as we did in the regression case.\n",
|
||
"This is normally done in two steps. Let us however first rewrite the cost function as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "71c85471",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}w_i^{m}\\exp{(-y_i\\beta G(x_i))},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2d5be340",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined $w_i^m= \\exp{(-y_if_{m-1}(x_i))}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e426517c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Building up AdaBoost\n",
|
||
"\n",
|
||
"First, for any $\\beta > 0$, we optimize $G$ by setting"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c0c7e993",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"G_m(x) = \\mathrm{sign} \\sum_{i=0}^{n-1} w_i^m I(y_i \\ne G_(x_i)),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7457a096",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which is the classifier that minimizes the weighted error rate in predicting $y$.\n",
|
||
"\n",
|
||
"We can do this by rewriting"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "424d5bc9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\exp{-(\\beta)}\\sum_{y_i=G(x_i)}w_i^m+\\exp{(\\beta)}\\sum_{y_i\\ne G(x_i)}w_i^m,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d1fa658b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which can be rewritten as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f8fc6b15",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\exp{(\\beta)}-\\exp{-(\\beta)})\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i))+\\exp{(-\\beta)}\\sum_{i=0}^{n-1}w_i^m=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9ca82f54",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which leads to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6c028686",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_m = \\frac{1}{2}\\log{\\frac{1-\\mathrm{\\overline{err}}}{\\mathrm{\\overline{err}}}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4007a0ef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have redefined the error as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ba456347",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{\\overline{err}}_m=\\frac{1}{n}\\frac{\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i)}{\\sum_{i=0}^{n-1}w_i^m},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c8df4ef3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which leads to an update of"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "da46f9d9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_m(x) = f_{m-1}(x) +\\beta_m G_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5c60f30d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"This leads to the new weights"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a5bc4dfe",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"w_i^{m+1} = w_i^m \\exp{(-y_i\\beta_m G_m(x_i))}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3987cc1e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Adaptive boosting: AdaBoost, Basic Algorithm\n",
|
||
"\n",
|
||
"The algorithm here is rather straightforward. Assume that our weak\n",
|
||
"classifier is a decision tree and we consider a binary set of outputs\n",
|
||
"with $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
|
||
"observations. Our design matrix is given in terms of the\n",
|
||
"feature/predictor vectors\n",
|
||
"$\\boldsymbol{X}=[\\boldsymbol{x}_0\\boldsymbol{x}_1\\dots\\boldsymbol{x}_{p-1}]$. Finally, we define also a\n",
|
||
"classifier determined by our data via a function $G(x)$. This function tells us how well we are able to classify our outputs/targets $\\boldsymbol{y}$. \n",
|
||
"\n",
|
||
"We have already defined the misclassification error $\\mathrm{err}$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b35df09e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(x_i)),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5b6a209c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where the function $I()$ is one if we misclassify and zero if we classify correctly."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d619a097",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Basic Steps of AdaBoost\n",
|
||
"\n",
|
||
"With the above definitions we are now ready to set up the algorithm for AdaBoost.\n",
|
||
"The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.\n",
|
||
"1. We start by initializing all weights to $w_i = 1/n$, with $i=0,1,2,\\dots n-1$. It is easy to see that we must have $\\sum_{i=0}^{n-1}w_i = 1$.\n",
|
||
"\n",
|
||
"2. We rewrite the misclassification error as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b7311abb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{\\overline{err}}_m=\\frac{\\sum_{i=0}^{n-1}w_i^m I(y_i\\ne G(x_i))}{\\sum_{i=0}^{n-1}w_i},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4bfb4209",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"1. Then we start looping over all attempts at classifying, namely we start an iterative process for $m=1:M$, where $M$ is the final number of classifications. Our given classifier could for example be a plain decision tree.\n",
|
||
"\n",
|
||
"a. Fit then a given classifier to the training set using the weights $w_i$.\n",
|
||
"\n",
|
||
"b. Compute then $\\mathrm{err}$ and figure out which events are classified properly and which are classified wrongly.\n",
|
||
"\n",
|
||
"c. Define a quantity $\\alpha_{m} = \\log{(1-\\mathrm{\\overline{err}}_m)/\\mathrm{\\overline{err}}_m}$\n",
|
||
"\n",
|
||
"d. Set the new weights to $w_i = w_i\\times \\exp{(\\alpha_m I(y_i\\ne G(x_i)}$.\n",
|
||
"\n",
|
||
"5. Compute the new classifier $G(x)= \\sum_{i=0}^{n-1}\\alpha_m I(y_i\\ne G(x_i)$.\n",
|
||
"\n",
|
||
"For the iterations with $m \\le 2$ the weights are modified\n",
|
||
"individually at each steps. The observations which were misclassified\n",
|
||
"at iteration $m-1$ have a weight which is larger than those which were\n",
|
||
"classified properly. As this proceeds, the observations which were\n",
|
||
"difficult to classifiy correctly are given a larger influence. Each\n",
|
||
"new classification step $m$ is then forced to concentrate on those\n",
|
||
"observations that are missed in the previous iterations."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4cf4c1f4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## AdaBoost Examples\n",
|
||
"\n",
|
||
"Using **Scikit-Learn** it is easy to apply the adaptive boosting algorithm, as done here."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "453dff54",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.ensemble import AdaBoostClassifier\n",
|
||
"\n",
|
||
"ada_clf = AdaBoostClassifier(\n",
|
||
" DecisionTreeClassifier(max_depth=2), n_estimators=200,\n",
|
||
" algorithm=\"SAMME.R\", learning_rate=0.01, random_state=42)\n",
|
||
"ada_clf.fit(X_train, y_train)\n",
|
||
"y_pred = ada_clf.predict(X_test)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = ada_clf.predict_proba(X_test)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d6470164",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Making an ADAboost code yourself"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "b6e01886",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Predictions: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"class DecisionStump:\n",
|
||
" def fit(self, X, y, weights):\n",
|
||
" m, n = X.shape\n",
|
||
" self.alpha = 0\n",
|
||
" self.threshold = None\n",
|
||
" self.polarity = 1\n",
|
||
"\n",
|
||
" min_error = float('inf')\n",
|
||
"\n",
|
||
" for feature in range(n):\n",
|
||
" feature_values = np.unique(X[:, feature])\n",
|
||
"\n",
|
||
" for threshold in feature_values:\n",
|
||
" for polarity in [1, -1]:\n",
|
||
" predictions = np.ones(m)\n",
|
||
" predictions[X[:, feature] < threshold] = -1\n",
|
||
" predictions *= polarity\n",
|
||
"\n",
|
||
" error = sum(weights[predictions != y])\n",
|
||
"\n",
|
||
" if error < min_error:\n",
|
||
" min_error = error\n",
|
||
" self.alpha = 0.5 * np.log((1 - error) / (error + 1e-10))\n",
|
||
" self.threshold = threshold\n",
|
||
" self.feature_index = feature\n",
|
||
" self.polarity = polarity\n",
|
||
"\n",
|
||
" def predict(self, X):\n",
|
||
" m = X.shape[0]\n",
|
||
" predictions = np.ones(m)\n",
|
||
" if self.polarity == 1:\n",
|
||
" predictions[X[:, self.feature_index] < self.threshold] = -1\n",
|
||
" else:\n",
|
||
" predictions[X[:, self.feature_index] >= self.threshold] = -1\n",
|
||
" return predictions\n",
|
||
"\n",
|
||
"class AdaBoost:\n",
|
||
" def fit(self, X, y, n_estimators):\n",
|
||
" m = X.shape[0]\n",
|
||
" self.alphas = []\n",
|
||
" self.models = []\n",
|
||
"\n",
|
||
" weights = np.ones(m) / m\n",
|
||
"\n",
|
||
" for _ in range(n_estimators):\n",
|
||
" stump = DecisionStump()\n",
|
||
" stump.fit(X, y, weights)\n",
|
||
" predictions = stump.predict(X)\n",
|
||
"\n",
|
||
" error = sum(weights[predictions != y])\n",
|
||
" if error == 0:\n",
|
||
" break\n",
|
||
"\n",
|
||
" self.models.append(stump)\n",
|
||
" self.alphas.append(stump.alpha)\n",
|
||
"\n",
|
||
" weights *= np.exp(-stump.alpha * y * predictions)\n",
|
||
" weights /= np.sum(weights)\n",
|
||
"\n",
|
||
" def predict(self, X):\n",
|
||
" final_predictions = np.zeros(X.shape[0])\n",
|
||
" for alpha, model in zip(self.alphas, self.models):\n",
|
||
" final_predictions += alpha * model.predict(X)\n",
|
||
" return np.sign(final_predictions)\n",
|
||
"\n",
|
||
"# Example dataset (X, y)\n",
|
||
"X = np.array([[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]])\n",
|
||
"y = np.array([-1, -1, -1, -1, 1, 1, 1, 1, 1, 1]) # Labels must be -1 or 1\n",
|
||
"\n",
|
||
"# Train AdaBoost\n",
|
||
"ada = AdaBoost()\n",
|
||
"ada.fit(X, y, n_estimators=10)\n",
|
||
"\n",
|
||
"# Predictions\n",
|
||
"predictions = ada.predict(X)\n",
|
||
"print(\"Predictions:\", predictions)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3cede4c9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent\n",
|
||
"\n",
|
||
"Gradient boosting is again a similar technique to Adaptive boosting,\n",
|
||
"it combines so-called weak classifiers or regressors into a strong\n",
|
||
"method via a series of iterations.\n",
|
||
"\n",
|
||
"In order to understand the method, let us illustrate its basics by\n",
|
||
"bringing back the essential steps in linear regression, where our cost\n",
|
||
"function was the least squares function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "94e3b59f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The Squared-Error again! Steepest Descent\n",
|
||
"\n",
|
||
"We start again with our cost function ${\\cal C}(\\boldsymbol{y}m\\boldsymbol{f})=\\sum_{i=0}^{n-1}{\\cal L}(y_i, f(x_i))$ where we want to minimize\n",
|
||
"This means that for every iteration, we need to optimize"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2f000f62",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\hat{\\boldsymbol{f}}) = \\mathrm{argmin}_{\\boldsymbol{f}}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "014da5e9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We define a real function $h_m(x)$ that defines our final function $f_M(x)$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "022aee06",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{m=0}^M h_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d0d3e174",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the steepest decent approach we approximate $h_m(x) = -\\rho_m g_m(x)$, where $\\rho_m$ is a scalar and $g_m(x)$ the gradient defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8af32042",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"g_m(x_i) = \\left[ \\frac{\\partial {\\cal L}(y_i, f(x_i))}{\\partial f(x_i)}\\right]_{f(x_i)=f_{m-1}(x_i)}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4a384d95",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"With the new gradient we can update $f_m(x) = f_{m-1}(x) -\\rho_m g_m(x)$. Using the above squared-error function we see that\n",
|
||
"the gradient is $g_m(x_i) = -2(y_i-f(x_i))$.\n",
|
||
"\n",
|
||
"Choosing $f_0(x)=0$ we obtain $g_m(x) = -2y_i$ and inserting this into the minimization problem for the cost function we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bd5b9bb9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\rho_1) = \\mathrm{argmin}_{\\rho}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i+2\\rho y_i)^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "560b3106",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Steepest Descent Example\n",
|
||
"\n",
|
||
"Optimizing with respect to $\\rho$ we obtain (taking the derivative) that $\\rho_1 = -1/2$. We have then that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4742d327",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_1(x) = f_{0}(x) -\\rho_1 g_1(x)=-y_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d160a37f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can then proceed and compute"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f3cde07e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"g_2(x_i) = \\left[ \\frac{\\partial {\\cal L}(y_i, f(x_i))}{\\partial f(x_i)}\\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cf95ad5e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and find a new value for $\\rho_2=-1/2$ and continue till we have reached $m=M$. We can modify the steepest descent method, or steepest boosting, by introducing what is called **gradient boosting**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bb614b9d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Boosting, algorithm\n",
|
||
"\n",
|
||
"Steepest descent is however not much used, since it only optimizes $f$ at a fixed set of $n$ points,\n",
|
||
"so we do not learn a function that can generalize. However, we can modify the algorithm by\n",
|
||
"fitting a weak learner to approximate the negative gradient signal. \n",
|
||
"\n",
|
||
"Suppose we have a cost function $C(f)=\\sum_{i=0}^{n-1}L(y_i, f(x_i))$ where $y_i$ is our target and $f(x_i)$ the function which is meant to model $y_i$. The above cost function could be our standard squared-error function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "19e3e8fa",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f})=\\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9330b34b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The way we proceed in an iterative fashion is to\n",
|
||
"1. Initialize our estimate $f_0(x)$.\n",
|
||
"\n",
|
||
"2. For $m=1:M$, we\n",
|
||
"\n",
|
||
"a. compute the negative gradient vector $\\boldsymbol{u}_m = -\\partial C(\\boldsymbol{y},\\boldsymbol{f})/\\partial \\boldsymbol{f}(x)$ at $f(x) = f_{m-1}(x)$;\n",
|
||
"\n",
|
||
"b. fit the so-called base-learner to the negative gradient $h_m(u_m,x)$;\n",
|
||
"\n",
|
||
"c. update the estimate $f_m(x) = f_{m-1}(x)+h_m(u_m,x)$;\n",
|
||
"\n",
|
||
"4. The final estimate is then $f_M(x) = \\sum_{m=1}^M h_m(u_m,x)$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e648539a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Boosting, Examples of Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "d12810d3",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Max depth: 1\n",
|
||
"Error: 0.4203129333425336\n",
|
||
"Bias^2: 0.21226966048908316\n",
|
||
"Var: 0.20804327285345042\n",
|
||
"0.4203129333425336 >= 0.21226966048908316 + 0.20804327285345042 = 0.4203129333425336\n",
|
||
"Max depth: 2\n",
|
||
"Error: 0.40767639731018696\n",
|
||
"Bias^2: 0.21200998139721822\n",
|
||
"Var: 0.19566641591296877\n",
|
||
"0.40767639731018696 >= 0.21200998139721822 + 0.19566641591296877 = 0.407676397310187\n",
|
||
"Max depth: 3\n",
|
||
"Error: 0.4076774836661818\n",
|
||
"Bias^2: 0.2120099429256955\n",
|
||
"Var: 0.19566754074048626\n",
|
||
"0.4076774836661818 >= 0.2120099429256955 + 0.19566754074048626 = 0.40767748366618173\n",
|
||
"Max depth: 4\n",
|
||
"Error: 0.4076774836661818\n",
|
||
"Bias^2: 0.2120099429256955\n",
|
||
"Var: 0.19566754074048626\n",
|
||
"0.4076774836661818 >= 0.2120099429256955 + 0.19566754074048626 = 0.40767748366618173\n",
|
||
"Max depth: 5\n",
|
||
"Error: 0.4076774836661816\n",
|
||
"Bias^2: 0.2120099429256955\n",
|
||
"Var: 0.1956675407404862\n",
|
||
"0.4076774836661816 >= 0.2120099429256955 + 0.1956675407404862 = 0.40767748366618173\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:424: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:424: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:424: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:424: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:424: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.ensemble import GradientBoostingRegressor\n",
|
||
"import scikitplot as skplt\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"maxdegree = 6\n",
|
||
"\n",
|
||
"# Make data set.\n",
|
||
"x = np.linspace(-3, 3, n).reshape(-1, 1)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n",
|
||
"\n",
|
||
"error = np.zeros(maxdegree)\n",
|
||
"bias = np.zeros(maxdegree)\n",
|
||
"variance = np.zeros(maxdegree)\n",
|
||
"polydegree = np.zeros(maxdegree)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
|
||
"\n",
|
||
"for degree in range(1,maxdegree):\n",
|
||
" model = GradientBoostingRegressor(max_depth=degree, n_estimators=100, learning_rate=1.0) \n",
|
||
" model.fit(X_train,y_train)\n",
|
||
" y_pred = model.predict(X_test)\n",
|
||
" polydegree[degree] = degree\n",
|
||
" error[degree] = np.mean( np.mean((y_test - y_pred)**2) )\n",
|
||
" bias[degree] = np.mean( (y_test - np.mean(y_pred))**2 )\n",
|
||
" variance[degree] = np.mean( np.var(y_pred) )\n",
|
||
" print('Max depth:', degree)\n",
|
||
" print('Error:', error[degree])\n",
|
||
" print('Bias^2:', bias[degree])\n",
|
||
" print('Var:', variance[degree])\n",
|
||
" print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n",
|
||
"\n",
|
||
"plt.xlim(1,maxdegree-1)\n",
|
||
"plt.plot(polydegree, error, label='Error')\n",
|
||
"plt.plot(polydegree, bias, label='bias')\n",
|
||
"plt.plot(polydegree, variance, label='Variance')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f3e95eca",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Boosting, Classification Example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "d6426469",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[0.93333333 0.93333333 0.93333333 0.92857143 1. 0.92857143\n",
|
||
" 1. 0.92857143 0.85714286 0.92857143]\n",
|
||
"Test set accuracy with Gradient boosting and scaled data: 0.99\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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E4cOH0b9/f7i6uiIzMxO7du3CyZMnVXeemzJlCr7++mu89NJLGDduHBwdHbF+/XpcuXIFO3bsqDDyoI+RI0di9OjReO2119C9e3ecO3cOBw4cqNDL9fHxQdeuXeHv7w9HR0ecOnUK27dvx9ixYys9dk1+pnx9feHr6/vYOt7e3mjatCkmTZqEa9euwc7ODjt27NA4p+/v7w8AGDduHEJCQmBhYYE33nhD57jGjx+PW7du4YcffoCFhQV69uyJkSNHYu7cuejTp88TYyaqkhpbj08G9fDlbo8KDQ0VAahd7iaKolhaWipGR0eLjRs3FmvXri16eHiIU6dOFe/du6dWz9PTU+OlT+WXX23btk2rWDRdfrR7926xbdu2okKhEL28vMSPP/5YXLt2rQhAvHLliqreky53K29T0/bo5WmHDx8WQ0JCRHt7e1GhUIhNmzYVw8LCxFOnTqnV27Fjh9iqVStRLpeLPj4+4rfffiuGhoY+8XK3h23fvl3s0aOH6OjoKNaqVUts0KCBOHDgQDExMVGt3qVLl8T+/fuLDg4OokKhEAMCAsS9e/dWiFvTz1vTZVaVXe5WVlYmTp48WXRychKtra3FkJAQMS0trcLlbnPnzhUDAgJEBwcH0crKSvT29hbnzZundlnjo5e7iaL+n6lH/z9XBv9c7vY4mn4Gv//+uxgcHCza2NiITk5O4qhRo8Rz585V+Pndv39ffO+998T69euLgiCozrP8Z71gwYIK7T36/+G///2vCEBcuHChWr2CggLR09NT9PX1Vft5EhmKIIp6rLghIiKipwrn2ImIiMwIEzsREZEZYWInIiIyI0zsRERERnDkyBH06tULbm5uEAQBu3bteuI+iYmJaN++PeRyOZo1a6Z6WqAumNiJiIiMoKioCL6+vqrHAD/JlStX8Morr6Bbt25ITk7GhAkTMHLkSNWdC7XFVfFERERGJggCdu7c+djbTE+ePBn79u3Db7/9pip74403kJeXh/3792vdlknfoEapVOL69euwtbU16C0giYioeoiiiNu3b8PNzc2gN2N61L1791BSUqL3cURRrJBv5HI55HK53sdOSkqqcLvrkJAQTJgwQafjmHRiv379eoUniBERkenJyMhAw4YNjXLse/fuwcq2HnD/jt7HsrGxqXD3ycjISERFRel97MzMTLi4uKiVubi4oKCgAHfv3tX64UMmndjLn3dt6TsKgoXlE2oTmabL++c+uRKRibp9uwDeTT1Vf8+NoaSkBLh/B3KfUECfXFFWgsLf1yMjI0P1eGYABumtG5JJJ/by4RDBwhKCxdP1gyUylIf/gBCZq2qZTq2l0KsTKAoPpgrs7OyM8nvp6uqKrKwstbKsrCzY2dnp9Khgk07sREREWhMA6PMFwsjfPYKCghAfH69WdvDgQQQFBel0HF7uRkRE0iDI9N90UFhYiOTkZCQnJwN4cDlbcnIy0tPTAQBTp07FsGHDVPVHjx6Ny5cv48MPP8SFCxewYsUKbN26FRMnTtSpXSZ2IiIiIzh16hTatWuHdu3aAQAiIiLQrl07zJo1CwBw48YNVZIHgMaNG2Pfvn04ePAgfH19sXDhQqxZswYhISE6tcuheCIikgZB0HMoXrd9u3btisfdKkbTXeW6du2Ks2fP6hqZGiZ2IiKShioMp1fY3wSYRpRERESkFfbYiYhIGqp5KL6mMLETEZFE6DkUbyKD3KYRJREREWmFPXYiIpIGDsUTERGZEa6KJyIiIlPDHjsREUkDh+KJiIjMiESG4pnYiYhIGiTSYzeNrx9ERESkFfbYiYhIGjgUT0REZEYEQc/EzqF4IiIiqmbssRMRkTTIhAebPvubACZ2IiKSBonMsZtGlERERKQV9tiJiEgaJHIdOxM7ERFJA4fiiYiIyNSwx05ERNLAoXgiIiIzIpGheCZ2IiKSBon02E3j6wcRERFphT12IiKSBg7FExERmREOxRMREZGpYY+diIgkQs+heBPpCzOxExGRNHAonoiIiEwNe+xERCQNgqDnqnjT6LEzsRMRkTRI5HI304iSiIiItMIeOxERSYNEFs8xsRMRkTRIZCieiZ2IiKRBIj120/j6QURERFphj52IiKSBQ/FERERmhEPxREREZGrYYyciIkkQBAGCBHrsTOxERCQJUknsHIonIiIyI+yxExGRNAj/bPrsbwKY2ImISBI4FE9EREQmhz12IiKSBKn02JnYiYhIEpjYiYiIzIhUEjvn2ImIiMwIe+xERCQNvNyNiIjIfHAonoiIiEwOe+xERCQJD57aqk+P3XCxGBMTOxERSYIAPYfiTSSzcyieiIjIjLDHTkREkiCVxXNM7EREJA0SudyNQ/FERERmhD12IiKSBj2H4kUOxRMRET099J1j129FffVhYiciIkmQSmLnHDsREZERLV++HF5eXlAoFAgMDMTJkycfW3/x4sVo2bIlrKys4OHhgYkTJ+LevXtat8fETkRE0iAYYNPRli1bEBERgcjISJw5cwa+vr4ICQlBdna2xvqbN2/GlClTEBkZiZSUFHz55ZfYsmULpk2bpnWbTOxERCQJ5UPx+my6WrRoEUaNGoXw8HD4+PggNjYW1tbWWLt2rcb6x48fx3PPPYfBgwfDy8sLPXr0wKBBg57Yy38YEzsREZEOCgoK1Lbi4mKN9UpKSnD69GkEBwerymQyGYKDg5GUlKRxn44dO+L06dOqRH758mXEx8fj5Zdf1jo+Lp4jIiJJMNTiOQ8PD7XyyMhIREVFVaifk5ODsrIyuLi4qJW7uLjgwoULGtsYPHgwcnJy0KlTJ4iiiPv372P06NE6DcUzsRMRkSQYKrFnZGTAzs5OVS6Xy/WOrVxiYiLmz5+PFStWIDAwEGlpaRg/fjzmzJmDmTNnanUMJnYiIiId2NnZqSX2yjg5OcHCwgJZWVlq5VlZWXB1ddW4z8yZMzF06FCMHDkSANCmTRsUFRXhrbfewvTp0yGTPXkGnXPsREQkCdW9eM7S0hL+/v5ISEhQlSmVSiQkJCAoKEjjPnfu3KmQvC0sLAAAoihq1S577EREJA018BCYiIgIhIaGokOHDggICMDixYtRVFSE8PBwAMCwYcPg7u6OmJgYAECvXr2waNEitGvXTjUUP3PmTPTq1UuV4J+EiZ2IiMhIBg4ciJs3b2LWrFnIzMyEn58f9u/fr1pQl56ertZDnzFjBgRBwIwZM3Dt2jXUr18fvXr1wrx587RuUxC17ds/hQoKCmBvbw95+zEQLAy3eIHoaXLz6IKaDoHIaAoKCuDuXBf5+flazVtXtQ17e3u4Dv8KMkvrKh9HWXIHmWvfNGqshsAeOxERSYJU7hXPxE5ERJIglcTOVfFERERmhD12IiKShhpYFV8TmNiJiEgSOBRPREREJoeJXeLe7v8cLuyajr+PfoQja8ehg49HpXVrWcgwdUR3nP92Kv4++hFObHof3Z9tqVZHJhMw6+2eSNk1DblHPsL5b6diyvDgSo5IZHyrYlfgmRZN4GRvjW6dg3Dqf49//OXOHdvQvq0PnOytEejviwP741XvlZaWYub0KQj094WLoy2aN26It4aH4sb168Y+DTKAmnhsa014KhL78uXL4eXlBYVCgcDAQJ2eO0tV1z/YDx9P6I15a75H0LDP8Msf17F7yVuoX9dGY/2od17CyFeDEPHpTrQb+AnWfHscWz4Jh28Ld1Wd94e9gFGvdcTEBTvhN/BjzFi2DxFDu+HdAZ2q67SIVHZs24KpH76PKdNn4tjPp9C6TVu82usl3MzO1lj/56TjCB82BMPChuPYidP4v159MOj1fvj9/G8AHtzu89zZM5g8dTqO/nwKm77Zjj/+uIiB/ftW41lRVQnQM7GbyCR7jSf2LVu2ICIiApGRkThz5gx8fX0REhKC7Ep+8chwxg1+Hut2/YyNe/+HC1ey8N5HO3D3XilCewVorD/4JX98EpeAA8cv4Or1XKzekYQDx1MwfkgXVZ1n23ph75HfsP+nFKTf+Bs7D/2ChBMX0eGZRtV1WkQqy5YsRtjwkRgaGg7vVj74fNlKWFlbY8P6dRrrr1y+BME9QjAhYhK8vVthZtRs+LZrjy9WLgcA2NvbY3f89+jXfwBatGiJgMBn8elnS3D2zGlkpKdX56kRVarGE/uiRYswatQohIeHw8fHB7GxsbC2tsbatWtrOjSzVruWBdp5N8Sh//2hKhNFEYf+dxEBbTw17mNpWQv3SkrVyu4Wl6Kjb2PV659/uYpuHZqjWSMnAECb5g0Q5NsY3x/X/OxhImMpKSnB2TOn0fWFF1VlMpkMXbu9iJMnkjTuc/Lnn9HtBfWpo+DgHjh54udK2ynIz4cgCLB3cDBI3GQ8UhmKr9FV8SUlJTh9+jSmTp2qKpPJZAgODkZSkuZfPDIMJ4c6qFXLAtm5t9XKs3ML0dLTWeM+P/ycinGDu+DY2cu4/NctdPtPc/Tp1gYWD93n+NP1h2BXR4FzWyejTCnCQiYgcuV3+ObAGaOeD9GjbuXkoKysDM7OLmrlzi4u+ONiqsZ9srIy4ezsXKF+Vlamxvr37t3DrBlT8fqAN57qW4zSP3i5m/Hl/POLV34z/HIuLi64cKFiD6+4uBjFxcWq1wUFBUaPkf41aeEurJg+AOe2ToYoirh87RY27Pmf2tB9/2BfvNGzPcJmbsLvlzPRtoU7FkT0wY2cAmzad6oGoycyrNLSUgwbMhCiKOKzpStqOhwiFZO6jj0mJgbR0dE1HYZZyMkrwv37ZXB2tFUrd3a0Qeat25XuM+CDdZBb1kI9e2tcv1mAuWNfwZXrt1R15o/rhU/XH8K2g8kAgPOXMtGoQV18EPoiEztVq3pOTrCwsEB2dpZaeXZWFpwf6UyUc3FxrbC+JzsrCy4urmpl5Uk9Iz0de/f/wN66ieB17NXA6Z9fvKws9V+8rKwsuLq6Vqg/depU5Ofnq7aMjIzqCtXslN4vw9kLf6Hbf5qrygRBQLcOzXHy1z8fu29xyX1cv1mAWhYy9O3WFnt//E31npWiNpSiUq1+WZkSMplp/EKQ+bC0tES79v748fAhVZlSqcSPiYcQEBikcZ+AZ59F4uEEtbJDh35AQOCzqtflSf1SWhp2x3+PevXqGecEyOA4x14NLC0t4e/vj4SEBPTt2xfAg1+8hIQEjB07tkJ9uVwOuZyPZzWUJZuPYHXkGzidkoFT59Mx9o3nYW1liQ17H1xuuCZqEK5n52PWigfX8f7nmUZwq2+Pcxevwd3ZHtNHhUAmE7Bo42HVMeOP/o7JYcHIyMzD75cz4dfSHeMGd8GGPbyEkarf2HET8PbIcLRr7w///wRgxdLPcaeoCEOHhQEA3hoeigZu7oieOx8A8M6YcXipezcsWbwIIS+9jB1bt+Ds6VNYujwWwIOk/uag13Hu7Fls27kbyrIyZGU+mH+v6+gIS0vLGjlP0o4gPNj02d8U1PhQfEREBEJDQ9GhQwcEBARg8eLFKCoqQnh4eE2HZva2/5AMp7p1MOutELjUs8MvF6+hz/jVyM4tBAB4uDhAqRRV9eWWtRA5uicau9dD4d0SHDieghGRm5FfeE9VJ+LTnYh8uyc+/7Af6te1xY2cfHy5Mwnz1xys9vMjeu31gcjJycG82VHIyspEW18/fLs7XjUUn5GRAeGhxZ/PBnXE2vVfYXbULETPmo6mzZrj623fwueZ1gCA69euIX7vHgBAx4D2am3FH0hA5y5dq+W8iB5HEEVRfHI141q2bBkWLFiAzMxM+Pn5YcmSJQgMDHzifgUFBbC3t4e8/RgIFuzJk3m6eXRBTYdAZDQFBQVwd66L/Px8o61VKM8VTd7bDpm8TpWPoywuwuWl/Y0aqyHUeI8dAMaOHatx6J2IiMhg9ByKN5XL3Wr8BjVERERkOE9Fj52IiMjYpHK5GxM7ERFJglRWxXMonoiIyIywx05ERJIgkwl63SxLNJEbbTGxExGRJHAonoiIiEwOe+xERCQJXBVPRERkRqQyFM/ETkREkiCVHjvn2ImIiMwIe+xERCQJUumxM7ETEZEkSGWOnUPxREREZoQ9diIikgQBeg7Fm8hzW5nYiYhIEjgUT0RERCaHPXYiIpIEroonIiIyIxyKJyIiIpPDHjsREUkCh+KJiIjMiFSG4pnYiYhIEqTSY+ccOxERkRlhj52IiKRBz6F4E7nxHBM7ERFJA4fiiYiIyOSwx05ERJLAVfFERERmhEPxREREZHLYYyciIkngUDwREZEZ4VA8ERERmRz22ImISBKk0mNnYiciIkngHDsREZEZkUqPnXPsREREZoQ9diIikgQOxRMREZkRDsUTERGRyWGPnYiIJEGAnkPxBovEuJjYiYhIEmSCAJkemV2ffasTh+KJiIjMCHvsREQkCVwVT0REZEa4Kp6IiMiMyAT9t6pYvnw5vLy8oFAoEBgYiJMnTz62fl5eHsaMGYMGDRpALpejRYsWiI+P17o99tiJiIiMZMuWLYiIiEBsbCwCAwOxePFihISEIDU1Fc7OzhXql5SUoHv37nB2dsb27dvh7u6OP//8Ew4ODlq3ycRORETSIOg5nF6FXRctWoRRo0YhPDwcABAbG4t9+/Zh7dq1mDJlSoX6a9euRW5uLo4fP47atWsDALy8vHRqk0PxREQkCeWL5/TZAKCgoEBtKy4u1theSUkJTp8+jeDgYFWZTCZDcHAwkpKSNO6ze/duBAUFYcyYMXBxcUHr1q0xf/58lJWVaX2eTOxEREQ68PDwgL29vWqLiYnRWC8nJwdlZWVwcXFRK3dxcUFmZqbGfS5fvozt27ejrKwM8fHxmDlzJhYuXIi5c+dqHR+H4omISBKEf/7psz8AZGRkwM7OTlUul8v1jq2cUqmEs7MzVq1aBQsLC/j7++PatWtYsGABIiMjtToGEzsREUmCPivby/cHADs7O7XEXhknJydYWFggKytLrTwrKwuurq4a92nQoAFq164NCwsLVVmrVq2QmZmJkpISWFpaPjnOJ9YgIiIinVlaWsLf3x8JCQmqMqVSiYSEBAQFBWnc57nnnkNaWhqUSqWq7OLFi2jQoIFWSR1gYiciIokov0GNPpuuIiIisHr1aqxfvx4pKSl45513UFRUpFolP2zYMEydOlVV/5133kFubi7Gjx+PixcvYt++fZg/fz7GjBmjdZtaDcXv3r1b6wP27t1b67pERETVpSZuKTtw4EDcvHkTs2bNQmZmJvz8/LB//37Vgrr09HTIZP/2sT08PHDgwAFMnDgRbdu2hbu7O8aPH4/JkydrH6coiuKTKj3c6GMPJgg6LcnXV0FBAezt7SFvPwaCheEWLxA9TW4eXVDTIRAZTUFBAdyd6yI/P1+reeuqtmFvb4+XlxxGbSubKh+n9G4h4sd1M2qshqBVj/3hsX4iIiJTJJXHtuq1Kv7evXtQKBSGioWIiMhopPJ0N50Xz5WVlWHOnDlwd3eHjY0NLl++DACYOXMmvvzyS4MHSEREZAg1sXiuJuic2OfNm4e4uDh88sknakvvW7dujTVr1hg0OCIiItKNzol9w4YNWLVqFYYMGaJ2Ab2vry8uXLhg0OCIiIgMxVD3in/a6TzHfu3aNTRr1qxCuVKpRGlpqUGCIiIiMjSpLJ7Tucfu4+ODo0ePVijfvn072rVrZ5CgiIiIqGp07rHPmjULoaGhuHbtGpRKJb799lukpqZiw4YN2Lt3rzFiJCIi0puAKj1SXW1/U6Bzj71Pnz7Ys2cPfvjhB9SpUwezZs1CSkoK9uzZg+7duxsjRiIiIr1JZVV8la5j79y5Mw4ePGjoWIiIiEhPVb5BzalTp5CSkgLgwby7v7+/wYIiIiIyNEM9tvVpp3Ni/+uvvzBo0CD89NNPcHBwAADk5eWhY8eO+Oabb9CwYUNDx0hERKQ3fYfTTWUoXuc59pEjR6K0tBQpKSnIzc1Fbm4uUlJSoFQqMXLkSGPESERERFrSucf+448/4vjx42jZsqWqrGXLlli6dCk6d+5s0OCIiIgMyUQ63XrRObF7eHhovBFNWVkZ3NzcDBIUERGRoXEovhILFizAe++9h1OnTqnKTp06hfHjx+PTTz81aHBERESGUr54Tp/NFGjVY69bt67aN5WioiIEBgaiVq0Hu9+/fx+1atXC8OHD0bdvX6MESkRERE+mVWJfvHixkcMgIiIyLqkMxWuV2ENDQ40dBxERkVFJ5ZayVb5BDQDcu3cPJSUlamV2dnZ6BURERERVp3NiLyoqwuTJk7F161bcunWrwvtlZWUGCYyIiMiQ+NjWSnz44Yc4dOgQVq5cCblcjjVr1iA6Ohpubm7YsGGDMWIkIiLSmyDov5kCnXvse/bswYYNG9C1a1eEh4ejc+fOaNasGTw9PbFp0yYMGTLEGHESERGRFnTusefm5qJJkyYAHsyn5+bmAgA6deqEI0eOGDY6IiIiA5HKY1t1TuxNmjTBlStXAADe3t7YunUrgAc9+fKHwhARET1tpDIUr3NiDw8Px7lz5wAAU6ZMwfLly6FQKDBx4kR88MEHBg+QiIiItKfzHPvEiRNV/x0cHIwLFy7g9OnTaNasGdq2bWvQ4IiIiAxFKqvi9bqOHQA8PT3h6elpiFiIiIiMRt/hdBPJ69ol9iVLlmh9wHHjxlU5GCIiImPhLWUf8tlnn2l1MEEQmNiJiIhqkFaJvXwV/NMq/eB83sqWzFbd/4yt6RCIjEYsK3lyJQORoQorxh/Z3xToPcdORERkCqQyFG8qX0CIiIhIC+yxExGRJAgCIOOqeCIiIvMg0zOx67NvdeJQPBERkRmpUmI/evQo3nzzTQQFBeHatWsAgI0bN+LYsWMGDY6IiMhQ+BCYSuzYsQMhISGwsrLC2bNnUVxcDADIz8/H/PnzDR4gERGRIZQPxeuzmQKdE/vcuXMRGxuL1atXo3bt2qry5557DmfOnDFocERERKQbnRfPpaam4vnnn69Qbm9vj7y8PEPEREREZHBSuVe8zj12V1dXpKWlVSg/duwYmjRpYpCgiIiIDK386W76bKZA58Q+atQojB8/HidOnIAgCLh+/To2bdqESZMm4Z133jFGjERERHqTGWAzBToPxU+ZMgVKpRIvvvgi7ty5g+effx5yuRyTJk3Ce++9Z4wYiYiISEs6J3ZBEDB9+nR88MEHSEtLQ2FhIXx8fGBjY2OM+IiIiAxCKnPsVb7znKWlJXx8fAwZCxERkdHIoN88uQymkdl1TuzdunV77EX6hw4d0isgIiIiqjqdE7ufn5/a69LSUiQnJ+O3335DaGiooeIiIiIyKA7FV+Kzzz7TWB4VFYXCwkK9AyIiIjIGPgRGR2+++SbWrl1rqMMRERFRFRjssa1JSUlQKBSGOhwREZFBPXgee9W73WY7FN+vXz+116Io4saNGzh16hRmzpxpsMCIiIgMiXPslbC3t1d7LZPJ0LJlS8yePRs9evQwWGBERESkO50Se1lZGcLDw9GmTRvUrVvXWDEREREZHBfPaWBhYYEePXrwKW5ERGRyBAP8MwU6r4pv3bo1Ll++bIxYiIiIjKa8x67PZgp0Tuxz587FpEmTsHfvXty4cQMFBQVqGxEREdUcrefYZ8+ejffffx8vv/wyAKB3795qt5YVRRGCIKCsrMzwURIREelJKnPsWif26OhojB49GocPHzZmPEREREYhCMJjn3Wizf6mQOvELooiAKBLly5GC4aIiIj0o9PlbqbybYWIiOhRHIrXoEWLFk9M7rm5uXoFREREZAy885wG0dHRFe48R0RERE8PnRL7G2+8AWdnZ2PFQkREZDQyQdDrITD67FudtL6OnfPrRERkymrqBjXLly+Hl5cXFAoFAgMDcfLkSa32++abbyAIAvr27atTe1on9vJV8URERKSdLVu2ICIiApGRkThz5gx8fX0REhKC7Ozsx+539epVTJo0CZ07d9a5Ta0Tu1Kp5DA8ERGZLuHfBXRV2apyq/hFixZh1KhRCA8Ph4+PD2JjY2FtbY21a9dWuk9ZWRmGDBmC6OhoNGnSROc2db6lLBERkSmSQdB7A1DhVurFxcUa2yspKcHp06cRHBz8bwwyGYKDg5GUlFRpnLNnz4azszNGjBhRxfMkIiKSAH166w9fKufh4QF7e3vVFhMTo7G9nJwclJWVwcXFRa3cxcUFmZmZGvc5duwYvvzyS6xevbrK56nTqngiIiKpy8jIgJ2dneq1XC43yHFv376NoUOHYvXq1XBycqrycZjYiYhIEgx15zk7Ozu1xF4ZJycnWFhYICsrS608KysLrq6uFepfunQJV69eRa9evVRlSqUSAFCrVi2kpqaiadOmT47ziTWIiIjMQPl17PpsurC0tIS/vz8SEhJUZUqlEgkJCQgKCqpQ39vbG7/++iuSk5NVW+/evdGtWzckJyfDw8NDq3bZYyciIjKSiIgIhIaGokOHDggICMDixYtRVFSE8PBwAMCwYcPg7u6OmJgYKBQKtG7dWm1/BwcHAKhQ/jhM7EREJAk1ca/4gQMH4ubNm5g1axYyMzPh5+eH/fv3qxbUpaenQyYz7OA5EzsREUmCDHreUrYqF7IDGDt2LMaOHavxvcTExMfuGxcXp3N7nGMnIiIyI+yxExGRJPCxrURERGZEBv2GqU1liNtU4iQiIiItsMdORESSIAiCXo8gN5XHlzOxExGRJFTxAW1q+5sCJnYiIpKEqtw97tH9TQHn2ImIiMwIe+xERCQZptHn1g8TOxERSYJUrmPnUDwREZEZYY+diIgkgZe7ERERmRHeeY6IiIhMDnvsREQkCRyKJyIiMiNSufMch+KJiIjMCHvsREQkCRyKJyIiMiNSWRXPxE5ERJIglR67qXwBISIiIi2wx05ERJIglVXxTOxERCQJfAgMERERmRz22ImISBJkECDTY0Bdn32rExM7ERFJAofiiYiIyOSwx05ERJIg/PNPn/1NARM7ERFJAofiiYiIyOSwx05ERJIg6LkqnkPxRERETxGpDMUzsRMRkSRIJbFzjp2IiMiMsMdORESSwMvdiIiIzIhMeLDps78p4FA8ERGRGWGPnYiIJIFD8URERGaEq+KJiIjI5LDHTkREkiBAv+F0E+mwM7ETEZE0cFU8ERERmRwmdlITu2I5WjbzgoONAp07BuJ/J08+tv6O7dvg29obDjYKdPBrg/3fxVdTpES6e659U2xf/DYufz8Pd88uQ6+ubZ+4T2f/5ji+eTLyTnyG3/4biTd7BVZDpGQMggH+mYIaTexHjhxBr1694ObmBkEQsGvXrpoMR/K2bd2CyR9EYPqMSCSdPIO2bX3R+5UQZGdna6yfdPw4Qt8chNDwEfj5f2fRq09fDHitL87/9ls1R06knTpWcvx68RomxGzRqr6nWz3sXDoaR05dROAbH2HZ5sNYOWswgoNaGTlSMobyVfH6bKagRhN7UVERfH19sXz58poMg/6xZPEihI8YhWFh4Wjl44OlK2JhZW2N9XFrNdZfvuxz9AjpiYj3P4B3q1aIjJ4Dv3btEbtiWTVHTqSd73/6HdEr9mL34V+0qj+qfydcvXYLUxbtROqVLMRuOYKdCcl4b0g3I0dKxiAYYDMFNZrYX3rpJcydOxevvvpqTYZBAEpKSnD2zGm88GKwqkwmk+GFF4Jx8uckjfuc+DkJ3V4IVivr3iMEJyqpT2RqAn0b4/CJVLWyg8dTENi2cQ1FRPRkJrUqvri4GMXFxarXBQUFNRiNecnJyUFZWRmcnV3Uyp1dXJCaekHjPlmZmXB2eaS+swuysjKNFidRdXKpZ4es3NtqZdm5BbC3tYJCXhv3iktrKDKqChkEyPQYT5eZSJ/dpBbPxcTEwN7eXrV5eHjUdEhERGQiOBT/FJo6dSry8/NVW0ZGRk2HZDacnJxgYWGB7OwstfLsrCy4urpq3MfF1RXZWY/Uz86Ci4vm+kSmJutWAVwcbdXKnB3tkH/7Lnvr9NQyqcQul8thZ2entpFhWFpaol17fxw+lKAqUyqVOHw4AQHPBmncJ/DZICQeTlArS/jhIAIrqU9kak6cu4KuAS3Vyl581hsnfrlSQxGRXiTSZTepxE7GNW5CBNZ9uRpfbViPCykpGDfmHdwpKsKw0HAAwIiwYZg5faqq/pix4/H9gf1Y/NlCpF64gLmzo3Dm9CmMfndsDZ0B0ePVsbJE2xbuaNvCHQDg5V4PbVu4w8O1LgBg9nu9sWbOUFX91duPoXHDepg3vg9aeLngrdc747Xu7bB00+EaiZ/0I5Xr2Gt08VxhYSHS0tJUr69cuYLk5GQ4OjqiUaNGNRiZNL0+YCBybt7E7OhZyMrMRFtfP/x37364/LNALiMjHTLZv98Fgzp2RNzGzYiOnIHIGdPQrHlzbN2xC8+0bl1Tp0D0WO19PPH9mvGq159Meg0AsHH3z3gr8iu4OtnBw9VR9f6f12/h1fdi8cmkfhgzuCuuZeXhndmb8UNSSrXHTqQtQRRFsaYaT0xMRLduFa8HDQ0NRVxc3BP3LygogL29PbJu5XNYnsxW3f9wBITMl1hWguJfVyM/33h/x8tzRUJyOmxsq95G4e0CvOjXyKixGkKN9ti7du2KGvxeQUREEqLvNLlpDMRzjp2IiMismNQNaoiIiKpMIl12JnYiIpIEfVe2c1U8ERHRU0TfJ7Tx6W5ERERU7dhjJyIiSZDIFDsTOxERSYREMjuH4omIiMwIEzsREUlCTd0rfvny5fDy8oJCoUBgYCBOnjxZad3Vq1ejc+fOqFu3LurWrYvg4ODH1teEiZ2IiCShfFW8PpuutmzZgoiICERGRuLMmTPw9fVFSEgIsrOzNdZPTEzEoEGDcPjwYSQlJcHDwwM9evTAtWvXtG6TiZ2IiMhIFi1ahFGjRiE8PBw+Pj6IjY2FtbU11q5dq7H+pk2b8O6778LPzw/e3t5Ys2YNlEolEhISNNbXhImdiIgkwVCPYy8oKFDbiouLNbZXUlKC06dPIzg4WFUmk8kQHByMpKQkrWK+c+cOSktL4ejo+OTK5W1oXZOIiMiUGSize3h4wN7eXrXFxMRobC4nJwdlZWWqR1+Xc3FxQWZmplYhT548GW5ubmpfDp6El7sRERHpICMjQ+2xrXK53CjtfPTRR/jmm2+QmJgIhUKh9X5M7EREJAmGule8nZ2dVs9jd3JygoWFBbKystTKs7Ky4Orq+th9P/30U3z00Uf44Ycf0LZtW53i5FA8ERFJQnWvire0tIS/v7/awrfyhXBBQUGV7vfJJ59gzpw52L9/Pzp06KDzebLHTkREklATN56LiIhAaGgoOnTogICAACxevBhFRUUIDw8HAAwbNgzu7u6qefqPP/4Ys2bNwubNm+Hl5aWai7exsYGNjY1WbTKxExERGcnAgQNx8+ZNzJo1C5mZmfDz88P+/ftVC+rS09Mhk/07eL5y5UqUlJSgf//+aseJjIxEVFSUVm0ysRMRkTTU0L3ix44di7Fjx2p8LzExUe311atXq9bIQ5jYiYhIEgy1eO5px8VzREREZoQ9diIikoSq3u/94f1NARM7ERFJgkQex86heCIiInPCHjsREUmDRLrsTOxERCQJXBVPREREJoc9diIikgSuiiciIjIjEpliZ2InIiKJkEhm5xw7ERGRGWGPnYiIJEEqq+KZ2ImISBr0XDxnInmdQ/FERETmhD12IiKSBImsnWNiJyIiiZBIZudQPBERkRlhj52IiCSBq+KJiIjMiFRuKcuheCIiIjPCHjsREUmCRNbOMbETEZFESCSzM7ETEZEkSGXxHOfYiYiIzAh77EREJAkC9FwVb7BIjIuJnYiIJEEiU+wciiciIjIn7LETEZEkSOUGNUzsREQkEdIYjOdQPBERkRlhj52IiCSBQ/FERERmRBoD8RyKJyIiMivssRMRkSRwKJ6IiMiMSOVe8UzsREQkDRKZZOccOxERkRlhj52IiCRBIh12JnYiIpIGqSye41A8ERGRGWGPnYiIJIGr4omIiMyJRCbZORRPRERkRthjJyIiSZBIh52JnYiIpIGr4omIiMjksMdOREQSod+qeFMZjGdiJyIiSeBQPBEREZkcJnYiIiIzwqF4IiKSBKkMxTOxExGRJEjllrIciiciIjIj7LETEZEkcCieiIjIjEjllrIciiciIjIj7LETEZE0SKTLzsRORESSwFXxREREZHLYYyciIkngqngiIiIzIpEpdg7FExGRRAgG2Kpg+fLl8PLygkKhQGBgIE6ePPnY+tu2bYO3tzcUCgXatGmD+Ph4ndpjYiciIjKSLVu2ICIiApGRkThz5gx8fX0REhKC7OxsjfWPHz+OQYMGYcSIETh79iz69u2Lvn374rffftO6TUEURdFQJ1DdCgoKYG9vj6xb+bCzs6vpcIiMou5/xtZ0CERGI5aVoPjX1cjPN97f8fJckZmjXxsFBQVwdbLXKdbAwED85z//wbJlywAASqUSHh4eeO+99zBlypQK9QcOHIiioiLs3btXVfbss8/Cz88PsbGxWrXJHjsREUlC+eI5fTZdlJSU4PTp0wgODlaVyWQyBAcHIykpSeM+SUlJavUBICQkpNL6mpj04rnywYbbBQU1HAmR8YhlJTUdApHRlH++q2PwuEDPXFG+/6PHkcvlkMvlFern5OSgrKwMLi4uauUuLi64cOGCxjYyMzM11s/MzNQ6TpNO7Ldv3wYANGvsUcOREBGRPm7fvg17e3ujHNvS0hKurq5oboBcYWNjAw8P9eNERkYiKipK72Mbikkndjc3N2RkZMDW1haCqVxgaOIKCgrg4eGBjIwMrmsgs8PPd/UTRRG3b9+Gm5ub0dpQKBS4cuUKSkr0H/0SRbFCvtHUWwcAJycnWFhYICsrS608KysLrq6uGvdxdXXVqb4mJp3YZTIZGjZsWNNhSJKdnR3/8JHZ4ue7ehmrp/4whUIBhUJh9HYeZmlpCX9/fyQkJKBv374AHiyeS0hIwNixmhfFBgUFISEhARMmTFCVHTx4EEFBQVq3a9KJnYiI6GkWERGB0NBQdOjQAQEBAVi8eDGKiooQHh4OABg2bBjc3d0RExMDABg/fjy6dOmChQsX4pVXXsE333yDU6dOYdWqVVq3ycRORERkJAMHDsTNmzcxa9YsZGZmws/PD/v371ctkEtPT4dM9u8Fah07dsTmzZsxY8YMTJs2Dc2bN8euXbvQunVrrds06evYqfoVFxcjJiYGU6dOrXReichU8fNN5oCJnYiIyIzwBjVERERmhImdiIjIjDCxExERmREmdiIiIjPCxE5a0/WZwkSm4siRI+jVqxfc3NwgCAJ27dpV0yERVRkTO2lF12cKE5mSoqIi+Pr6Yvny5TUdCpHeeLkbaUXXZwoTmSpBELBz507VLUCJTA177PREVXmmMBER1Qwmdnqixz1TWJdnBBMRkfExsRMREZkRJnZ6oqo8U5iIiGoGEzs90cPPFC5X/kxhXZ4RTERExsfHtpJWnvRMYSJTVlhYiLS0NNXrK1euIDk5GY6OjmjUqFENRkakO17uRlpbtmwZFixYoHqm8JIlSxAYGFjTYRHpLTExEd26datQHhoairi4uOoPiEgPTOxERERmhHPsREREZoSJnYiIyIwwsRMREZkRJnYiIiIzwsRORERkRpjYiYiIzAgTOxERkRlhYifSU1hYmNqzu7t27YoJEyZUexyJiYkQBAF5eXmV1hEEAbt27dL6mFFRUfDz89MrrqtXr0IQBCQnJ+t1HCLSDhM7maWwsDAIggBBEGBpaYlmzZph9uzZuH//vtHb/vbbbzFnzhyt6mqTjImIdMF7xZPZ6tmzJ9atW4fi4mLEx8djzJgxqF27NqZOnVqhbklJCSwtLQ3SrqOjo0GOQ0RUFeyxk9mSy+VwdXWFp6cn3nnnHQQHB2P37t0A/h0+nzdvHtzc3NCyZUsAQEZGBgYMGAAHBwc4OjqiT58+uHr1quqYZWVliIiIgIODA+rVq4cPP/wQj96V+dGh+OLiYkyePBkeHh6Qy+Vo1qwZvvzyS1y9elV1f/K6detCEASEhYUBePD0vJiYGDRu3BhWVlbw9fXF9u3b1dqJj49HixYtYGVlhW7duqnFqa3JkyejRYsWsLa2RpMmTTBz5kyUlpZWqPfFF1/Aw8MD1tbWGDBgAPLz89XeX7NmDVq1agWFQgFvb2+sWLFC51iIyDCY2EkyrKysUFJSonqdkJCA1NRUHDx4EHv37kVpaSlCQkJga2uLo0eP4qeffoKNjQ169uyp2m/hwoWIi4vD2rVrcezYMeTm5mLnzp2PbXfYsGH4+uuvsWTJEqSkpOCLL76AjY0NPDw8sGPHDgBAamoqbty4gc8//xwAEBMTgw0bNiA2Nhbnz5/HxIkT8eabb+LHH38E8OALSL9+/dCrVy8kJydj5MiRmDJlis4/E1tbW8TFxeH333/H559/jtWrV+Ozzz5Tq5OWloatW7diz5492L9/P86ePYt3331X9f6mTZswa9YszJs3DykpKZg/fz5mzpyJ9evX6xwPERmASGSGQkNDxT59+oiiKIpKpVI8ePCgKJfLxUmTJqned3FxEYuLi1X7bNy4UWzZsqWoVCpVZcXFxaKVlZV44MABURRFsUGDBuInn3yier+0tFRs2LChqi1RFMUuXbqI48ePF0VRFFNTU0UA4sGDBzXGefjwYRGA+Pfff6vK7t27J1pbW4vHjx9XqztixAhx0KBBoiiK4tSpU0UfHx+19ydPnlzhWI8CIO7cubPS9xcsWCD6+/urXkdGRooWFhbiX3/9pSr77rvvRJlMJt64cUMURVFs2rSpuHnzZrXjzJkzRwwKChJFURSvXLkiAhDPnj1babtEZDicYyeztXfvXtjY2KC0tBRKpRKDBw9GVFSU6v02bdqozaufO3cOaWlpsLW1VTvOvXv3cOnSJeTn5+PGjRtqj6qtVasWOnToUGE4vlxycjIsLCzQpUsXreNOS0vDnTt30L17d7XykpIStGvXDgCQkpJS4ZG5QUFBWrdRbsuWLViyZAkuXbqEwsJC3L9/H3Z2dmp1GjVqBHd3d7V2lEolUlNTYWtri0uXLmHEiBEYNWqUqs79+/dhb2+vczxEpD8mdjJb3bp1w8qVK2FpaQk3NzfUqqX+ca9Tp47a68LCQvj7+2PTpk0VjlW/fv0qxWBlZaXzPoWFhQCAffv2qSVU4MG6AUNJSkrCkCFDEB0djZCQENjb2+Obb77BwoULdY519erVFb5oWFhYGCxWItIeEzuZrTp16qBZs2Za12/fvj22bNkCZ2fnCr3Wcg0aNMCJEyfw/PPPA3jQMz19+jTat2+vsX6bNm2gVCrx448/Ijg4uML75SMGZWVlqjIfHx/I5XKkp6dX2tNv1aqVaiFguZ9//vnJJ/mQ48ePw9PTE9OnT1eV/fnnnxXqpaen4/r163Bzc1O1I5PJ0LJlS7i4uMDNzQ2XL1/GkCFDdGqfiIyDi+eI/jFkyBA4OTmhT58+OHr0KK5cuYLExESMGzcOf/31FwBg/Pjx+Oijj7Br1y5cuHAB77777mOvQffy8kJoaCiGDx+OXbt2qY65detWAICnpycEQcDevXtx8+ZNFBYWwtbWFpMmTcLEiROxfv16XLp0CWfOnMHSpUtVC9JGjx6NP/74Ax988AFSU1OxefNmxMXF6XS+zZs3R3p6Or755htcunQJS5Ys0bgQUKFQIDQ0FOfOncPRo0cxbtw4DBgwAK6urgCA6OhoxMTEYMmSJbh48SJ+/fVXrFu3DosWLdIpHiIyDCZ2on9YW1vjyJEjaNSoEfr164dWrVphxIgRuHfvnqoH//7772Po0KEIDQ1FUFAQbG1t8eqrrz72uCtXrkT//v3x7rvvwtvbG6NGjUJRUREAwN3dHdHR0ZgyZQpcXFwwduxYAMCcOXMwc+ZMxMTEoFWrVujZsyf27duHxo0bA3gw771jxw7s2rULvr6+iI2Nxfz583U63969e2PixIkYO3Ys/Pz8cPz4ccycObNCvWbNmqFfv354+eWX0aNHD7Rt21btcraRI0dizZo1WLduHdq0aYMuXbogLi5OFSsRVS9BrGzVDxEREZkc9tiJiIjMCBM7ERGRGWFiJyIiMiNM7ERERGaEiZ2IiMiMMLETERGZESZ2IiIiM8LETkREZEaY2ImIiMwIEzsREZEZYWInIiIyI0zsREREZuT/AUmscionurdGAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"import scikitplot as skplt\n",
|
||
"from sklearn.ensemble import GradientBoostingClassifier\n",
|
||
"from sklearn.model_selection import cross_validate\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"\n",
|
||
"gd_clf = GradientBoostingClassifier(max_depth=3, n_estimators=100, learning_rate=1.0) \n",
|
||
"gd_clf.fit(X_train_scaled, y_train)\n",
|
||
"#Cross validation\n",
|
||
"accuracy = cross_validate(gd_clf,X_test_scaled,y_test,cv=10)['test_score']\n",
|
||
"print(accuracy)\n",
|
||
"print(\"Test set accuracy with Gradient boosting and scaled data: {:.2f}\".format(gd_clf.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"import scikitplot as skplt\n",
|
||
"y_pred = gd_clf.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = gd_clf.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8de56415",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## XGBoost: Extreme Gradient Boosting\n",
|
||
"\n",
|
||
"[XGBoost](https://github.com/dmlc/xgboost) or Extreme Gradient\n",
|
||
"Boosting, is an optimized distributed gradient boosting library\n",
|
||
"designed to be highly efficient, flexible and portable. It implements\n",
|
||
"machine learning algorithms under the Gradient Boosting\n",
|
||
"framework. XGBoost provides a parallel tree boosting that solve many\n",
|
||
"data science problems in a fast and accurate way. See the [article by Chen and Guestrin](https://arxiv.org/abs/1603.02754).\n",
|
||
"\n",
|
||
"The authors design and build a highly scalable end-to-end tree\n",
|
||
"boosting system. It has a theoretically justified weighted quantile\n",
|
||
"sketch for efficient proposal calculation. It introduces a novel sparsity-aware algorithm for parallel tree learning and an effective cache-aware block structure for out-of-core tree learning.\n",
|
||
"\n",
|
||
"It is now the algorithm which wins essentially all ML competitions!!!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dfc59b18",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Xgboost on the Cancer Data\n",
|
||
"\n",
|
||
"As you will see from the confusion matrix below, XGBoots does an excellent job on the Wisconsin cancer data and outperforms essentially all agorithms we have discussed till now."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "79e4cc00",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n",
|
||
"Test set accuracy with Gradient Boosting and scaled data: 1.00\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
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"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 5000x1000 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.preprocessing import LabelEncoder\n",
|
||
"from sklearn.model_selection import cross_validate\n",
|
||
"import scikitplot as skplt\n",
|
||
"import xgboost as xgb\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"\n",
|
||
"xg_clf = xgb.XGBClassifier()\n",
|
||
"xg_clf.fit(X_train_scaled,y_train)\n",
|
||
"\n",
|
||
"y_test = xg_clf.predict(X_test_scaled)\n",
|
||
"\n",
|
||
"print(\"Test set accuracy with Gradient Boosting and scaled data: {:.2f}\".format(xg_clf.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"import scikitplot as skplt\n",
|
||
"y_pred = xg_clf.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = xg_clf.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"xgb.plot_tree(xg_clf,num_trees=0)\n",
|
||
"plt.rcParams['figure.figsize'] = [50, 10]\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"xgb.plot_importance(xg_clf)\n",
|
||
"plt.rcParams['figure.figsize'] = [5, 5]\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c4700b19",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient boosting, making our own code for a regression case"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "eb0594c5",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Predictions: [1.49999399 1.69995637 3.49991627 3.6998795 4.99984484]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"class DecisionTreeRegressor:\n",
|
||
" def __init__(self, max_depth=3):\n",
|
||
" self.max_depth = max_depth\n",
|
||
" self.tree = None\n",
|
||
" def fit(self, X, y):\n",
|
||
" self.tree = self._grow_tree(X, y)\n",
|
||
" def _grow_tree(self, X, y, depth=0):\n",
|
||
" n_samples, n_features = X.shape\n",
|
||
" if depth < self.max_depth:\n",
|
||
" best_feature, best_threshold = self._best_split(X, y)\n",
|
||
" if best_feature is not None:\n",
|
||
" left_indices = X[:, best_feature] < best_threshold\n",
|
||
" right_indices = X[:, best_feature] >= best_threshold\n",
|
||
" left_child = self._grow_tree(X[left_indices], y[left_indices], depth + 1)\n",
|
||
" right_child = self._grow_tree(X[right_indices], y[right_indices], depth + 1)\n",
|
||
" return (best_feature, best_threshold, left_child, right_child)\n",
|
||
" return np.mean(y)\n",
|
||
" def _best_split(self, X, y):\n",
|
||
" best_mse = float('inf')\n",
|
||
" best_feature, best_threshold = None, None\n",
|
||
" n_samples, n_features = X.shape\n",
|
||
" \n",
|
||
" for feature in range(n_features):\n",
|
||
" thresholds = np.unique(X[:, feature])\n",
|
||
" for threshold in thresholds:\n",
|
||
" left_indices = X[:, feature] < threshold\n",
|
||
" right_indices = X[:, feature] >= threshold\n",
|
||
" if len(y[left_indices]) > 0 and len(y[right_indices]) > 0:\n",
|
||
" left_mse = np.mean((y[left_indices] - np.mean(y[left_indices])) ** 2)\n",
|
||
" right_mse = np.mean((y[right_indices] - np.mean(y[right_indices])) ** 2)\n",
|
||
" mse = (len(y[left_indices]) * left_mse + len(y[right_indices]) * right_mse) / n_samples\n",
|
||
" \n",
|
||
" if mse < best_mse:\n",
|
||
" best_mse = mse\n",
|
||
" best_feature = feature\n",
|
||
" best_threshold = threshold\n",
|
||
" return best_feature, best_threshold\n",
|
||
" def predict(self, X):\n",
|
||
" return np.array([self._predict_sample(sample, self.tree) for sample in X])\n",
|
||
" def _predict_sample(self, sample, node):\n",
|
||
" if isinstance(node, tuple):\n",
|
||
" feature, threshold, left_child, right_child = node\n",
|
||
" if sample[feature] < threshold:\n",
|
||
" return self._predict_sample(sample, left_child)\n",
|
||
" else:\n",
|
||
" return self._predict_sample(sample, right_child)\n",
|
||
" return node\n",
|
||
"class GradientBoostingRegressor:\n",
|
||
" def __init__(self, n_estimators=100, learning_rate=0.1, max_depth=3):\n",
|
||
" self.n_estimators = n_estimators\n",
|
||
" self.learning_rate = learning_rate\n",
|
||
" self.max_depth = max_depth\n",
|
||
" self.models = []\n",
|
||
" def fit(self, X, y):\n",
|
||
" y_pred = np.zeros(y.shape)\n",
|
||
" for _ in range(self.n_estimators):\n",
|
||
" residuals = y - y_pred\n",
|
||
" model = DecisionTreeRegressor(max_depth=self.max_depth)\n",
|
||
" model.fit(X, residuals)\n",
|
||
" y_pred += self.learning_rate * model.predict(X)\n",
|
||
" self.models.append(model)\n",
|
||
" def predict(self, X):\n",
|
||
" y_pred = np.zeros(X.shape[0])\n",
|
||
" for model in self.models:\n",
|
||
" y_pred += self.learning_rate * model.predict(X)\n",
|
||
" return y_pred\n",
|
||
"# Example usage\n",
|
||
"if __name__ == \"__main__\":\n",
|
||
" # Sample data\n",
|
||
" X = np.array([[1], [2], [3], [4], [5]])\n",
|
||
" y = np.array([1.5, 1.7, 3.5, 3.7, 5.0])\n",
|
||
" model = GradientBoostingRegressor(n_estimators=100, learning_rate=0.1, max_depth=2)\n",
|
||
" model.fit(X, y)\n",
|
||
" predictions = model.predict(X)\n",
|
||
" print(\"Predictions:\", predictions)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bbf154c4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Summary of course"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "84d512fc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## What? Me worry? No final exam in this course!\n",
|
||
"<!-- dom:FIGURE: [figures/exam1.jpeg, width=500 frac=0.6] -->\n",
|
||
"<!-- begin figure -->\n",
|
||
"\n",
|
||
"<img src=\"figures/exam1.jpeg\" width=\"500\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
|
||
"<!-- end figure -->"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "71b8eb59",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Topics we have covered this year\n",
|
||
"\n",
|
||
"The course has two central parts\n",
|
||
"\n",
|
||
"1. Statistical analysis and optimization of data\n",
|
||
"\n",
|
||
"2. Machine learning"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "473329b7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Statistical analysis and optimization of data\n",
|
||
"\n",
|
||
"The following topics have been discussed:\n",
|
||
"1. Basic concepts, expectation values, variance, covariance, correlation functions and errors;\n",
|
||
"\n",
|
||
"2. Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;\n",
|
||
"\n",
|
||
"3. Central elements from linear algebra, matrix inversion and SVD\n",
|
||
"\n",
|
||
"4. Gradient methods for data optimization\n",
|
||
"\n",
|
||
"5. Estimation of errors using cross-validation, bootstrapping and jackknife methods;\n",
|
||
"\n",
|
||
"6. Practical optimization using Singular-value decomposition and least squares for parameterizing data.\n",
|
||
"\n",
|
||
"7. Not discussed: Principal Component Analysis to reduce the number of features."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6c94f44a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Machine learning\n",
|
||
"\n",
|
||
"* Linear methods for regression and classification:\n",
|
||
"\n",
|
||
"a. Ordinary Least Squares\n",
|
||
"\n",
|
||
"b. Ridge regression\n",
|
||
"\n",
|
||
"c. Lasso regression\n",
|
||
"\n",
|
||
"d. Logistic regression\n",
|
||
"\n",
|
||
"* Neural networks and deep learning:\n",
|
||
"\n",
|
||
"a. Feed Forward Neural Networks\n",
|
||
"\n",
|
||
"b. Convolutional Neural Networks\n",
|
||
"\n",
|
||
"c. Recurrent Neural Networks\n",
|
||
"\n",
|
||
"* Decisions trees and ensemble methods:\n",
|
||
"\n",
|
||
"a. Decision trees\n",
|
||
"\n",
|
||
"b. Bagging and voting\n",
|
||
"\n",
|
||
"c. Random forests\n",
|
||
"\n",
|
||
"d. Boosting and gradient boosting\n",
|
||
"\n",
|
||
"* Not discussed this year: Support vector machines\n",
|
||
"\n",
|
||
"a. Binary classification and multiclass classification\n",
|
||
"\n",
|
||
"b. Kernel methods\n",
|
||
"\n",
|
||
"c. Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d9942ded",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Learning outcomes and overarching aims of this course\n",
|
||
"\n",
|
||
"The course introduces a variety of central algorithms and methods\n",
|
||
"essential for studies of data analysis and machine learning. The\n",
|
||
"course is project based and through the various projects, normally\n",
|
||
"three, you will be exposed to fundamental research problems\n",
|
||
"in these fields, with the aim to reproduce state of the art scientific\n",
|
||
"results. The students will learn to develop and structure large codes\n",
|
||
"for studying these systems, get acquainted with computing facilities\n",
|
||
"and learn to handle large scientific projects. A good scientific and\n",
|
||
"ethical conduct is emphasized throughout the course. \n",
|
||
"\n",
|
||
"* Understand linear methods for regression and classification;\n",
|
||
"\n",
|
||
"* Learn about neural network;\n",
|
||
"\n",
|
||
"* Learn about bagging, boosting and trees\n",
|
||
"<!-- * Support vector machines -->\n",
|
||
"\n",
|
||
"* Learn about basic data analysis;\n",
|
||
"\n",
|
||
"* Be capable of extending the acquired knowledge to other systems and cases;\n",
|
||
"\n",
|
||
"* Have an understanding of central algorithms used in data analysis and machine learning;\n",
|
||
"\n",
|
||
"* Work on numerical projects to illustrate the theory. The projects play a central role."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7818c700",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Perspective on Machine Learning\n",
|
||
"\n",
|
||
"1. Rapidly emerging application area\n",
|
||
"\n",
|
||
"2. Experiment AND theory are evolving in many many fields. \n",
|
||
"\n",
|
||
"3. Requires education/retraining for more widespread adoption\n",
|
||
"\n",
|
||
"4. A lot of “word-of-mouth” development methods\n",
|
||
"\n",
|
||
"Huge amounts of data sets require automation, classical analysis tools often inadequate. \n",
|
||
"High energy physics hit this wall in the 90’s.\n",
|
||
"In 2009 single top quark production was determined via [Boosted decision trees, Bayesian\n",
|
||
"Neural Networks, etc.](https://arxiv.org/pdf/0903.0850.pdf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cc946602",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Machine Learning Research\n",
|
||
"\n",
|
||
"Where to find recent results:\n",
|
||
"1. Conference proceedings, arXiv and blog posts!\n",
|
||
"\n",
|
||
"2. **NIPS**: [Neural Information Processing Systems](https://papers.nips.cc)\n",
|
||
"\n",
|
||
"3. **ICLR**: [International Conference on Learning Representations](https://openreview.net/group?id=ICLR.cc/2018/Conference#accepted-oral-papers)\n",
|
||
"\n",
|
||
"4. **ICML**: International Conference on Machine Learning\n",
|
||
"\n",
|
||
"5. [Journal of Machine Learning Research](http://www.jmlr.org/papers/v19/) \n",
|
||
"\n",
|
||
"6. [Follow ML on ArXiv](https://arxiv.org/list/cs.LG/recent)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c2b75185",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Starting your Machine Learning Project\n",
|
||
"\n",
|
||
"1. Identify problem type: classification, regression\n",
|
||
"\n",
|
||
"2. Consider your data carefully\n",
|
||
"\n",
|
||
"3. Choose a simple model that fits 1 and 2\n",
|
||
"\n",
|
||
"4. Consider your data carefully again! Think of data representation more carefully.\n",
|
||
"\n",
|
||
"5. Based on your results, feedback loop to earliest possible point"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4600986a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Choose a Model and Algorithm\n",
|
||
"\n",
|
||
"* Supervised?\n",
|
||
"\n",
|
||
"* Start with the simplest model that fits your problem\n",
|
||
"\n",
|
||
"* Start with minimal processing of data"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cfb572d5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Preparing Your Data\n",
|
||
"\n",
|
||
"* Shuffle your data\n",
|
||
"\n",
|
||
"* Mean center your data\n",
|
||
"\n",
|
||
" * Why?\n",
|
||
"\n",
|
||
"* Normalize the variance\n",
|
||
"\n",
|
||
" * Why?\n",
|
||
"\n",
|
||
"* **Whitening**\n",
|
||
"\n",
|
||
" * Decorrelates data\n",
|
||
"\n",
|
||
" * Can be hit or miss\n",
|
||
"\n",
|
||
" * When to do train/test split?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3e38f862",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Which activation and weights to choose in neural networks\n",
|
||
"\n",
|
||
"* RELU? ELU? GELU? etc\n",
|
||
"\n",
|
||
"* Sigmoid or Tanh?\n",
|
||
"\n",
|
||
"* Set all weights to 0? Terrible idea\n",
|
||
"\n",
|
||
"* Set all weights to random values? Small random values"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "76abe122",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Optimization Methods and Hyperparameters\n",
|
||
"* Stochastic gradient descent\n",
|
||
"\n",
|
||
" * Stochastic gradient descent + momentum\n",
|
||
"\n",
|
||
"* State-of-the-art approaches:\n",
|
||
"\n",
|
||
"a. RMSProp\n",
|
||
"\n",
|
||
"b. Adam\n",
|
||
"\n",
|
||
"c. and more\n",
|
||
"\n",
|
||
"Which regularization and hyperparameters? $L_1$ or $L_2$, soft\n",
|
||
"classifiers, depths of trees and many other. Need to explore a large\n",
|
||
"set of hyperparameters and regularization methods."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0b246db8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Resampling\n",
|
||
"\n",
|
||
"When do we resample?\n",
|
||
"\n",
|
||
"1. [Bootstrap](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A)\n",
|
||
"\n",
|
||
"2. [Cross-validation](https://www.youtube.com/watch?v=fSytzGwwBVw&ab_channel=StatQuestwithJoshStarmer)\n",
|
||
"\n",
|
||
"3. Jackknife and many other"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9a6555fc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Other courses on Data science and Machine Learning at UiO\n",
|
||
"\n",
|
||
"1. [FYS5429 – Advanced machine learning and data analysis for the physical sciences](https://www.uio.no/studier/emner/matnat/fys/FYS5429/index-eng.html)\n",
|
||
"\n",
|
||
"2. [IN3050/IN4050 Introduction to Artificial Intelligence and Machine Learning](https://www.uio.no/studier/emner/matnat/ifi/IN3050/index-eng.html). Introductory course in machine learning and AI\n",
|
||
"\n",
|
||
"3. [STK-INF3000/4000 Selected Topics in Data Science](http://www.uio.no/studier/emner/matnat/math/STK-INF3000/index-eng.html). The course provides insight into selected contemporary relevant topics within Data Science. \n",
|
||
"\n",
|
||
"4. [IN4080 Natural Language Processing](https://www.uio.no/studier/emner/matnat/ifi/IN4080/index.html). Probabilistic and machine learning techniques applied to natural language processing. \n",
|
||
"\n",
|
||
"5. [STK-IN4300 – Statistical learning methods in Data Science](https://www.uio.no/studier/emner/matnat/math/STK-IN4300/index-eng.html). An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.\n",
|
||
"\n",
|
||
"6. [IN-STK5000 Responsible Data Science](https://www.uio.no/studier/emner/matnat/ifi/IN-STK5000/index-eng.html). Methods for adaptive collection and processing of data based on machine learning techniques. \n",
|
||
"\n",
|
||
"7. [IN4310 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN4310/index.html). An introduction to deep learning with particular emphasis on applications within Image analysis, but useful for other application areas too.\n",
|
||
"\n",
|
||
"8. [IN5310 – Advanced Deep Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5310/index.html)\n",
|
||
"\n",
|
||
"9. [IN5490 – Advanced Topics in Artificial Intelligence for Intelligent Systems](https://www.uio.no/studier/emner/matnat/ifi/IN5490/index.html)\n",
|
||
"\n",
|
||
"10. [TEK5040 – Deep learning for autonomous systems](https://www.uio.no/studier/emner/matnat/its/TEK5040/). The course addresses advanced algorithms and architectures for deep learning with neural networks. The course provides an introduction to how deep-learning techniques can be used in the construction of key parts of advanced autonomous systems that exist in physical environments and cyber environments."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c2561e72",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Additional courses of interest\n",
|
||
"\n",
|
||
"1. [STK4051 Computational Statistics](https://www.uio.no/studier/emner/matnat/math/STK4051/index-eng.html)\n",
|
||
"\n",
|
||
"2. [STK4021 Applied Bayesian Analysis and Numerical Methods](https://www.uio.no/studier/emner/matnat/math/STK4021/index-eng.html)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "796637c8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## What's the future like?\n",
|
||
"\n",
|
||
"Based on multi-layer nonlinear neural networks, deep learning can\n",
|
||
"learn directly from raw data, automatically extract and abstract\n",
|
||
"features from layer to layer, and then achieve the goal of regression,\n",
|
||
"classification, or ranking. Deep learning has made breakthroughs in\n",
|
||
"computer vision, speech processing and natural language, and reached\n",
|
||
"or even surpassed human level. The success of deep learning is mainly\n",
|
||
"due to the three factors: big data, big model, and big computing.\n",
|
||
"\n",
|
||
"In the past few decades, many different architectures of deep neural\n",
|
||
"networks have been proposed, such as\n",
|
||
"1. Convolutional neural networks, which are mostly used in image and video data processing, and have also been applied to sequential data such as text processing;\n",
|
||
"\n",
|
||
"2. Recurrent neural networks, which can process sequential data of variable length and have been widely used in natural language understanding and speech processing;\n",
|
||
"\n",
|
||
"3. Encoder-decoder framework, which is mostly used for image or sequence generation, such as machine translation, text summarization, and image captioning."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6afdb59e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Types of Machine Learning, a repetition\n",
|
||
"\n",
|
||
"The approaches to machine learning are many, but are often split into two main categories. \n",
|
||
"In *supervised learning* we know the answer to a problem,\n",
|
||
"and let the computer deduce the logic behind it. On the other hand, *unsupervised learning*\n",
|
||
"is a method for finding patterns and relationship in data sets without any prior knowledge of the system.\n",
|
||
"Some authours also operate with a third category, namely *reinforcement learning*. This is a paradigm \n",
|
||
"of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, \n",
|
||
"solely from rewards and punishment.\n",
|
||
"\n",
|
||
"Another way to categorize machine learning tasks is to consider the desired output of a system.\n",
|
||
"Some of the most common tasks are:\n",
|
||
"\n",
|
||
" * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.\n",
|
||
"\n",
|
||
" * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.\n",
|
||
"\n",
|
||
" * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.\n",
|
||
"\n",
|
||
" * Other unsupervised learning algortihms like **Boltzmann machines**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "95097424",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Why Boltzmann machines?\n",
|
||
"\n",
|
||
"What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. \n",
|
||
"One of the major reasons is that they can be stacked layer-wise to build deep neural networks that capture complicated statistics.\n",
|
||
"\n",
|
||
"The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images. \n",
|
||
"\n",
|
||
"Furthermore, they have been used to solve complicated [quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "31a33cea",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Boltzmann Machines\n",
|
||
"\n",
|
||
"Why use a generative model rather than the more well known discriminative deep neural networks (DNN)? \n",
|
||
"\n",
|
||
"* Discriminitave methods have several limitations: They are mainly supervised learning methods, thus requiring labeled data. And there are tasks they cannot accomplish, like drawing new examples from an unknown probability distribution.\n",
|
||
"\n",
|
||
"* A generative model can learn to represent and sample from a probability distribution. The core idea is to learn a parametric model of the probability distribution from which the training data was drawn. As an example\n",
|
||
"\n",
|
||
"a. A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.\n",
|
||
"\n",
|
||
"b. Generate a sample of an ordered or disordered phase, having been given samples of such phases.\n",
|
||
"\n",
|
||
"c. Model the trial function for [Monte Carlo calculations](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d6583875",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Some similarities and differences from DNNs\n",
|
||
"\n",
|
||
"1. Both use gradient-descent based learning procedures for minimizing cost functions\n",
|
||
"\n",
|
||
"2. Energy based models don't use backpropagation and automatic differentiation for computing gradients, instead turning to Markov Chain Monte Carlo methods.\n",
|
||
"\n",
|
||
"3. DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.\n",
|
||
"\n",
|
||
"History: The RBM was developed by amongst others [Geoffrey Hinton](https://en.wikipedia.org/wiki/Geoffrey_Hinton), called by some the \"Godfather of Deep Learning\", working with the University of Toronto and Google."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "285bbf5d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Boltzmann machines (BM)\n",
|
||
"\n",
|
||
"A BM is what we would call an undirected probabilistic graphical model\n",
|
||
"with stochastic continuous or discrete units.\n",
|
||
"\n",
|
||
"It is interpreted as a stochastic recurrent neural network where the\n",
|
||
"state of each unit(neurons/nodes) depends on the units it is connected\n",
|
||
"to. The weights in the network represent thus the strength of the\n",
|
||
"interaction between various units/nodes.\n",
|
||
"\n",
|
||
"It turns into a Hopfield network if we choose deterministic rather\n",
|
||
"than stochastic units. In contrast to a Hopfield network, a BM is a\n",
|
||
"so-called generative model. It allows us to generate new samples from\n",
|
||
"the learned distribution."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5b51dec9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## A standard BM setup\n",
|
||
"\n",
|
||
"A standard BM network is divided into a set of observable and visible units $\\hat{x}$ and a set of unknown hidden units/nodes $\\hat{h}$.\n",
|
||
"\n",
|
||
"Additionally there can be bias nodes for the hidden and visible layers. These biases are normally set to $1$.\n",
|
||
"\n",
|
||
"BMs are stackable, meaning they cwe can train a BM which serves as input to another BM. We can construct deep networks for learning complex PDFs. The layers can be trained one after another, a feature which makes them popular in deep learning\n",
|
||
"\n",
|
||
"However, they are often hard to train. This leads to the introduction of so-called restricted BMs, or RBMS.\n",
|
||
"Here we take away all lateral connections between nodes in the visible layer as well as connections between nodes in the hidden layer. The network is illustrated in the figure below."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4cb37b8f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The structure of the RBM network\n",
|
||
"\n",
|
||
"<!-- dom:FIGURE: [figures/RBM.png, width=800 frac=1.0] -->\n",
|
||
"<!-- begin figure -->\n",
|
||
"\n",
|
||
"<img src=\"figures/RBM.png\" width=\"800\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
|
||
"<!-- end figure -->"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "45fe33d7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The network\n",
|
||
"\n",
|
||
"**The network layers**:\n",
|
||
"1. A function $\\mathbf{x}$ that represents the visible layer, a vector of $M$ elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.\n",
|
||
"\n",
|
||
"2. The function $\\mathbf{h}$ represents the hidden, or latent, layer. A vector of $N$ elements (nodes). Also called \"feature detectors\"."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3bbbaa88",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Goals\n",
|
||
"\n",
|
||
"The goal of the hidden layer is to increase the model's expressive\n",
|
||
"power. We encode complex interactions between visible variables by\n",
|
||
"introducing additional, hidden variables that interact with visible\n",
|
||
"degrees of freedom in a simple manner, yet still reproduce the complex\n",
|
||
"correlations between visible degrees in the data once marginalized\n",
|
||
"over (integrated out).\n",
|
||
"\n",
|
||
"**The network parameters, to be optimized/learned**:\n",
|
||
"1. $\\mathbf{a}$ represents the visible bias, a vector of same length as $\\mathbf{x}$.\n",
|
||
"\n",
|
||
"2. $\\mathbf{b}$ represents the hidden bias, a vector of same lenght as $\\mathbf{h}$.\n",
|
||
"\n",
|
||
"3. $W$ represents the interaction weights, a matrix of size $M\\times N$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d6a9f606",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Joint distribution\n",
|
||
"\n",
|
||
"The restricted Boltzmann machine is described by a Boltzmann distribution"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "81aaff6e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto1\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tP_{rbm}(\\mathbf{x},\\mathbf{h}) = \\frac{1}{Z} e^{-\\frac{1}{T_0}E(\\mathbf{x},\\mathbf{h})},\n",
|
||
"\\label{_auto1} \\tag{1}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9f856eb3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $Z$ is the normalization constant or partition function, defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f15429d1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto2\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tZ = \\int \\int e^{-\\frac{1}{T_0}E(\\mathbf{x},\\mathbf{h})} d\\mathbf{x} d\\mathbf{h}.\n",
|
||
"\\label{_auto2} \\tag{2}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e8a8f8e7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"It is common to ignore $T_0$ by setting it to one."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4fb17989",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Network Elements, the energy function\n",
|
||
"\n",
|
||
"The function $E(\\mathbf{x},\\mathbf{h})$ gives the **energy** of a\n",
|
||
"configuration (pair of vectors) $(\\mathbf{x}, \\mathbf{h})$. The lower\n",
|
||
"the energy of a configuration, the higher the probability of it. This\n",
|
||
"function also depends on the parameters $\\mathbf{a}$, $\\mathbf{b}$ and\n",
|
||
"$W$. Thus, when we adjust them during the learning procedure, we are\n",
|
||
"adjusting the energy function to best fit our problem.\n",
|
||
"\n",
|
||
"An expression for the energy function is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0bed5ddd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"E(\\hat{x},\\hat{h}) = -\\sum_{ia}^{NA}b_i^a \\alpha_i^a(x_i)-\\sum_{jd}^{MD}c_j^d \\beta_j^d(h_j)-\\sum_{ijad}^{NAMD}b_i^a \\alpha_i^a(x_i)c_j^d \\beta_j^d(h_j)w_{ij}^{ad}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f8e64229",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here $\\beta_j^d(h_j)$ and $\\alpha_i^a(x_j)$ are so-called transfer functions that map a given input value to a desired feature value. The labels $a$ and $d$ denote that there can be multiple transfer functions per variable. The first sum depends only on the visible units. The second on the hidden ones. **Note** that there is no connection between nodes in a layer.\n",
|
||
"\n",
|
||
"The quantities $b$ and $c$ can be interpreted as the visible and hidden biases, respectively.\n",
|
||
"\n",
|
||
"The connection between the nodes in the two layers is given by the weights $w_{ij}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f8f02179",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Defining different types of RBMs\n",
|
||
"There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function $E(\\mathbf{x},\\mathbf{h})$. \n",
|
||
"\n",
|
||
"**Binary-Binary RBM:**\n",
|
||
"\n",
|
||
"RBMs were first developed using binary units in both the visible and hidden layer. The corresponding energy function is defined as follows:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "19008689",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto3\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tE(\\mathbf{x}, \\mathbf{h}) = - \\sum_i^M x_i a_i- \\sum_j^N b_j h_j - \\sum_{i,j}^{M,N} x_i w_{ij} h_j,\n",
|
||
"\\label{_auto3} \\tag{3}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a3d31b3a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where the binary values taken on by the nodes are most commonly 0 and 1.\n",
|
||
"\n",
|
||
"**Gaussian-Binary RBM:**\n",
|
||
"\n",
|
||
"Another varient is the RBM where the visible units are Gaussian while the hidden units remain binary:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "79d29641",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto4\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tE(\\mathbf{x}, \\mathbf{h}) = \\sum_i^M \\frac{(x_i - a_i)^2}{2\\sigma_i^2} - \\sum_j^N b_j h_j - \\sum_{i,j}^{M,N} \\frac{x_i w_{ij} h_j}{\\sigma_i^2}. \n",
|
||
"\\label{_auto4} \\tag{4}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4d19d779",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More about RBMs\n",
|
||
"1. Useful when we model continuous data (i.e., we wish $\\mathbf{x}$ to be continuous)\n",
|
||
"\n",
|
||
"2. Requires a smaller learning rate, since there's no upper bound to the value a component might take in the reconstruction\n",
|
||
"\n",
|
||
"Other types of units include:\n",
|
||
"1. Softmax and multinomial units\n",
|
||
"\n",
|
||
"2. Gaussian visible and hidden units\n",
|
||
"\n",
|
||
"3. Binomial units\n",
|
||
"\n",
|
||
"4. Rectified linear units\n",
|
||
"\n",
|
||
"To read more, see [Lectures on Boltzmann machines in Physics](https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/notebook2/ipynb/notebook2.ipynb)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b8fa06ec",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Autoencoders: Overarching view\n",
|
||
"\n",
|
||
"Autoencoders are artificial neural networks capable of learning\n",
|
||
"efficient representations of the input data (these representations are called codings) without\n",
|
||
"any supervision (i.e., the training set is unlabeled). These codings\n",
|
||
"typically have a much lower dimensionality than the input data, making\n",
|
||
"autoencoders useful for dimensionality reduction. \n",
|
||
"\n",
|
||
"More importantly, autoencoders act as powerful feature detectors, and\n",
|
||
"they can be used for unsupervised pretraining of deep neural networks.\n",
|
||
"\n",
|
||
"Lastly, they are capable of randomly generating new data that looks\n",
|
||
"very similar to the training data; this is called a generative\n",
|
||
"model. For example, you could train an autoencoder on pictures of\n",
|
||
"faces, and it would then be able to generate new faces. Surprisingly,\n",
|
||
"autoencoders work by simply learning to copy their inputs to their\n",
|
||
"outputs. This may sound like a trivial task, but we will see that\n",
|
||
"constraining the network in various ways can make it rather\n",
|
||
"difficult. For example, you can limit the size of the internal\n",
|
||
"representation, or you can add noise to the inputs and train the\n",
|
||
"network to recover the original inputs. These constraints prevent the\n",
|
||
"autoencoder from trivially copying the inputs directly to the outputs,\n",
|
||
"which forces it to learn efficient ways of representing the data. In\n",
|
||
"short, the codings are byproducts of the autoencoder’s attempt to\n",
|
||
"learn the identity function under some constraints.\n",
|
||
"\n",
|
||
"[Video on autoencoders](https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3)\n",
|
||
"\n",
|
||
"See also A. Geron's textbook, chapter 15."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "262fc510",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Bayesian Machine Learning\n",
|
||
"\n",
|
||
"This is an important topic if we aim at extracting a probability\n",
|
||
"distribution. This gives us also a confidence interval and error\n",
|
||
"estimates.\n",
|
||
"\n",
|
||
"Bayesian machine learning allows us to encode our prior beliefs about\n",
|
||
"what those models should look like, independent of what the data tells\n",
|
||
"us. This is especially useful when we don’t have a ton of data to\n",
|
||
"confidently learn our model.\n",
|
||
"\n",
|
||
"[Video on Bayesian deep learning](https://www.youtube.com/watch?v=E1qhGw8QxqY&ab_channel=AndrewGordonWilson)\n",
|
||
"\n",
|
||
"See also the [slides here](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Articles/lec03.pdf)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "36608f14",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Reinforcement Learning\n",
|
||
"\n",
|
||
"Reinforcement Learning (RL) is one of the most exciting fields of\n",
|
||
"Machine Learning today, and also one of the oldest. It has been around\n",
|
||
"since the 1950s, producing many interesting applications over the\n",
|
||
"years.\n",
|
||
"\n",
|
||
"It studies\n",
|
||
"how agents take actions based on trial and error, so as to maximize\n",
|
||
"some notion of cumulative reward in a dynamic system or\n",
|
||
"environment. Due to its generality, the problem has also been studied\n",
|
||
"in many other disciplines, such as game theory, control theory,\n",
|
||
"operations research, information theory, multi-agent systems, swarm\n",
|
||
"intelligence, statistics, and genetic algorithms.\n",
|
||
"\n",
|
||
"In March 2016, AlphaGo, a computer program that plays the board game\n",
|
||
"Go, beat Lee Sedol in a five-game match. This was the first time a\n",
|
||
"computer Go program had beaten a 9-dan (highest rank) professional\n",
|
||
"without handicaps. AlphaGo is based on deep convolutional neural\n",
|
||
"networks and reinforcement learning. AlphaGo’s victory was a major\n",
|
||
"milestone in artificial intelligence and it has also made\n",
|
||
"reinforcement learning a hot research area in the field of machine\n",
|
||
"learning.\n",
|
||
"\n",
|
||
"[Lecture on Reinforcement Learning](https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline).\n",
|
||
"\n",
|
||
"See also A. Geron's textbook, chapter 16."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a2b4652f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Transfer learning\n",
|
||
"\n",
|
||
"The goal of transfer learning is to transfer the model or knowledge\n",
|
||
"obtained from a source task to the target task, in order to resolve\n",
|
||
"the issues of insufficient training data in the target task. The\n",
|
||
"rationality of doing so lies in that usually the source and target\n",
|
||
"tasks have inter-correlations, and therefore either the features,\n",
|
||
"samples, or models in the source task might provide useful information\n",
|
||
"for us to better solve the target task. Transfer learning is a hot\n",
|
||
"research topic in recent years, with many problems still waiting to be studied.\n",
|
||
"\n",
|
||
"[Lecture on transfer learning](https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8cef8c03",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Adversarial learning\n",
|
||
"\n",
|
||
"The conventional deep generative model has a potential problem: the\n",
|
||
"model tends to generate extreme instances to maximize the\n",
|
||
"probabilistic likelihood, which will hurt its performance. Adversarial\n",
|
||
"learning utilizes the adversarial behaviors (e.g., generating\n",
|
||
"adversarial instances or training an adversarial model) to enhance the\n",
|
||
"robustness of the model and improve the quality of the generated\n",
|
||
"data. In recent years, one of the most promising unsupervised learning\n",
|
||
"technologies, generative adversarial networks (GAN), has already been\n",
|
||
"successfully applied to image, speech, and text.\n",
|
||
"\n",
|
||
"[Lecture on adversial learning](https://www.youtube.com/watch?v=CIfsB_EYsVI&ab_channel=StanfordUniversitySchoolofEngineering)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "df85a3e6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Dual learning\n",
|
||
"\n",
|
||
"Dual learning is a new learning paradigm, the basic idea of which is\n",
|
||
"to use the primal-dual structure between machine learning tasks to\n",
|
||
"obtain effective feedback/regularization, and guide and strengthen the\n",
|
||
"learning process, thus reducing the requirement of large-scale labeled\n",
|
||
"data for deep learning. The idea of dual learning has been applied to\n",
|
||
"many problems in machine learning, including machine translation,\n",
|
||
"image style conversion, question answering and generation, image\n",
|
||
"classification and generation, text classification and generation,\n",
|
||
"image-to-text, and text-to-image."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f01aaa3c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Distributed machine learning\n",
|
||
"\n",
|
||
"Distributed computation will speed up machine learning algorithms,\n",
|
||
"significantly improve their efficiency, and thus enlarge their\n",
|
||
"application. When distributed meets machine learning, more than just\n",
|
||
"implementing the machine learning algorithms in parallel is required."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0005330c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Meta learning\n",
|
||
"\n",
|
||
"Meta learning is an emerging research direction in machine\n",
|
||
"learning. Roughly speaking, meta learning concerns learning how to\n",
|
||
"learn, and focuses on the understanding and adaptation of the learning\n",
|
||
"itself, instead of just completing a specific learning task. That is,\n",
|
||
"a meta learner needs to be able to evaluate its own learning methods\n",
|
||
"and adjust its own learning methods according to specific learning\n",
|
||
"tasks."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "efcfaccf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The Challenges Facing Machine Learning\n",
|
||
"\n",
|
||
"While there has been much progress in machine learning, there are also challenges.\n",
|
||
"\n",
|
||
"For example, the mainstream machine learning technologies are\n",
|
||
"black-box approaches, making us concerned about their potential\n",
|
||
"risks. To tackle this challenge, we may want to make machine learning\n",
|
||
"more explainable and controllable. As another example, the\n",
|
||
"computational complexity of machine learning algorithms is usually\n",
|
||
"very high and we may want to invent lightweight algorithms or\n",
|
||
"implementations. Furthermore, in many domains such as physics,\n",
|
||
"chemistry, biology, and social sciences, people usually seek elegantly\n",
|
||
"simple equations (e.g., the Schrödinger equation) to uncover the\n",
|
||
"underlying laws behind various phenomena. In the field of machine\n",
|
||
"learning, can we reveal simple laws instead of designing more complex\n",
|
||
"models for data fitting? Although there are many challenges, we are\n",
|
||
"still very optimistic about the future of machine learning. As we look\n",
|
||
"forward to the future, here are what we think the research hotspots in\n",
|
||
"the next ten years will be.\n",
|
||
"\n",
|
||
"See the article on [Discovery of Physics From Data: Universal Laws and Discrepancies](https://www.frontiersin.org/articles/10.3389/frai.2020.00025/full)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f7b109c9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Explainable machine learning\n",
|
||
"\n",
|
||
"Machine learning, especially deep learning, evolves rapidly. The\n",
|
||
"ability gap between machine and human on many complex cognitive tasks\n",
|
||
"becomes narrower and narrower. However, we are still in the very early\n",
|
||
"stage in terms of explaining why those effective models work and how\n",
|
||
"they work.\n",
|
||
"\n",
|
||
"**What is missing: the gap between correlation and causation**. Standard Machine Learning is based on what e have called a frequentist approach. \n",
|
||
"\n",
|
||
"Most\n",
|
||
"machine learning techniques, especially the statistical ones, depend\n",
|
||
"highly on correlations in data sets to make predictions and analyses. In\n",
|
||
"contrast, rational humans tend to reply on clear and trustworthy\n",
|
||
"causality relations obtained via logical reasoning on real and clear\n",
|
||
"facts. It is one of the core goals of explainable machine learning to\n",
|
||
"transition from solving problems by data correlation to solving\n",
|
||
"problems by logical reasoning.\n",
|
||
"\n",
|
||
"**Bayesian Machine Learning is one of the exciting research directions in this field**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e9142380",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum machine learning\n",
|
||
"\n",
|
||
"Quantum machine learning is an emerging interdisciplinary research\n",
|
||
"area at the intersection of quantum computing and machine learning.\n",
|
||
"\n",
|
||
"Quantum computers use effects such as quantum coherence and quantum\n",
|
||
"entanglement to process information, which is fundamentally different\n",
|
||
"from classical computers. Quantum algorithms have surpassed the best\n",
|
||
"classical algorithms in several problems (e.g., searching for an\n",
|
||
"unsorted database, inverting a sparse matrix), which we call quantum\n",
|
||
"acceleration.\n",
|
||
"\n",
|
||
"When quantum computing meets machine learning, it can be a mutually\n",
|
||
"beneficial and reinforcing process, as it allows us to take advantage\n",
|
||
"of quantum computing to improve the performance of classical machine\n",
|
||
"learning algorithms. In addition, we can also use the machine learning\n",
|
||
"algorithms (on classic computers) to analyze and improve quantum\n",
|
||
"computing systems.\n",
|
||
"\n",
|
||
"[Lecture on Quantum ML](https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29).\n",
|
||
"\n",
|
||
"[Read interview with Maria Schuld on her work on Quantum Machine Learning](https://physics.aps.org/articles/v13/179?utm_campaign=weekly&utm_medium=email&utm_source=emailalert). See also [her recent textbook](https://www.springer.com/gp/book/9783319964232)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cb638c92",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum machine learning algorithms based on linear algebra\n",
|
||
"\n",
|
||
"Many quantum machine learning algorithms are based on variants of\n",
|
||
"quantum algorithms for solving linear equations, which can efficiently\n",
|
||
"solve N-variable linear equations with complexity of O(log2 N) under\n",
|
||
"certain conditions. The quantum matrix inversion algorithm can\n",
|
||
"accelerate many machine learning methods, such as least square linear\n",
|
||
"regression, least square version of support vector machine, Gaussian\n",
|
||
"process, and more. The training of these algorithms can be simplified\n",
|
||
"to solve linear equations. The key bottleneck of this type of quantum\n",
|
||
"machine learning algorithms is data input—that is, how to initialize\n",
|
||
"the quantum system with the entire data set. Although efficient\n",
|
||
"data-input algorithms exist for certain situations, how to efficiently\n",
|
||
"input data into a quantum system is as yet unknown for most cases."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "676fd56e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum reinforcement learning\n",
|
||
"\n",
|
||
"In quantum reinforcement learning, a quantum agent interacts with the\n",
|
||
"classical environment to obtain rewards from the environment, so as to\n",
|
||
"adjust and improve its behavioral strategies. In some cases, it\n",
|
||
"achieves quantum acceleration by the quantum processing capabilities\n",
|
||
"of the agent or the possibility of exploring the environment through\n",
|
||
"quantum superposition. Such algorithms have been proposed in\n",
|
||
"superconducting circuits and systems of trapped ions."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ac1d93d3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum deep learning\n",
|
||
"\n",
|
||
"Dedicated quantum information processors, such as quantum annealers\n",
|
||
"and programmable photonic circuits, are well suited for building deep\n",
|
||
"quantum networks. The simplest deep quantum network is the Boltzmann\n",
|
||
"machine. The classical Boltzmann machine consists of bits with tunable\n",
|
||
"interactions and is trained by adjusting the interaction of these bits\n",
|
||
"so that the distribution of its expression conforms to the statistics\n",
|
||
"of the data. To quantize the Boltzmann machine, the neural network can\n",
|
||
"simply be represented as a set of interacting quantum spins that\n",
|
||
"correspond to an adjustable Ising model. Then, by initializing the\n",
|
||
"input neurons in the Boltzmann machine to a fixed state and allowing\n",
|
||
"the system to heat up, we can read out the output qubits to get the\n",
|
||
"result."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5047fcb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Social machine learning\n",
|
||
"\n",
|
||
"Machine learning aims to imitate how humans\n",
|
||
"learn. While we have developed successful machine learning algorithms,\n",
|
||
"until now we have ignored one important fact: humans are social. Each\n",
|
||
"of us is one part of the total society and it is difficult for us to\n",
|
||
"live, learn, and improve ourselves, alone and isolated. Therefore, we\n",
|
||
"should design machines with social properties. Can we let machines\n",
|
||
"evolve by imitating human society so as to achieve more effective,\n",
|
||
"intelligent, interpretable “social machine learning”?\n",
|
||
"\n",
|
||
"And much more."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bdd66000",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The last words?\n",
|
||
"\n",
|
||
"Early computer scientist Alan Kay said, **The best way to predict the\n",
|
||
"future is to create it**. Therefore, all machine learning\n",
|
||
"practitioners, whether scholars or engineers, professors or students,\n",
|
||
"need to work together to advance these important research\n",
|
||
"topics. Together, we will not just predict the future, but create it."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7fb56aeb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Best wishes to you all and thanks so much for your heroic efforts this semester\n",
|
||
"\n",
|
||
"<!-- dom:FIGURE: [figures/Nebbdyr2.png, width=500 frac=0.6] -->\n",
|
||
"<!-- begin figure -->\n",
|
||
"\n",
|
||
"<img src=\"figures/Nebbdyr2.png\" width=\"500\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
|
||
"<!-- end figure -->"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.15"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |