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<!DOCTYPE html>
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<title>Chapter 19 Conclusion | Machine Learning for Factor Investing</title>
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<li class="chapter" data-level="1" data-path="preface.html"><a href="preface.html"><i class="fa fa-check"></i><b>1</b> Preface</a><ul>
<li class="chapter" data-level="1.1" data-path="preface.html"><a href="preface.html#foreword"><i class="fa fa-check"></i><b>1.1</b> Foreword</a></li>
<li class="chapter" data-level="1.2" data-path="preface.html"><a href="preface.html#what-this-book-is-not-about"><i class="fa fa-check"></i><b>1.2</b> What this book is not about</a></li>
<li class="chapter" data-level="1.3" data-path="preface.html"><a href="preface.html#the-targeted-audience"><i class="fa fa-check"></i><b>1.3</b> The targeted audience</a></li>
<li class="chapter" data-level="1.4" data-path="preface.html"><a href="preface.html#how-this-book-is-structured"><i class="fa fa-check"></i><b>1.4</b> How this book is structured</a></li>
<li class="chapter" data-level="1.5" data-path="preface.html"><a href="preface.html#companion-website"><i class="fa fa-check"></i><b>1.5</b> Companion website</a></li>
<li class="chapter" data-level="1.6" data-path="preface.html"><a href="preface.html#why-r"><i class="fa fa-check"></i><b>1.6</b> Why R?</a></li>
<li class="chapter" data-level="1.7" data-path="preface.html"><a href="preface.html#coding-instructions"><i class="fa fa-check"></i><b>1.7</b> Coding instructions</a></li>
<li class="chapter" data-level="1.8" data-path="preface.html"><a href="preface.html#acknowledgements"><i class="fa fa-check"></i><b>1.8</b> Acknowledgements</a></li>
<li class="chapter" data-level="1.9" data-path="preface.html"><a href="preface.html#future-developments"><i class="fa fa-check"></i><b>1.9</b> Future developments</a></li>
</ul></li>
<li class="chapter" data-level="2" data-path="notdata.html"><a href="notdata.html"><i class="fa fa-check"></i><b>2</b> Notations and data</a><ul>
<li class="chapter" data-level="2.1" data-path="notdata.html"><a href="notdata.html#notations"><i class="fa fa-check"></i><b>2.1</b> Notations</a></li>
<li class="chapter" data-level="2.2" data-path="notdata.html"><a href="notdata.html#dataset"><i class="fa fa-check"></i><b>2.2</b> Dataset</a></li>
</ul></li>
<li class="chapter" data-level="3" data-path="intro.html"><a href="intro.html"><i class="fa fa-check"></i><b>3</b> Introduction</a><ul>
<li class="chapter" data-level="3.1" data-path="intro.html"><a href="intro.html#context"><i class="fa fa-check"></i><b>3.1</b> Context</a></li>
<li class="chapter" data-level="3.2" data-path="intro.html"><a href="intro.html#portfolio-construction-the-workflow"><i class="fa fa-check"></i><b>3.2</b> Portfolio construction: the workflow</a></li>
<li class="chapter" data-level="3.3" data-path="intro.html"><a href="intro.html#machine-learning-is-no-magic-wand"><i class="fa fa-check"></i><b>3.3</b> Machine Learning is no Magic Wand</a></li>
</ul></li>
<li class="chapter" data-level="4" data-path="factor.html"><a href="factor.html"><i class="fa fa-check"></i><b>4</b> Factor investing and asset pricing anomalies</a><ul>
<li class="chapter" data-level="4.1" data-path="factor.html"><a href="factor.html#introduction"><i class="fa fa-check"></i><b>4.1</b> Introduction</a></li>
<li class="chapter" data-level="4.2" data-path="factor.html"><a href="factor.html#detecting-anomalies"><i class="fa fa-check"></i><b>4.2</b> Detecting anomalies</a><ul>
<li class="chapter" data-level="4.2.1" data-path="factor.html"><a href="factor.html#simple-portfolio-sorts"><i class="fa fa-check"></i><b>4.2.1</b> Simple portfolio sorts</a></li>
<li class="chapter" data-level="4.2.2" data-path="factor.html"><a href="factor.html#factors"><i class="fa fa-check"></i><b>4.2.2</b> Factors</a></li>
<li class="chapter" data-level="4.2.3" data-path="factor.html"><a href="factor.html#predictive-regressions-sorts-and-p-value-issues"><i class="fa fa-check"></i><b>4.2.3</b> Predictive regressions, sorts, and p-value issues</a></li>
<li class="chapter" data-level="4.2.4" data-path="factor.html"><a href="factor.html#fama-macbeth-regressions"><i class="fa fa-check"></i><b>4.2.4</b> Fama-Macbeth regressions</a></li>
<li class="chapter" data-level="4.2.5" data-path="factor.html"><a href="factor.html#factor-competition"><i class="fa fa-check"></i><b>4.2.5</b> Factor competition</a></li>
<li class="chapter" data-level="4.2.6" data-path="factor.html"><a href="factor.html#advanced-techniques"><i class="fa fa-check"></i><b>4.2.6</b> Advanced techniques</a></li>
</ul></li>
<li class="chapter" data-level="4.3" data-path="factor.html"><a href="factor.html#factors-or-characteristics"><i class="fa fa-check"></i><b>4.3</b> Factors or characteristics?</a></li>
<li class="chapter" data-level="4.4" data-path="factor.html"><a href="factor.html#momentum-and-timing"><i class="fa fa-check"></i><b>4.4</b> Momentum and timing</a><ul>
<li class="chapter" data-level="4.4.1" data-path="factor.html"><a href="factor.html#factor-momentum"><i class="fa fa-check"></i><b>4.4.1</b> Factor momentum</a></li>
<li class="chapter" data-level="4.4.2" data-path="factor.html"><a href="factor.html#factor-timing"><i class="fa fa-check"></i><b>4.4.2</b> Factor timing</a></li>
</ul></li>
<li class="chapter" data-level="4.5" data-path="factor.html"><a href="factor.html#the-link-with-machine-learning"><i class="fa fa-check"></i><b>4.5</b> The link with machine learning</a><ul>
<li class="chapter" data-level="4.5.1" data-path="factor.html"><a href="factor.html#a-short-list-of-recent-references"><i class="fa fa-check"></i><b>4.5.1</b> A short list of recent references</a></li>
<li class="chapter" data-level="4.5.2" data-path="factor.html"><a href="factor.html#explicit-connexions-with-asset-pricing-models"><i class="fa fa-check"></i><b>4.5.2</b> Explicit connexions with asset pricing models</a></li>
</ul></li>
<li class="chapter" data-level="4.6" data-path="factor.html"><a href="factor.html#coding-exercises"><i class="fa fa-check"></i><b>4.6</b> Coding exercises</a></li>
</ul></li>
<li class="chapter" data-level="5" data-path="Data.html"><a href="Data.html"><i class="fa fa-check"></i><b>5</b> Data preprocessing</a><ul>
<li class="chapter" data-level="5.1" data-path="Data.html"><a href="Data.html#know-your-data"><i class="fa fa-check"></i><b>5.1</b> Know your data</a></li>
<li class="chapter" data-level="5.2" data-path="Data.html"><a href="Data.html#missing-data"><i class="fa fa-check"></i><b>5.2</b> Missing data</a></li>
<li class="chapter" data-level="5.3" data-path="Data.html"><a href="Data.html#outlier-detection"><i class="fa fa-check"></i><b>5.3</b> Outlier detection</a></li>
<li class="chapter" data-level="5.4" data-path="Data.html"><a href="Data.html#feateng"><i class="fa fa-check"></i><b>5.4</b> Feature engineering</a><ul>
<li class="chapter" data-level="5.4.1" data-path="Data.html"><a href="Data.html#feature-selection"><i class="fa fa-check"></i><b>5.4.1</b> Feature selection</a></li>
<li class="chapter" data-level="5.4.2" data-path="Data.html"><a href="Data.html#scaling"><i class="fa fa-check"></i><b>5.4.2</b> Scaling the predictors</a></li>
</ul></li>
<li class="chapter" data-level="5.5" data-path="Data.html"><a href="Data.html#labelling"><i class="fa fa-check"></i><b>5.5</b> Labelling</a><ul>
<li class="chapter" data-level="5.5.1" data-path="Data.html"><a href="Data.html#simple-labels"><i class="fa fa-check"></i><b>5.5.1</b> Simple labels</a></li>
<li class="chapter" data-level="5.5.2" data-path="Data.html"><a href="Data.html#categorical-labels"><i class="fa fa-check"></i><b>5.5.2</b> Categorical labels</a></li>
<li class="chapter" data-level="5.5.3" data-path="Data.html"><a href="Data.html#the-triple-barrier-method"><i class="fa fa-check"></i><b>5.5.3</b> The triple barrier method</a></li>
<li class="chapter" data-level="5.5.4" data-path="Data.html"><a href="Data.html#filtering-the-sample"><i class="fa fa-check"></i><b>5.5.4</b> Filtering the sample</a></li>
<li class="chapter" data-level="5.5.5" data-path="Data.html"><a href="Data.html#horizons"><i class="fa fa-check"></i><b>5.5.5</b> Return horizons</a></li>
</ul></li>
<li class="chapter" data-level="5.6" data-path="Data.html"><a href="Data.html#pers"><i class="fa fa-check"></i><b>5.6</b> Handling persistence</a></li>
<li class="chapter" data-level="5.7" data-path="Data.html"><a href="Data.html#extensions"><i class="fa fa-check"></i><b>5.7</b> Extensions</a><ul>
<li class="chapter" data-level="5.7.1" data-path="Data.html"><a href="Data.html#transforming-features"><i class="fa fa-check"></i><b>5.7.1</b> Transforming features</a></li>
<li class="chapter" data-level="5.7.2" data-path="Data.html"><a href="Data.html#macrovar"><i class="fa fa-check"></i><b>5.7.2</b> Macro-economic variables</a></li>
</ul></li>
<li class="chapter" data-level="5.8" data-path="Data.html"><a href="Data.html#additional-code-and-results"><i class="fa fa-check"></i><b>5.8</b> Additional code and results</a><ul>
<li class="chapter" data-level="5.8.1" data-path="Data.html"><a href="Data.html#impact-of-rescaling-graphical-representation"><i class="fa fa-check"></i><b>5.8.1</b> Impact of rescaling: graphical representation</a></li>
<li class="chapter" data-level="5.8.2" data-path="Data.html"><a href="Data.html#impact-of-rescaling-toy-example"><i class="fa fa-check"></i><b>5.8.2</b> Impact of rescaling: toy example</a></li>
</ul></li>
<li class="chapter" data-level="5.9" data-path="Data.html"><a href="Data.html#coding-exercises-1"><i class="fa fa-check"></i><b>5.9</b> Coding exercises</a></li>
</ul></li>
<li class="chapter" data-level="6" data-path="lasso.html"><a href="lasso.html"><i class="fa fa-check"></i><b>6</b> Penalized regressions and sparse hedging for minimum variance portfolios</a><ul>
<li class="chapter" data-level="6.1" data-path="lasso.html"><a href="lasso.html#penalised-regressions"><i class="fa fa-check"></i><b>6.1</b> Penalised regressions</a><ul>
<li class="chapter" data-level="6.1.1" data-path="lasso.html"><a href="lasso.html#simple-regressions"><i class="fa fa-check"></i><b>6.1.1</b> Simple regressions</a></li>
<li class="chapter" data-level="6.1.2" data-path="lasso.html"><a href="lasso.html#forms-of-penalizations"><i class="fa fa-check"></i><b>6.1.2</b> Forms of penalizations</a></li>
<li class="chapter" data-level="6.1.3" data-path="lasso.html"><a href="lasso.html#illustrations"><i class="fa fa-check"></i><b>6.1.3</b> Illustrations</a></li>
</ul></li>
<li class="chapter" data-level="6.2" data-path="lasso.html"><a href="lasso.html#sparse-hedging-for-minimum-variance-portfolios"><i class="fa fa-check"></i><b>6.2</b> Sparse hedging for minimum variance portfolios</a><ul>
<li class="chapter" data-level="6.2.1" data-path="lasso.html"><a href="lasso.html#presentation-and-derivations"><i class="fa fa-check"></i><b>6.2.1</b> Presentation and derivations</a></li>
<li class="chapter" data-level="6.2.2" data-path="lasso.html"><a href="lasso.html#sparseex"><i class="fa fa-check"></i><b>6.2.2</b> Example</a></li>
</ul></li>
<li class="chapter" data-level="6.3" data-path="lasso.html"><a href="lasso.html#predictive-regressions"><i class="fa fa-check"></i><b>6.3</b> Predictive regressions</a><ul>
<li class="chapter" data-level="6.3.1" data-path="lasso.html"><a href="lasso.html#literature-review-and-principle"><i class="fa fa-check"></i><b>6.3.1</b> Literature review and principle</a></li>
<li class="chapter" data-level="6.3.2" data-path="lasso.html"><a href="lasso.html#code-and-results"><i class="fa fa-check"></i><b>6.3.2</b> Code and results</a></li>
</ul></li>
<li class="chapter" data-level="6.4" data-path="lasso.html"><a href="lasso.html#coding-exercises-2"><i class="fa fa-check"></i><b>6.4</b> Coding exercises</a></li>
</ul></li>
<li class="chapter" data-level="7" data-path="trees.html"><a href="trees.html"><i class="fa fa-check"></i><b>7</b> Tree-based methods</a><ul>
<li class="chapter" data-level="7.1" data-path="trees.html"><a href="trees.html#simple-trees"><i class="fa fa-check"></i><b>7.1</b> Simple trees</a><ul>
<li class="chapter" data-level="7.1.1" data-path="trees.html"><a href="trees.html#principle"><i class="fa fa-check"></i><b>7.1.1</b> Principle</a></li>
<li class="chapter" data-level="7.1.2" data-path="trees.html"><a href="trees.html#further-details-on-classification"><i class="fa fa-check"></i><b>7.1.2</b> Further details on classification</a></li>
<li class="chapter" data-level="7.1.3" data-path="trees.html"><a href="trees.html#pruning-criteria"><i class="fa fa-check"></i><b>7.1.3</b> Pruning criteria</a></li>
<li class="chapter" data-level="7.1.4" data-path="trees.html"><a href="trees.html#code-and-interpretation"><i class="fa fa-check"></i><b>7.1.4</b> Code and interpretation</a></li>
</ul></li>
<li class="chapter" data-level="7.2" data-path="trees.html"><a href="trees.html#random-forests"><i class="fa fa-check"></i><b>7.2</b> Random forests</a><ul>
<li class="chapter" data-level="7.2.1" data-path="trees.html"><a href="trees.html#principle-1"><i class="fa fa-check"></i><b>7.2.1</b> Principle</a></li>
<li class="chapter" data-level="7.2.2" data-path="trees.html"><a href="trees.html#code-and-results-1"><i class="fa fa-check"></i><b>7.2.2</b> Code and results</a></li>
</ul></li>
<li class="chapter" data-level="7.3" data-path="trees.html"><a href="trees.html#adaboost"><i class="fa fa-check"></i><b>7.3</b> Boosted trees: Adaboost</a><ul>
<li class="chapter" data-level="7.3.1" data-path="trees.html"><a href="trees.html#methodology"><i class="fa fa-check"></i><b>7.3.1</b> Methodology</a></li>
<li class="chapter" data-level="7.3.2" data-path="trees.html"><a href="trees.html#illustration"><i class="fa fa-check"></i><b>7.3.2</b> Illustration</a></li>
</ul></li>
<li class="chapter" data-level="7.4" data-path="trees.html"><a href="trees.html#boosted-trees-extreme-gradient-boosting"><i class="fa fa-check"></i><b>7.4</b> Boosted trees: extreme gradient boosting</a><ul>
<li class="chapter" data-level="7.4.1" data-path="trees.html"><a href="trees.html#managing-loss"><i class="fa fa-check"></i><b>7.4.1</b> Managing Loss</a></li>
<li class="chapter" data-level="7.4.2" data-path="trees.html"><a href="trees.html#penalisation"><i class="fa fa-check"></i><b>7.4.2</b> Penalisation</a></li>
<li class="chapter" data-level="7.4.3" data-path="trees.html"><a href="trees.html#aggregation"><i class="fa fa-check"></i><b>7.4.3</b> Aggregation</a></li>
<li class="chapter" data-level="7.4.4" data-path="trees.html"><a href="trees.html#tree-structure"><i class="fa fa-check"></i><b>7.4.4</b> Tree structure</a></li>
<li class="chapter" data-level="7.4.5" data-path="trees.html"><a href="trees.html#boostext"><i class="fa fa-check"></i><b>7.4.5</b> Extensions</a></li>
<li class="chapter" data-level="7.4.6" data-path="trees.html"><a href="trees.html#boostcode"><i class="fa fa-check"></i><b>7.4.6</b> Code and results</a></li>
<li class="chapter" data-level="7.4.7" data-path="trees.html"><a href="trees.html#instweight"><i class="fa fa-check"></i><b>7.4.7</b> Instance weighting</a></li>
</ul></li>
<li class="chapter" data-level="7.5" data-path="trees.html"><a href="trees.html#discussion"><i class="fa fa-check"></i><b>7.5</b> Discussion</a></li>
<li class="chapter" data-level="7.6" data-path="trees.html"><a href="trees.html#coding-exercises-3"><i class="fa fa-check"></i><b>7.6</b> Coding exercises</a></li>
</ul></li>
<li class="chapter" data-level="8" data-path="NN.html"><a href="NN.html"><i class="fa fa-check"></i><b>8</b> Neural networks</a><ul>
<li class="chapter" data-level="8.1" data-path="NN.html"><a href="NN.html#the-original-perceptron"><i class="fa fa-check"></i><b>8.1</b> The original perceptron</a></li>
<li class="chapter" data-level="8.2" data-path="NN.html"><a href="NN.html#multilayer-perceptron"><i class="fa fa-check"></i><b>8.2</b> Multilayer perceptron</a><ul>
<li class="chapter" data-level="8.2.1" data-path="NN.html"><a href="NN.html#introduction-and-notations"><i class="fa fa-check"></i><b>8.2.1</b> Introduction and notations</a></li>
<li class="chapter" data-level="8.2.2" data-path="NN.html"><a href="NN.html#universal-approximation"><i class="fa fa-check"></i><b>8.2.2</b> Universal approximation</a></li>
<li class="chapter" data-level="8.2.3" data-path="NN.html"><a href="NN.html#backprop"><i class="fa fa-check"></i><b>8.2.3</b> Learning via back-propagation</a></li>
<li class="chapter" data-level="8.2.4" data-path="NN.html"><a href="NN.html#further-details-on-classification-1"><i class="fa fa-check"></i><b>8.2.4</b> Further details on classification</a></li>
</ul></li>
<li class="chapter" data-level="8.3" data-path="NN.html"><a href="NN.html#howdeep"><i class="fa fa-check"></i><b>8.3</b> How deep should we go? And other practical issues</a><ul>
<li class="chapter" data-level="8.3.1" data-path="NN.html"><a href="NN.html#architectural-choices"><i class="fa fa-check"></i><b>8.3.1</b> Architectural choices</a></li>
<li class="chapter" data-level="8.3.2" data-path="NN.html"><a href="NN.html#frequency-of-weight-updates-and-learning-duration"><i class="fa fa-check"></i><b>8.3.2</b> Frequency of weight updates and learning duration</a></li>
<li class="chapter" data-level="8.3.3" data-path="NN.html"><a href="NN.html#penalizations-and-dropout"><i class="fa fa-check"></i><b>8.3.3</b> Penalizations and dropout</a></li>
</ul></li>
<li class="chapter" data-level="8.4" data-path="NN.html"><a href="NN.html#code-samples-and-comments-for-vanilla-mlp"><i class="fa fa-check"></i><b>8.4</b> Code samples and comments for vanilla MLP</a><ul>
<li class="chapter" data-level="8.4.1" data-path="NN.html"><a href="NN.html#regression-example"><i class="fa fa-check"></i><b>8.4.1</b> Regression example</a></li>
<li class="chapter" data-level="8.4.2" data-path="NN.html"><a href="NN.html#classification-example"><i class="fa fa-check"></i><b>8.4.2</b> Classification example</a></li>
</ul></li>
<li class="chapter" data-level="8.5" data-path="NN.html"><a href="NN.html#recurrent-networks"><i class="fa fa-check"></i><b>8.5</b> Recurrent networks</a><ul>
<li class="chapter" data-level="8.5.1" data-path="NN.html"><a href="NN.html#presentation"><i class="fa fa-check"></i><b>8.5.1</b> Presentation</a></li>
<li class="chapter" data-level="8.5.2" data-path="NN.html"><a href="NN.html#code-and-results-2"><i class="fa fa-check"></i><b>8.5.2</b> Code and results</a></li>
</ul></li>
<li class="chapter" data-level="8.6" data-path="NN.html"><a href="NN.html#other-common-architectures"><i class="fa fa-check"></i><b>8.6</b> Other common architectures</a><ul>
<li class="chapter" data-level="8.6.1" data-path="NN.html"><a href="NN.html#generative-aversarial-networks"><i class="fa fa-check"></i><b>8.6.1</b> Generative adversarial networks</a></li>
<li class="chapter" data-level="8.6.2" data-path="NN.html"><a href="NN.html#autoencoders"><i class="fa fa-check"></i><b>8.6.2</b> Auto-encoders</a></li>
<li class="chapter" data-level="8.6.3" data-path="NN.html"><a href="NN.html#a-word-on-convolutional-networks"><i class="fa fa-check"></i><b>8.6.3</b> A word on convolutional networks</a></li>
<li class="chapter" data-level="8.6.4" data-path="NN.html"><a href="NN.html#advanced-architectures"><i class="fa fa-check"></i><b>8.6.4</b> Advanced architectures</a></li>
</ul></li>
<li class="chapter" data-level="8.7" data-path="NN.html"><a href="NN.html#coding-exercise"><i class="fa fa-check"></i><b>8.7</b> Coding exercise</a></li>
</ul></li>
<li class="chapter" data-level="9" data-path="svm.html"><a href="svm.html"><i class="fa fa-check"></i><b>9</b> Support vector machines</a><ul>
<li class="chapter" data-level="9.1" data-path="svm.html"><a href="svm.html#svm-for-classification"><i class="fa fa-check"></i><b>9.1</b> SVM for classification</a></li>
<li class="chapter" data-level="9.2" data-path="svm.html"><a href="svm.html#svm-for-regression"><i class="fa fa-check"></i><b>9.2</b> SVM for regression</a></li>
<li class="chapter" data-level="9.3" data-path="svm.html"><a href="svm.html#practice"><i class="fa fa-check"></i><b>9.3</b> Practice</a></li>
<li class="chapter" data-level="9.4" data-path="svm.html"><a href="svm.html#coding-exercises-4"><i class="fa fa-check"></i><b>9.4</b> Coding exercises</a></li>
</ul></li>
<li class="chapter" data-level="10" data-path="bayes.html"><a href="bayes.html"><i class="fa fa-check"></i><b>10</b> Bayesian methods</a><ul>
<li class="chapter" data-level="10.1" data-path="bayes.html"><a href="bayes.html#the-bayesian-framework"><i class="fa fa-check"></i><b>10.1</b> The Bayesian framework</a></li>
<li class="chapter" data-level="10.2" data-path="bayes.html"><a href="bayes.html#bayesian-sampling"><i class="fa fa-check"></i><b>10.2</b> Bayesian sampling</a><ul>
<li class="chapter" data-level="10.2.1" data-path="bayes.html"><a href="bayes.html#gibbs-sampling"><i class="fa fa-check"></i><b>10.2.1</b> Gibbs sampling</a></li>
<li class="chapter" data-level="10.2.2" data-path="bayes.html"><a href="bayes.html#metropolis-hastings-sampling"><i class="fa fa-check"></i><b>10.2.2</b> Metropolis-Hastings sampling</a></li>
</ul></li>
<li class="chapter" data-level="10.3" data-path="bayes.html"><a href="bayes.html#bayesian-linear-regression"><i class="fa fa-check"></i><b>10.3</b> Bayesian linear regression</a></li>
<li class="chapter" data-level="10.4" data-path="bayes.html"><a href="bayes.html#naive-bayes-classifier"><i class="fa fa-check"></i><b>10.4</b> Naive Bayes classifier</a></li>
<li class="chapter" data-level="10.5" data-path="bayes.html"><a href="bayes.html#BART"><i class="fa fa-check"></i><b>10.5</b> Bayesian additive trees</a><ul>
<li class="chapter" data-level="10.5.1" data-path="bayes.html"><a href="bayes.html#general-formulation"><i class="fa fa-check"></i><b>10.5.1</b> General formulation</a></li>
<li class="chapter" data-level="10.5.2" data-path="bayes.html"><a href="bayes.html#priors"><i class="fa fa-check"></i><b>10.5.2</b> Priors</a></li>
<li class="chapter" data-level="10.5.3" data-path="bayes.html"><a href="bayes.html#sampling-and-predictions"><i class="fa fa-check"></i><b>10.5.3</b> Sampling and predictions</a></li>
<li class="chapter" data-level="10.5.4" data-path="bayes.html"><a href="bayes.html#code"><i class="fa fa-check"></i><b>10.5.4</b> Code</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="11" data-path="valtune.html"><a href="valtune.html"><i class="fa fa-check"></i><b>11</b> Validating and tuning</a><ul>
<li class="chapter" data-level="11.1" data-path="valtune.html"><a href="valtune.html#mlmetrics"><i class="fa fa-check"></i><b>11.1</b> Learning metrics</a><ul>
<li class="chapter" data-level="11.1.1" data-path="valtune.html"><a href="valtune.html#regression-analysis"><i class="fa fa-check"></i><b>11.1.1</b> Regression analysis</a></li>
<li class="chapter" data-level="11.1.2" data-path="valtune.html"><a href="valtune.html#classification-analysis"><i class="fa fa-check"></i><b>11.1.2</b> Classification analysis</a></li>
</ul></li>
<li class="chapter" data-level="11.2" data-path="valtune.html"><a href="valtune.html#validation"><i class="fa fa-check"></i><b>11.2</b> Validation</a><ul>
<li class="chapter" data-level="11.2.1" data-path="valtune.html"><a href="valtune.html#the-variance-bias-tradeoff-theory"><i class="fa fa-check"></i><b>11.2.1</b> The variance-bias tradeoff: theory</a></li>
<li class="chapter" data-level="11.2.2" data-path="valtune.html"><a href="valtune.html#the-variance-bias-tradeoff-illustration"><i class="fa fa-check"></i><b>11.2.2</b> The variance-bias tradeoff: illustration</a></li>
<li class="chapter" data-level="11.2.3" data-path="valtune.html"><a href="valtune.html#the-risk-of-overfitting-principle"><i class="fa fa-check"></i><b>11.2.3</b> The risk of overfitting: principle</a></li>
<li class="chapter" data-level="11.2.4" data-path="valtune.html"><a href="valtune.html#the-risk-of-overfitting-some-solutions"><i class="fa fa-check"></i><b>11.2.4</b> The risk of overfitting: some solutions</a></li>
</ul></li>
<li class="chapter" data-level="11.3" data-path="valtune.html"><a href="valtune.html#the-search-for-good-hyperparameters"><i class="fa fa-check"></i><b>11.3</b> The search for good hyperparameters</a><ul>
<li class="chapter" data-level="11.3.1" data-path="valtune.html"><a href="valtune.html#methods"><i class="fa fa-check"></i><b>11.3.1</b> Methods</a></li>
<li class="chapter" data-level="11.3.2" data-path="valtune.html"><a href="valtune.html#example-grid-search"><i class="fa fa-check"></i><b>11.3.2</b> Example: grid search</a></li>
<li class="chapter" data-level="11.3.3" data-path="valtune.html"><a href="valtune.html#example-bayesian-optimization"><i class="fa fa-check"></i><b>11.3.3</b> Example: Bayesian optimization</a></li>
</ul></li>
<li class="chapter" data-level="11.4" data-path="valtune.html"><a href="valtune.html#short-discussion-on-validation-in-backtests"><i class="fa fa-check"></i><b>11.4</b> Short discussion on validation in backtests</a></li>
</ul></li>
<li class="chapter" data-level="12" data-path="ensemble.html"><a href="ensemble.html"><i class="fa fa-check"></i><b>12</b> Ensemble models</a><ul>
<li class="chapter" data-level="12.1" data-path="ensemble.html"><a href="ensemble.html#linear-ensembles"><i class="fa fa-check"></i><b>12.1</b> Linear ensembles</a><ul>
<li class="chapter" data-level="12.1.1" data-path="ensemble.html"><a href="ensemble.html#principles"><i class="fa fa-check"></i><b>12.1.1</b> Principles</a></li>
<li class="chapter" data-level="12.1.2" data-path="ensemble.html"><a href="ensemble.html#example"><i class="fa fa-check"></i><b>12.1.2</b> Example</a></li>
</ul></li>
<li class="chapter" data-level="12.2" data-path="ensemble.html"><a href="ensemble.html#stacked-ensembles"><i class="fa fa-check"></i><b>12.2</b> Stacked ensembles</a><ul>
<li class="chapter" data-level="12.2.1" data-path="ensemble.html"><a href="ensemble.html#two-stage-training"><i class="fa fa-check"></i><b>12.2.1</b> Two stage training</a></li>
<li class="chapter" data-level="12.2.2" data-path="ensemble.html"><a href="ensemble.html#code-and-results-3"><i class="fa fa-check"></i><b>12.2.2</b> Code and results</a></li>
</ul></li>
<li class="chapter" data-level="12.3" data-path="ensemble.html"><a href="ensemble.html#extensions-1"><i class="fa fa-check"></i><b>12.3</b> Extensions</a><ul>
<li class="chapter" data-level="12.3.1" data-path="ensemble.html"><a href="ensemble.html#exogenous-variables"><i class="fa fa-check"></i><b>12.3.1</b> Exogenous variables</a></li>
<li class="chapter" data-level="12.3.2" data-path="ensemble.html"><a href="ensemble.html#shrinking-inter-model-correlations"><i class="fa fa-check"></i><b>12.3.2</b> Shrinking inter-model correlations</a></li>
</ul></li>
<li class="chapter" data-level="12.4" data-path="ensemble.html"><a href="ensemble.html#exercise"><i class="fa fa-check"></i><b>12.4</b> Exercise</a></li>
</ul></li>
<li class="chapter" data-level="13" data-path="backtest.html"><a href="backtest.html"><i class="fa fa-check"></i><b>13</b> Portfolio backtesting</a><ul>
<li class="chapter" data-level="13.1" data-path="backtest.html"><a href="backtest.html#protocol"><i class="fa fa-check"></i><b>13.1</b> Setting the protocol</a></li>
<li class="chapter" data-level="13.2" data-path="backtest.html"><a href="backtest.html#turning-signals-into-portfolio-weights"><i class="fa fa-check"></i><b>13.2</b> Turning signals into portfolio weights</a></li>
<li class="chapter" data-level="13.3" data-path="backtest.html"><a href="backtest.html#perfmet"><i class="fa fa-check"></i><b>13.3</b> Performance metrics</a><ul>
<li class="chapter" data-level="13.3.1" data-path="backtest.html"><a href="backtest.html#discussion-1"><i class="fa fa-check"></i><b>13.3.1</b> Discussion</a></li>
<li class="chapter" data-level="13.3.2" data-path="backtest.html"><a href="backtest.html#pure-performance-and-risk-indicators"><i class="fa fa-check"></i><b>13.3.2</b> Pure performance and risk indicators</a></li>
<li class="chapter" data-level="13.3.3" data-path="backtest.html"><a href="backtest.html#factor-based-evaluation"><i class="fa fa-check"></i><b>13.3.3</b> Factor-based evaluation</a></li>
<li class="chapter" data-level="13.3.4" data-path="backtest.html"><a href="backtest.html#risk-adjusted-measures"><i class="fa fa-check"></i><b>13.3.4</b> Risk-adjusted measures</a></li>
<li class="chapter" data-level="13.3.5" data-path="backtest.html"><a href="backtest.html#transaction-costs-and-turnover"><i class="fa fa-check"></i><b>13.3.5</b> Transaction costs and turnover</a></li>
</ul></li>
<li class="chapter" data-level="13.4" data-path="backtest.html"><a href="backtest.html#common-errors-and-issues"><i class="fa fa-check"></i><b>13.4</b> Common errors and issues</a><ul>
<li class="chapter" data-level="13.4.1" data-path="backtest.html"><a href="backtest.html#forward-looking-data"><i class="fa fa-check"></i><b>13.4.1</b> Forward looking data</a></li>
<li class="chapter" data-level="13.4.2" data-path="backtest.html"><a href="backtest.html#backtest-overfitting"><i class="fa fa-check"></i><b>13.4.2</b> Backtest overfitting</a></li>
<li class="chapter" data-level="13.4.3" data-path="backtest.html"><a href="backtest.html#simple-saveguards"><i class="fa fa-check"></i><b>13.4.3</b> Simple saveguards</a></li>
</ul></li>
<li class="chapter" data-level="13.5" data-path="backtest.html"><a href="backtest.html#implication-of-non-stationarity-forecasting-is-hard"><i class="fa fa-check"></i><b>13.5</b> Implication of non-stationarity: forecasting is hard</a><ul>
<li class="chapter" data-level="13.5.1" data-path="backtest.html"><a href="backtest.html#general-comments"><i class="fa fa-check"></i><b>13.5.1</b> General comments</a></li>
<li class="chapter" data-level="13.5.2" data-path="backtest.html"><a href="backtest.html#the-no-free-lunch-theorem"><i class="fa fa-check"></i><b>13.5.2</b> The no free lunch theorem</a></li>
</ul></li>
<li class="chapter" data-level="13.6" data-path="backtest.html"><a href="backtest.html#example-1"><i class="fa fa-check"></i><b>13.6</b> Example</a></li>
<li class="chapter" data-level="13.7" data-path="backtest.html"><a href="backtest.html#coding-exercises-5"><i class="fa fa-check"></i><b>13.7</b> Coding exercises</a></li>
</ul></li>
<li class="chapter" data-level="14" data-path="interp.html"><a href="interp.html"><i class="fa fa-check"></i><b>14</b> Interpretability</a><ul>
<li class="chapter" data-level="14.1" data-path="interp.html"><a href="interp.html#global-interpretations"><i class="fa fa-check"></i><b>14.1</b> Global interpretations</a><ul>
<li class="chapter" data-level="14.1.1" data-path="interp.html"><a href="interp.html#variable-importance"><i class="fa fa-check"></i><b>14.1.1</b> Variable importance (tree-based)</a></li>
<li class="chapter" data-level="14.1.2" data-path="interp.html"><a href="interp.html#variable-importance-agnostic"><i class="fa fa-check"></i><b>14.1.2</b> Variable importance (agnostic)</a></li>
<li class="chapter" data-level="14.1.3" data-path="interp.html"><a href="interp.html#partial-dependence-plot"><i class="fa fa-check"></i><b>14.1.3</b> Partial dependence plot</a></li>
</ul></li>
<li class="chapter" data-level="14.2" data-path="interp.html"><a href="interp.html#local-interpretations"><i class="fa fa-check"></i><b>14.2</b> Local interpretations</a><ul>
<li class="chapter" data-level="14.2.1" data-path="interp.html"><a href="interp.html#lime"><i class="fa fa-check"></i><b>14.2.1</b> LIME</a></li>
<li class="chapter" data-level="14.2.2" data-path="interp.html"><a href="interp.html#shapley-values"><i class="fa fa-check"></i><b>14.2.2</b> Shapley values</a></li>
<li class="chapter" data-level="14.2.3" data-path="interp.html"><a href="interp.html#breakdown"><i class="fa fa-check"></i><b>14.2.3</b> Breakdown</a></li>
</ul></li>
</ul></li>
<li class="chapter" data-level="15" data-path="causality.html"><a href="causality.html"><i class="fa fa-check"></i><b>15</b> Two key concepts: causality and non-stationarity</a><ul>
<li class="chapter" data-level="15.1" data-path="causality.html"><a href="causality.html#causality-1"><i class="fa fa-check"></i><b>15.1</b> Causality</a><ul>
<li class="chapter" data-level="15.1.1" data-path="causality.html"><a href="causality.html#granger"><i class="fa fa-check"></i><b>15.1.1</b> Granger causality</a></li>
<li class="chapter" data-level="15.1.2" data-path="causality.html"><a href="causality.html#causal-additive-models"><i class="fa fa-check"></i><b>15.1.2</b> Causal additive models</a></li>
<li class="chapter" data-level="15.1.3" data-path="causality.html"><a href="causality.html#structural-time-series-models"><i class="fa fa-check"></i><b>15.1.3</b> Structural time-series models</a></li>
</ul></li>
<li class="chapter" data-level="15.2" data-path="causality.html"><a href="causality.html#nonstat"><i class="fa fa-check"></i><b>15.2</b> Dealing with changing environments</a><ul>
<li class="chapter" data-level="15.2.1" data-path="causality.html"><a href="causality.html#non-stationarity-an-obvious-illustration"><i class="fa fa-check"></i><b>15.2.1</b> Non-stationarity: an obvious illustration</a></li>
<li class="chapter" data-level="15.2.2" data-path="causality.html"><a href="causality.html#online-learning"><i class="fa fa-check"></i><b>15.2.2</b> Online learning</a></li>
<li class="chapter" data-level="15.2.3" data-path="causality.html"><a href="causality.html#homogeneous-transfer-learning"><i class="fa fa-check"></i><b>15.2.3</b> Homogeneous transfer learning</a></li>
<li class="chapter" data-level="15.2.4" data-path="causality.html"><a href="causality.html#active-learning"><i class="fa fa-check"></i><b>15.2.4</b> Active learning</a></li>
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<li class="chapter" data-level="16" data-path="unsup.html"><a href="unsup.html"><i class="fa fa-check"></i><b>16</b> Unsupervised learning</a><ul>
<li class="chapter" data-level="16.1" data-path="unsup.html"><a href="unsup.html#corpred"><i class="fa fa-check"></i><b>16.1</b> The problem with correlated predictors</a></li>
<li class="chapter" data-level="16.2" data-path="unsup.html"><a href="unsup.html#principal-component-analysis-and-autoencoders"><i class="fa fa-check"></i><b>16.2</b> Principal component analysis and autoencoders</a><ul>
<li class="chapter" data-level="16.2.1" data-path="unsup.html"><a href="unsup.html#a-bit-of-algebra"><i class="fa fa-check"></i><b>16.2.1</b> A bit of algebra</a></li>
<li class="chapter" data-level="16.2.2" data-path="unsup.html"><a href="unsup.html#pca"><i class="fa fa-check"></i><b>16.2.2</b> PCA</a></li>
<li class="chapter" data-level="16.2.3" data-path="unsup.html"><a href="unsup.html#ae"><i class="fa fa-check"></i><b>16.2.3</b> Autoencoders</a></li>
<li class="chapter" data-level="16.2.4" data-path="unsup.html"><a href="unsup.html#application"><i class="fa fa-check"></i><b>16.2.4</b> Application</a></li>
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<li class="chapter" data-level="16.3" data-path="unsup.html"><a href="unsup.html#clustering-via-k-means"><i class="fa fa-check"></i><b>16.3</b> Clustering via k-means</a></li>
<li class="chapter" data-level="16.4" data-path="unsup.html"><a href="unsup.html#nearest-neighbors"><i class="fa fa-check"></i><b>16.4</b> Nearest neighbors</a></li>
<li class="chapter" data-level="16.5" data-path="unsup.html"><a href="unsup.html#coding-exercise-1"><i class="fa fa-check"></i><b>16.5</b> Coding exercise</a></li>
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<li class="chapter" data-level="17" data-path="RL.html"><a href="RL.html"><i class="fa fa-check"></i><b>17</b> Reinforcement learning</a><ul>
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<li class="chapter" data-level="17.1.1" data-path="RL.html"><a href="RL.html#general-framework"><i class="fa fa-check"></i><b>17.1.1</b> General framework</a></li>
<li class="chapter" data-level="17.1.2" data-path="RL.html"><a href="RL.html#q-learning"><i class="fa fa-check"></i><b>17.1.2</b> Q-learning</a></li>
<li class="chapter" data-level="17.1.3" data-path="RL.html"><a href="RL.html#sarsa"><i class="fa fa-check"></i><b>17.1.3</b> SARSA</a></li>
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<li class="chapter" data-level="17.2" data-path="RL.html"><a href="RL.html#the-curse-of-dimensionality"><i class="fa fa-check"></i><b>17.2</b> The curse of dimensionality</a></li>
<li class="chapter" data-level="17.3" data-path="RL.html"><a href="RL.html#policy-gradient"><i class="fa fa-check"></i><b>17.3</b> Policy gradient</a><ul>
<li class="chapter" data-level="17.3.1" data-path="RL.html"><a href="RL.html#principle-2"><i class="fa fa-check"></i><b>17.3.1</b> Principle</a></li>
<li class="chapter" data-level="17.3.2" data-path="RL.html"><a href="RL.html#extensions-2"><i class="fa fa-check"></i><b>17.3.2</b> Extensions</a></li>
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<li class="chapter" data-level="17.4" data-path="RL.html"><a href="RL.html#simple-examples"><i class="fa fa-check"></i><b>17.4</b> Simple examples</a><ul>
<li class="chapter" data-level="17.4.1" data-path="RL.html"><a href="RL.html#q-learning-with-simulations"><i class="fa fa-check"></i><b>17.4.1</b> Q-learning with simulations</a></li>
<li class="chapter" data-level="17.4.2" data-path="RL.html"><a href="RL.html#q-learning-with-market-data"><i class="fa fa-check"></i><b>17.4.2</b> Q-learning with market data</a></li>
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<li class="chapter" data-level="17.5" data-path="RL.html"><a href="RL.html#concluding-remarks"><i class="fa fa-check"></i><b>17.5</b> Concluding remarks</a></li>
<li class="chapter" data-level="17.6" data-path="RL.html"><a href="RL.html#exercises"><i class="fa fa-check"></i><b>17.6</b> Exercises</a></li>
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<li class="chapter" data-level="18" data-path="NLP.html"><a href="NLP.html"><i class="fa fa-check"></i><b>18</b> Natural Language Processing</a></li>
<li class="chapter" data-level="19" data-path="conclusion.html"><a href="conclusion.html"><i class="fa fa-check"></i><b>19</b> Conclusion</a></li>
<li class="appendix"><span><b>Appendix</b></span></li>
<li class="chapter" data-level="A" data-path="data-description.html"><a href="data-description.html"><i class="fa fa-check"></i><b>A</b> Data Description</a></li>
<li class="chapter" data-level="B" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html"><i class="fa fa-check"></i><b>B</b> Solution to exercises</a><ul>
<li class="chapter" data-level="B.1" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-4"><i class="fa fa-check"></i><b>B.1</b> Chapter 4</a></li>
<li class="chapter" data-level="B.2" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-5"><i class="fa fa-check"></i><b>B.2</b> Chapter 5</a></li>
<li class="chapter" data-level="B.3" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-6"><i class="fa fa-check"></i><b>B.3</b> Chapter 6</a></li>
<li class="chapter" data-level="B.4" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-7"><i class="fa fa-check"></i><b>B.4</b> Chapter 7</a></li>
<li class="chapter" data-level="B.5" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-8-the-autoencoder-model"><i class="fa fa-check"></i><b>B.5</b> Chapter 8: the autoencoder model</a></li>
<li class="chapter" data-level="B.6" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-9"><i class="fa fa-check"></i><b>B.6</b> Chapter 9</a></li>
<li class="chapter" data-level="B.7" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-12"><i class="fa fa-check"></i><b>B.7</b> Chapter 12</a></li>
<li class="chapter" data-level="B.8" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#chapter-13"><i class="fa fa-check"></i><b>B.8</b> Chapter 13</a><ul>
<li class="chapter" data-level="B.8.1" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#functional-programming-in-the-backtest"><i class="fa fa-check"></i><b>B.8.1</b> Functional programming in the backtest</a></li>
<li class="chapter" data-level="B.8.2" data-path="solution-to-exercises.html"><a href="solution-to-exercises.html#advanced-weighting-function"><i class="fa fa-check"></i><b>B.8.2</b> Advanced weighting function</a></li>
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