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Machine Learning (ml) Is Changing Virtually Every Aspect Of Our Lives. Today Ml Algorithms Accomplish Tasks That Until Recently Only Expert Humans Could Perform. As It Relates To Finance, This Is The Most Exciting Time To Adopt A Disruptive Technology That Will Transform How Everyone Invests For Generations. Readers Will Learn How To Structure Big Data In A Way That Is Amenable To Ml Algorithms; How To Conduct Research With Ml Algorithms On That Data; How To Use Supercomputing Methods; How To Backtest Your Discoveries While Avoiding False Positives. The Book Addresses Real-life Problems Faced By Practitioners On A Daily Basis, And Explains Scientifically Sound Solutions Using Math, Supported By Code And Examples. Readers Become Active Users Who Can Test The Proposed Solutions In Their Particular Setting. Written By A Recognized Expert And Portfolio Manager, This Book Will Equip Investment Professionals With The Groundbreaking Tools Needed To Succeed In Modern Finance--,this Book Begins By Structuring Financial Data In A Way That Is Amenable To Machine Learning (ml) Algorithms. Then, The Author Discusses How To Conduct Research With Ml Algorithms On That Data And How To Backtest Your Discoveries. Most Of The Problems And Solutions Are Explained Using Math, Supported By Code. This Makes The Book Very Practical And Hands-on. Readers Become Active Users Who Can Test The Solutions Proposed In Their Work. Readers Will Learn How To Structure, Label, Weight, And Backtest Data. Machine Learning Is The Future, And This Book Will Equip Investment Professionals With The Tools To Utilize It Moving Forward-- 14.7.3 The Deflated Sharpe Ratio -- 14.7.4 Efficiency Statistics -- 14.8 Classification Scores -- 14.9 Attribution -- Exercises -- References -- Bibliography -- 15 Understanding Strategy Risk -- 15.1 Motivation -- 15.2 Symmetric Payouts -- 15.3 Asymmetric Payouts -- 15.4 The Probability of Strategy Failure -- 15.4.1 Algorithm -- 15.4.2 Implementation -- Exercises -- References -- 16 Machine Learning Asset Allocation -- 16.1 Motivation -- 16.2 The Problem with Convex Portfolio Optimization -- 16.3 Markowitzs Curse -- 16.4 From Geometric to Hierarchical Relationships -- 16.4.1 Tree Clustering -- 16.4.2 Quasi-Diagonalization -- 16.4.3 Recursive Bisection -- 16.5 A Numerical Example -- 16.6 Out-of-Sample Monte Carlo Simulations -- 16.7 Further Research -- 16.8 Conclusion -- APPENDICES -- 16.A.1 Correlation-based Metric -- 16.A.2 Inverse Variance Allocation -- 16.A.3 Reproducing the Numerical Example -- 16.A.4 Reproducing the Monte Carlo Experiment -- Exercises -- References -- PART 4 Useful Financial Features -- 17 Structural Breaks -- 17.1 Motivation -- 17.2 Types of Structural Break Tests -- 17.3 CUSUM Tests -- 17.3.1 Brown-Durbin-Evans CUSUM Test on Recursive Residuals -- 17.3.2 Chu-Stinchcombe-White CUSUM Test on Levels -- 17.4 Explosiveness Tests -- 17.4.1 Chow-Type Dickey-Fuller Test -- 17.4.2 Supremum Augmented Dickey-Fuller -- 17.4.3 Sub- and Super-Martingale Tests -- Exercises -- References -- 18 Entropy Features -- 18.1 Motivation -- 18.2 Shannons Entropy -- 18.3 The Plug-in (or Maximum Likelihood) Estimator -- 18.4 Lempel-Ziv Estimators -- 18.5 Encoding Schemes -- 18.5.1 Binary Encoding -- 18.5.2 Quantile Encoding -- 18.5.3 Sigma Encoding -- 18.6 Entropy of a Gaussian Process -- 18.7 Entropy and the Generalized Mean -- 18.8 A Few Financial Applications of Entropy -- 18.8.1 Market Efficiency -- 18.8.2 Maximum Entropy Generation Intro -- Advances in Financial Machine Learning -- Contents -- About the Author -- Preamble -- 1 Financial Machine Learning as a Distinct Subject -- 1.1 Motivation -- 1.2 The Main Reason Financial Machine Learning Projects Usually Fail -- 1.2.1 The Sisyphus Paradigm -- 1.2.2 The Meta-Strategy Paradigm -- 1.3 Book Structure -- 1.3.1 Structure by Production Chain -- 1.3.2 Structure by Strategy Component -- 1.3.3 Structure by Common Pitfall -- 1.4 Target Audience -- 1.5 Requisites -- 1.6 FAQs -- 1.7 Acknowledgments -- Exercises -- References -- Bibliography -- PART 1 Data Analysis -- 2 Financial Data Structures -- 2.1 Motivation -- 2.2 Essential Types of Financial Data -- 2.2.1 Fundamental Data -- 2.2.2 Market Data -- 2.2.3 Analytics -- 2.2.4 Alternative Data -- 2.3 Bars -- 2.3.1 Standard Bars -- 2.3.2 Information-Driven Bars -- 2.4 Dealing with Multi-Product Series -- 2.4.1 The ETF Trick -- 2.4.2 PCA Weights -- 2.4.3 Single Future Roll -- 2.5 Sampling Features -- 2.5.1 Sampling for Reduction -- 2.5.2 Event-Based Sampling -- Exercises -- References -- 3 Labeling -- 3.1 Motivation -- 3.2 The Fixed-Time Horizon Method -- 3.3 Computing Dynamic Thresholds -- 3.4 The Triple-Barrier Method -- 3.5 Learning Side and Size -- 3.6 Meta-Labeling -- 3.7 How to Use Meta-Labeling -- 3.8 The Quantamental Way -- 3.9 Dropping Unnecessary Labels -- Exercises -- Bibliography -- 4 Sample Weights -- 4.1 Motivation -- 4.2 Overlapping Outcomes -- 4.3 Number of Concurrent Labels -- 4.4 Average Uniqueness of a Label -- 4.5 Bagging Classifiers and Uniqueness -- 4.5.1 Sequential Bootstrap -- 4.5.2 Implementation of Sequential Bootstrap -- 4.5.3 A Numerical Example -- 4.5.4 Monte Carlo Experiments -- 4.6 Return Attribution -- 4.7 Time Decay -- 4.8 Class Weights -- Exercises -- References -- Bibliography -- 5 Fractionally Differentiated Features -- 5.1 Motivation 18.8.3 Portfolio Concentration -- 18.8.4 Market Microstructure -- Exercises -- References -- Bibliography -- 19 Microstructural Features -- 19.1 Motivation -- 19.2 Review of the Literature -- 19.3 First Generation: Price Sequences -- 19.3.1 The Tick Rule -- 19.3.2 The Roll Model -- 19.3.3 High-Low Volatility Estimator -- 19.3.4 Corwin and Schultz -- 19.4 Second Generation: Strategic Trade Models -- 19.4.1 Kyles Lambda -- 19.4.2 Amihuds Lambda -- 19.4.3 Hasbroucks Lambda -- 19.5 Third Generation: Sequential Trade Models -- 19.5.1 Probability of Information-based Trading -- 19.5.2 Volume-Synchronized Probability of Informed Trading -- 19.6 Additional Features from Microstructural Datasets -- 19.6.1 Distibution of Order Sizes -- 19.6.2 Cancellation Rates, Limit Orders, Market Orders -- 19.6.3 Time-Weighted Average Price Execution Algorithms -- 19.6.4 Options Markets -- 19.6.5 Serial Correlation of Signed Order Flow -- 19.7 What Is Microstructural Information? -- Exercises -- References -- PART 5 High-Performance Computing Recipes -- 20 Multiprocessing and Vectorization -- 20.1 Motivation -- 20.2 Vectorization Example -- 20.3 Single-Thread vs. Multithreading vs. Multiprocessing -- 20.4 Atoms and Molecules -- 20.4.1 Linear Partitions -- 20.4.2 Two-Nested Loops Partitions -- 20.5 Multiprocessing Engines -- 20.5.1 Preparing the Jobs -- 20.5.2 Asynchronous Calls -- 20.5.3 Unwrapping the Callback -- 20.5.4 Pickle/Unpickle Objects -- 20.5.5 Output Reduction -- 20.6 Multiprocessing Example -- Exercises -- Reference -- Bibliography -- 21 Brute Force and Quantum Computers -- 21.1 Motivation -- 21.2 Combinatorial Optimization -- 21.3 The Objective Function -- 21.4 The Problem -- 21.5 An Integer Optimization Approach -- 21.5.1 Pigeonhole Partitions -- 21.5.2 Feasible Static Solutions -- 21.5.3 Evaluating Trajectories -- 21.6 A Numerical Example 10.3 Bet Sizing from Predicted Probabilities -- 10.4 Averaging Active Bets -- 10.5 Size Discretization -- 10.6 Dynamic Bet Sizes and Limit Prices -- Exercises -- References -- Bibliography -- 11 The Dangers of Backtesting -- 11.1 Motivation -- 11.2 Mission Impossible: The Flawless Backtest -- 11.3 Even If Your Backtest Is Flawless, It Is Probably Wrong -- 11.4 Backtesting Is Not a Research Tool -- 11.5 A Few General Recommendations -- 11.6 Strategy Selection -- Exercises -- References -- Bibliography -- 12 Backtesting through Cross-Validation -- 12.1 Motivation -- 12.2 The Walk-Forward Method -- 12.2.1 Pitfalls of the Walk-Forward Method -- 12.3 The Cross-Validation Method -- 12.4 The Combinatorial Purged Cross-Validation Method -- 12.4.1 Combinatorial Splits -- 12.4.2 The Combinatorial Purged Cross-Validation Backtesting Algorithm -- 12.4.3 A Few Examples -- 12.5 How Combinatorial Purged Cross-Validation Addresses Backtest Overfitting -- Exercises -- References -- 13 Backtesting on Synthetic Data -- 13.1 Motivation -- 13.2 Trading Rules -- 13.3 The Problem -- 13.4 Our Framework -- 13.5 Numerical Determination of Optimal Trading Rules -- 13.5.1 The Algorithm -- 13.5.2 Implementation -- 13.6 Experimental Results -- 13.6.1 Cases with Zero Long-Run Equilibrium -- 13.6.2 Cases with Positive Long-Run Equilibrium -- 13.6.3 Cases with Negative Long-Run Equilibrium -- 13.7 Conclusion -- Exercises -- References -- 14 Backtest Statistics -- 14.1 Motivation -- 14.2 Types of Backtest Statistics -- 14.3 General Characteristics -- 14.4 Performance -- 14.4.1 Time-Weighted Rate of Return -- 14.5 Runs -- 14.5.1 Returns Concentration -- 14.5.2 Drawdown and Time under Water -- 14.5.3 Runs Statistics for Performance Evaluation -- 14.6 Implementation Shortfall -- 14.7 Efficiency -- 14.7.1 The Sharpe Ratio -- 14.7.2 The Probabilistic Sharpe Ratio 5.2 The Stationarity vs. Memory Dilemma -- 5.3 Literature Review -- 5.4 The Method -- 5.4.1 Long Memory -- 5.4.2 Iterative Estimation -- 5.4.3 Convergence -- 5.5 Implementation -- 5.5.1 Expanding Window -- 5.5.2 Fixed-Width Window Fracdiff -- 5.6 Stationarity with Maximum Memory Preservation -- 5.7 Conclusion -- Exercises -- References -- Bibliography -- PART 2 Modelling -- 6 Ensemble Methods -- 6.1 Motivation -- 6.2 The Three Sources of Errors -- 6.3 Bootstrap Aggregation -- 6.3.1 Variance Reduction -- 6.3.2 Improved Accuracy -- 6.3.3 Observation Redundancy -- 6.4 Random Forest -- 6.5 Boosting -- 6.6 Bagging vs. Boosting in Finance -- 6.7 Bagging for Scalability -- Exercises -- References -- Bibliography -- 7 Cross-Validation in Finance -- 7.1 Motivation -- 7.2 The Goal of Cross-Validation -- 7.3 Why K-Fold CV Fails in Finance -- 7.4 A Solution: Purged K-Fold CV -- 7.4.1 Purging the Training Set -- 7.4.2 Embargo -- 7.4.3 The Purged K-Fold Class -- 7.5 Bugs in Sklearns Cross-Validation -- Exercises -- Bibliography -- 8 Feature Importance -- 8.1 Motivation -- 8.2 The Importance of Feature Importance -- 8.3 Feature Importance with Substitution Effects -- 8.3.1 Mean Decrease Impurity -- 8.3.2 Mean Decrease Accuracy -- 8.4 Feature Importance without Substitution Effects -- 8.4.1 Single Feature Importance -- 8.4.2 Orthogonal Features -- 8.5 Parallelized vs. Stacked Feature Importance -- 8.6 Experiments with Synthetic Data -- Exercises -- References -- 9 Hyper-Parameter Tuning with Cross-Validation -- 9.1 Motivation -- 9.2 Grid Search Cross-Validation -- 9.3 Randomized Search Cross-Validation -- 9.3.1 Log-Uniform Distribution -- 9.4 Scoring and Hyper-parameter Tuning -- Exercises -- References -- Bibliography -- PART 3 Backtesting -- 10 Bet Sizing -- 10.1 Motivation -- 10.2 Strategy-Independent Bet Sizing Approaches Learn to understand and implement the latest machine learning innovations to improve your investment performance Machine learning (ML) is changing virtually every aspect of our lives. Today, ML algorithms accomplish tasks that – until recently – only expert humans could perform. And finance is ripe for disruptive innovations that will transform how the following generations understand money and invest. In the book, readers will learn how to: Structure big data in a way that is amenable to ML algorithms Conduct research with ML algorithms on big data Use supercomputing methods and back test their discoveries while avoiding false positives Advances in Financial Machine Learning addresses real life problems faced by practitioners every day, and explains scientifically sound solutions using math, supported by code and examples. Readers become active users who can test the proposed solutions in their individual setting. Written by a recognized expert and portfolio manager, this book will equip investment professionals with the groundbreaking tools needed to succeed in modern finance. Title Page 8 Copyright 9 Dedication 10 Epigraph 12 Contents 14 About the Author 26 Preamble 28 1 Financial Machine Learning as a Distinct Subject 30 Part 1: Data Analysis 48 2 Financial Data Structures 50 3 Labeling 70 4 Sample Weights 86 5 Fractionally Differentiated Features 102 Part 2: Modelling 118 6 Ensemble Methods 120 7 Cross-Validation in Finance 130 8 Feature Importance 140 9 Hyper-Parameter Tuning with Cross-Validation 156 Part 3: Backtesting 166 10 Bet Sizing 168 11 The Dangers of Backtesting 178 12 Backtesting through Cross-Validation 188 13 Backtesting on Synthetic Data 196 14 Backtest Statistics 222 15 Understanding Strategy Risk 238 16 Machine Learning Asset Allocation 248 Part 4: Useful Financial Features 274 17 Structural Breaks 276 18 Entropy Features 290 19 Microstructural Features 308 Part 5: High-Performance Computing Recipes 328 20 Multiprocessing and Vectorization 330 21 Brute Force and Quantum Computers 346 22 High-Performance Computational Intelligence and Forecasting Technologies 356 Index 380 "Machine learning (ML) is changing virtually every aspect of our lives. Today ML algorithms accomplish tasks that until recently only expert humans could perform. As it relates to finance, this is the most exciting time to adopt a disruptive technology that will transform how everyone invests for generations. Readers will learn how to structure Big data in a way that is amenable to ML algorithms; how to conduct research with ML algorithms on that data; how to use supercomputing methods; how to backtest your discoveries while avoiding false positives. The book addresses real-life problems faced by practitioners on a daily basis, and explains scientifically sound solutions using math, supported by code and examples. Readers become active users who can test the proposed solutions in their particular setting. Written by a recognized expert and portfolio manager, this book will equip investment professionals with the groundbreaking tools needed to succeed in modern finance"-- Provided by publisher

Machine learning (ML) is changing virtually every aspect of our lives. Today ML algorithms accomplish tasks that until recently only expert humans could perform. As it relates to finance, this is the most exciting time to adopt a disruptive technology that will transform how everyone invests for generations. Readers will learn how to structure Big data in a way that is amenable to ML algorithms; how to conduct research with ML algorithms on that data; how to use supercomputing methods; how to backtest your discoveries while avoiding false positives. The book addresses real-life problems faced by practitioners on a daily basis, and explains scientifically sound solutions using math, supported by code and examples. Readers become active users who can test the proposed solutions in their particular setting. Written by a recognized expert and portfolio manager, this book will equip investment professionals with the groundbreaking tools needed to succeed in modern finance.

"This book begins by structuring financial data in a way that is amenable to machine learning (ML) algorithms. Then, the author discusses how to conduct research with ML algorithms on that data and how to backtest your discoveries. Most of the problems and solutions are explained using math, supported by code. This makes the book very practical and hands-on. Readers become active users who can test the solutions proposed in their work. Readers will learn how to structure, label, weight, and backtest data. Machine learning is the future, and this book will equip investment professionals with the tools to utilize it moving forward"-- Provided by publisher This book constitutes the thoroughly refereed post-workshop proceedings of the 6th International Workshop on Big Data Benchmarking, WBDB 2015, held in Toronto, ON, Canada, in June 2015 and the 7th International Workshop, WBDB 2015, held in New Delhi, India, in December 2015. The 8 full papers presented in this book were carefully reviewed and selected from 22 submissions. They deal with recent trends in big data and HPC convergence, new proposals for big data benchmarking, as well as tooling and performance results. Marcos Lo��pez De Prado. Includes Bibliographical References And Index.