Details

Advances in Financial Machine Learning

1. Aufl.

von: Marcos Lopez de Prado
38,99 €
Verlag:	Wiley
Format:	EPUB
Veröffentl.:	02.02.2018
ISBN/EAN:	9781119482109
Sprache:	englisch
Anzahl Seiten:	400

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Beschreibungen

Titelbeschreibung

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: <ul> <li>Structure big data in a way that is amenable to ML algorithms</li> <li>Conduct research with ML algorithms on big data</li> <li>Use supercomputing methods and back test their discoveries while avoiding false positives</li> </ul> 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.

Inhaltsverzeichnis

About the Author xxi PREAMBLE 1 1 Financial Machine Learning as a Distinct Subject 3 1.1 Motivation, 3 1.2 The Main Reason Financial Machine Learning Projects Usually Fail, 4 1.2.1 The Sisyphus Paradigm, 4 1.2.2 The Meta-Strategy Paradigm, 5 1.3 Book Structure, 6 1.3.1 Structure by Production Chain, 6 1.3.2 Structure by Strategy Component, 9 1.3.3 Structure by Common Pitfall, 12 1.4 Target Audience, 12 1.5 Requisites, 13 1.6 FAQs, 14 1.7 Acknowledgments, 18 Exercises, 19 References, 20 Bibliography, 20 Part 1 Data Analysis 21 2 Financial Data Structures 23 2.1 Motivation, 23 2.2 Essential Types of Financial Data, 23 2.2.1 Fundamental Data, 23 2.2.2 Market Data, 24 2.2.3 Analytics, 25 2.2.4 Alternative Data, 25 2.3 Bars, 25 2.3.1 Standard Bars, 26 2.3.2 Information-Driven Bars, 29 2.4 Dealing with Multi-Product Series, 32 2.4.1 The ETF Trick, 33 2.4.2 PCA Weights, 35 2.4.3 Single Future Roll, 36 2.5 Sampling Features, 38 2.5.1 Sampling for Reduction, 38 2.5.2 Event-Based Sampling, 38 Exercises, 40 References, 41 3 Labeling 43 3.1 Motivation, 43 3.2 The Fixed-Time Horizon Method, 43 3.3 Computing Dynamic Thresholds, 44 3.4 The Triple-Barrier Method, 45 3.5 Learning Side and Size, 48 3.6 Meta-Labeling, 50 3.7 How to Use Meta-Labeling, 51 3.8 The Quantamental Way, 53 3.9 Dropping Unnecessary Labels, 54 Exercises, 55 Bibliography, 56 4 Sample Weights 59 4.1 Motivation, 59 4.2 Overlapping Outcomes, 59 4.3 Number of Concurrent Labels, 60 4.4 Average Uniqueness of a Label, 61 4.5 Bagging Classifiers and Uniqueness, 62 4.5.1 Sequential Bootstrap, 63 4.5.2 Implementation of Sequential Bootstrap, 64 4.5.3 A Numerical Example, 65 4.5.4 Monte Carlo Experiments, 66 4.6 Return Attribution, 68 4.7 Time Decay, 70 4.8 Class Weights, 71 Exercises, 72 References, 73 Bibliography, 73 5 Fractionally Differentiated Features 75 5.1 Motivation, 75 5.2 The Stationarity vs. Memory Dilemma, 75 5.3 Literature Review, 76 5.4 The Method, 77 5.4.1 Long Memory, 77 5.4.2 Iterative Estimation, 78 5.4.3 Convergence, 80 5.5 Implementation, 80 5.5.1 Expanding Window, 80 5.5.2 Fixed-Width Window Fracdiff, 82 5.6 Stationarity with Maximum Memory Preservation, 84 5.7 Conclusion, 88 Exercises, 88 References, 89 Bibliography, 89 Part 2 Modelling 91 6 Ensemble Methods 93 6.1 Motivation, 93 6.2 The Three Sources of Errors, 93 6.3 Bootstrap Aggregation, 94 6.3.1 Variance Reduction, 94 6.3.2 Improved Accuracy, 96 6.3.3 Observation Redundancy, 97 6.4 Random Forest, 98 6.5 Boosting, 99 6.6 Bagging vs. Boosting in Finance, 100 6.7 Bagging for Scalability, 101 Exercises, 101 References, 102 Bibliography, 102 7 Cross-Validation in Finance 103 7.1 Motivation, 103 7.2 The Goal of Cross-Validation, 103 7.3 Why K-Fold CV Fails in Finance, 104 7.4 A Solution: Purged K-Fold CV, 105 7.4.1 Purging the Training Set, 105 7.4.2 Embargo, 107 7.4.3 The Purged K-Fold Class, 108 7.5 Bugs in Sklearn’s Cross-Validation, 109 Exercises, 110 Bibliography, 111 8 Feature Importance 113 8.1 Motivation, 113 8.2 The Importance of Feature Importance, 113 8.3 Feature Importance with Substitution Effects, 114 8.3.1 Mean Decrease Impurity, 114 8.3.2 Mean Decrease Accuracy, 116 8.4 Feature Importance without Substitution Effects, 117 8.4.1 Single Feature Importance, 117 8.4.2 Orthogonal Features, 118 8.5 Parallelized vs. Stacked Feature Importance, 121 8.6 Experiments with Synthetic Data, 122 Exercises, 127 References, 127 9 Hyper-Parameter Tuning with Cross-Validation 129 9.1 Motivation, 129 9.2 Grid Search Cross-Validation, 129 9.3 Randomized Search Cross-Validation, 131 9.3.1 Log-Uniform Distribution, 132 9.4 Scoring and Hyper-parameter Tuning, 134 Exercises, 135 References, 136 Bibliography, 137 Part 3 Backtesting 139 10 Bet Sizing 141 10.1 Motivation, 141 10.2 Strategy-Independent Bet Sizing Approaches, 141 10.3 Bet Sizing from Predicted Probabilities, 142 10.4 Averaging Active Bets, 144 10.5 Size Discretization, 144 10.6 Dynamic Bet Sizes and Limit Prices, 145 Exercises, 148 References, 149 Bibliography, 149 11 The Dangers of Backtesting 151 11.1 Motivation, 151 11.2 Mission Impossible: The Flawless Backtest, 151 11.3 Even If Your Backtest Is Flawless, It Is Probably Wrong, 152 11.4 Backtesting Is Not a Research Tool, 153 11.5 A Few General Recommendations, 153 11.6 Strategy Selection, 155 Exercises, 158 References, 158 Bibliography, 159 12 Backtesting through Cross-Validation 161 12.1 Motivation, 161 12.2 The Walk-Forward Method, 161 12.2.1 Pitfalls of the Walk-Forward Method, 162 12.3 The Cross-Validation Method, 162 12.4 The Combinatorial Purged Cross-Validation Method, 163 12.4.1 Combinatorial Splits, 164 12.4.2 The Combinatorial Purged Cross-Validation Backtesting Algorithm, 165 12.4.3 A Few Examples, 165 12.5 How Combinatorial Purged Cross-Validation Addresses Backtest Overfitting, 166 Exercises, 167 References, 168 13 Backtesting on Synthetic Data 169 13.1 Motivation, 169 13.2 Trading Rules, 169 13.3 The Problem, 170 13.4 Our Framework, 172 13.5 Numerical Determination of Optimal Trading Rules, 173 13.5.1 The Algorithm, 173 13.5.2 Implementation, 174 13.6 Experimental Results, 176 13.6.1 Cases with Zero Long-Run Equilibrium, 177 13.6.2 Cases with Positive Long-Run Equilibrium, 180 13.6.3 Cases with Negative Long-Run Equilibrium, 182 13.7 Conclusion, 192 Exercises, 192 References, 193 14 Backtest Statistics 195 14.1 Motivation, 195 14.2 Types of Backtest Statistics, 195 14.3 General Characteristics, 196 14.4 Performance, 198 14.4.1 Time-Weighted Rate of Return, 198 14.5 Runs, 199 14.5.1 Returns Concentration, 199 14.5.2 Drawdown and Time under Water, 201 14.5.3 Runs Statistics for Performance Evaluation, 201 14.6 Implementation Shortfall, 202 14.7 Efficiency, 203 14.7.1 The Sharpe Ratio, 203 14.7.2 The Probabilistic Sharpe Ratio, 203 14.7.3 The Deflated Sharpe Ratio, 204 14.7.4 Efficiency Statistics, 205 14.8 Classification Scores, 206 14.9 Attribution, 207 Exercises, 208 References, 209 Bibliography, 209 15 Understanding Strategy Risk 211 15.1 Motivation, 211 15.2 Symmetric Payouts, 211 15.3 Asymmetric Payouts, 213 15.4 The Probability of Strategy Failure, 216 15.4.1 Algorithm, 217 15.4.2 Implementation, 217 Exercises, 219 References, 220 16 Machine Learning Asset Allocation 221 16.1 Motivation, 221 16.2 The Problem with Convex Portfolio Optimization, 221 16.3 Markowitz’s Curse, 222 16.4 From Geometric to Hierarchical Relationships, 223 16.4.1 Tree Clustering, 224 16.4.2 Quasi-Diagonalization, 229 16.4.3 Recursive Bisection, 229 16.5 A Numerical Example, 231 16.6 Out-of-Sample Monte Carlo Simulations, 234 16.7 Further Research, 236 16.8 Conclusion, 238 Appendices, 239 16.A.1 Correlation-based Metric, 239 16.A.2 Inverse Variance Allocation, 239 16.A.3 Reproducing the Numerical Example, 240 16.A.4 Reproducing the Monte Carlo Experiment, 242 Exercises, 244 References, 245 Part 4 Useful Financial Features 247 17 Structural Breaks 249 17.1 Motivation, 249 17.2 Types of Structural Break Tests, 249 17.3 CUSUM Tests, 250 17.3.1 Brown-Durbin-Evans CUSUM Test on Recursive Residuals, 250 17.3.2 Chu-Stinchcombe-White CUSUM Test on Levels, 251 17.4 Explosiveness Tests, 251 17.4.1 Chow-Type Dickey-Fuller Test, 251 17.4.2 Supremum Augmented Dickey-Fuller, 252 17.4.3 Sub- and Super-Martingale Tests, 259 Exercises, 261 References, 261 18 Entropy Features 263 18.1 Motivation, 263 18.2 Shannon’s Entropy, 263 18.3 The Plug-in (or Maximum Likelihood) Estimator, 264 18.4 Lempel-Ziv Estimators, 265 18.5 Encoding Schemes, 269 18.5.1 Binary Encoding, 270 18.5.2 Quantile Encoding, 270 18.5.3 Sigma Encoding, 270 18.6 Entropy of a Gaussian Process, 271 18.7 Entropy and the Generalized Mean, 271 18.8 A Few Financial Applications of Entropy, 275 18.8.1 Market Efficiency, 275 18.8.2 Maximum Entropy Generation, 275 18.8.3 Portfolio Concentration, 275 18.8.4 Market Microstructure, 276 Exercises, 277 References, 278 Bibliography, 279 19 Microstructural Features 281 19.1 Motivation, 281 19.2 Review of the Literature, 281 19.3 First Generation: Price Sequences, 282 19.3.1 The Tick Rule, 282 19.3.2 The Roll Model, 282 19.3.3 High-Low Volatility Estimator, 283 19.3.4 Corwin and Schultz, 284 19.4 Second Generation: Strategic Trade Models, 286 19.4.1 Kyle’s Lambda, 286 19.4.2 Amihud’s Lambda, 288 19.4.3 Hasbrouck’s Lambda, 289 19.5 Third Generation: Sequential Trade Models, 290 19.5.1 Probability of Information-based Trading, 290 19.5.2 Volume-Synchronized Probability of Informed Trading, 292 19.6 Additional Features from Microstructural Datasets, 293 19.6.1 Distibution of Order Sizes, 293 19.6.2 Cancellation Rates, Limit Orders, Market Orders, 293 19.6.3 Time-Weighted Average Price Execution Algorithms, 294 19.6.4 Options Markets, 295 19.6.5 Serial Correlation of Signed Order Flow, 295 19.7 What Is Microstructural Information?, 295 Exercises, 296 References, 298 Part 5 High-performance Computing Recipes 301 20 Multiprocessing and Vectorization 303 20.1 Motivation, 303 20.2 Vectorization Example, 303 20.3 Single-Thread vs. Multithreading vs. Multiprocessing, 304 20.4 Atoms and Molecules, 306 20.4.1 Linear Partitions, 306 20.4.2 Two-Nested Loops Partitions, 307 20.5 Multiprocessing Engines, 309 20.5.1 Preparing the Jobs, 309 20.5.2 Asynchronous Calls, 311 20.5.3 Unwrapping the Callback, 312 20.5.4 Pickle/Unpickle Objects, 313 20.5.5 Output Reduction, 313 20.6 Multiprocessing Example, 315 Exercises, 316 Reference, 317 Bibliography, 317 21 Brute Force and Quantum Computers 319 21.1 Motivation, 319 21.2 Combinatorial Optimization, 319 21.3 The Objective Function, 320 21.4 The Problem, 321 21.5 An Integer Optimization Approach, 321 21.5.1 Pigeonhole Partitions, 321 21.5.2 Feasible Static Solutions, 323 21.5.3 Evaluating Trajectories, 323 21.6 A Numerical Example, 325 21.6.1 Random Matrices, 325 21.6.2 Static Solution, 326 21.6.3 Dynamic Solution, 327 Exercises, 327 References, 328 22 High-Performance Computational Intelligence and Forecasting Technologies 329 Kesheng Wu and Horst D. Simon 22.1 Motivation, 329 22.2 Regulatory Response to the Flash Crash of 2010, 329 22.3 Background, 330 22.4 HPC Hardware, 331 22.5 HPC Software, 335 22.5.1 Message Passing Interface, 335 22.5.2 Hierarchical Data Format 5, 336 22.5.3 In Situ Processing, 336 22.5.4 Convergence, 337 22.6 Use Cases, 337 22.6.1 Supernova Hunting, 337 22.6.2 Blobs in Fusion Plasma, 338 22.6.3 Intraday Peak Electricity Usage, 340 22.6.4 The Flash Crash of 2010, 341 22.6.5 Volume-synchronized Probability of Informed Trading Calibration, 346 22.6.6 Revealing High Frequency Events with Non-uniform Fast Fourier Transform, 347 22.7 Summary and Call for Participation, 349 22.8 Acknowledgments, 350 References, 350 Index 353

Autorenportrait

DR. MARCOS LÓPEZ DE PRADO is a principal at AQR Capital Management, and its head of machine learning. Marcos is also a research fellow at Lawrence Berkeley National Laboratory (U.S. Department of Energy, Office of Science). SSRN ranks him as one of the most-read authors in economics, and he has published dozens of scientific articles on machine learning and supercomputing in the leading academic journals. Marcos earned a PhD in financial economics (2003), a second PhD in mathematical finance (2011) from Universidad Complutense de Madrid, and is a recipient of Spain's National Award for Academic Excellence (1999). He completed his post-doctoral research at Harvard University and Cornell University, where he teaches a graduate course in financial machine learning at the School of Engineering. Marcos has an Erdös #2 and an Einstein #4 according to the American Mathematical Society.

Back cover copy

Praise for ADVANCES in FINANCIAL MACHINE LEARNING "Dr. López de Prado has written the first comprehensive book describing the application of modern ML to financial modeling. The book blends the latest technological developments in ML with critical life lessons learned from the author's decades of financial experience in leading academic and industrial institutions. I highly recommend this exciting book to both prospective students of financial ML and the professors and supervisors who teach and guide them." —PROF. PETER CARR, Chair of the Finance and Risk Engineering Department, NYU Tandon School of Engineering "Financial problems require very distinct machine learning solutions. Dr. López de Prado's book is the first one to characterize what makes standard machine learning tools fail when applied to the field of finance, and the first one to provide practical solutions to unique challenges faced by asset managers. Everyone who wants to understand the future of finance should read this book." —PROF. FRANK FABOZZI, EDHEC Business School; Editor of The Journal of Portfolio Management "Marcos has assembled in one place an invaluable set of lessons and techniques for practitioners seeking to deploy machine learning methods in finance. Marcos's insightful book is laden with useful advice to help keep a curious practitioner from going down any number of blind alleys, or shooting oneself in the foot." —ROSS GARON, Head of Cubist Systematic Strategies; Managing Director, Point72 Asset Management "The first wave of quantitative innovation in finance was led by Markowitz optimization. Machine learning is the second wave and it will touch every aspect of finance. López de Prado's Advances in Financial Machine Learning is essential for readers who want to be ahead of the technology rather than being replaced by it." —PROF. CAMPBELL HARVEY, Duke University; Former President of the American Finance Association "The author's academic and professional first-rate credentials shine through the pages of this book— indeed, I could think of few, if any, authors better suited to explaining both the theoretical and the practical aspects of this new and (for most)unfamiliar subject. Destined to become a classic in this rapidly burgeoning field." —PROF. RICCARDO REBONATO, EDHEC Business School; Former Global Head of Rates and FX Analytics at PIMCO

Unpublished endorsement

"In his new book Advances in Financial Machine Learning, noted financial scholar Marcos López de Prado strikes a well-aimed karate chop at the naive and often statistically overfit techniques that are so prevalent in the financial world today. He points out that not only are business-as-usual approaches largely impotent in today's high-tech finance, but in many cases they are actually prone to lose money. But López de Prado does more than just expose the mathematical and statistical sins of the finance world. Instead, he offers a technically sound roadmap for finance professionals to join the wave of machine learning. What is particularly refreshing is the author's empirical approach — his focus is on real-world data analysis, not on purely theoretical methods that may look pretty on paper but which in many cases are largely ineffective in practice. The book is geared to finance professionals who are already familiar with statistical data analysis techniques, but it is well worth the effort for those who want to do real state-of-the-art work in the field." —Dr. David H. Bailey, former Complex Systems Lead, Lawrence Berkeley National Laboratory. Co-discoverer of the BBP spigot algorithm "Finance has evolved from a compendium of heuristics based on historical financial statements to a highly sophisticated scientific discipline relying on computer farms to analyze massive data streams in real time. The recent highly impressive advances in machine learning (ML) are fraught with both promise and peril when applied to modern finance. While finance offers up the non-linearities and large data sets upon which ML thrives, it also offers up noisy data and the human element which presently lie beyond the scope of standard ML techniques. To err is human but if you really want to f**k things up, use a computer. Against this background, Dr. López de Prado has written the first comprehensive book describing the application of modern ML to financial modeling. The book blends the latest technological developments in ML with critical life lessons learned from the author's decades of financial experience in leading academic and industrial institutions. I highly recommend this exciting book to both prospective students of financial ML and the professors and supervisors who teach and guide them." —Prof. Peter Carr, Chair of the Finance and Risk Engineering Department, NYU Tandon School of Engineering "Marcos is a visionary who works tirelessly to advance the finance field. His writing is comprehensive and masterfully connects the theory to the application. It is not often you find a book that can cross that divide. This book is an essential read for both practitioners and technologists working on solutions for the investment community." —Landon Downs, President and co-Founder, 1QBit "Academics who want to understand modern investment management need to read this book. In it, Marcos Lopez de Prado explains how portfolio managers use machine learning to derive, test and employ trading strategies. He does this from a very unusual combination of an academic perspective and extensive experience in industry allowing him to both explain in detail what happens in industry and to explain how it works. I suspect that some readers will find parts of the book that they do not understand or that they disagree with, but everyone interested in understanding the application of machine learning to finance will benefit from reading this book." —Prof. David Easley, Cornell University. Chair of the NASDAQ-OMX Economic Advisory Board "For many decades, finance has relied on overly simplistic statistical techniques to identify patterns in data. Machine learning promises to change that by allowing researchers to use modern non-linear and highly-dimensional techniques, similar to those used in scientific fields like DNA analysis and astrophysics. At the same time, applying those machine learning algorithms to model financial problems would be dangerous. Financial problems require very distinct machine learning solutions. Dr. López de Prado's book is the first one to characterize what makes standard machine learning tools fail when applied to the field of finance, and the first one to provide practical solutions to unique challenges faced by asset managers. Everyone who wants to understand the future of finance should read this book." —Prof. Frank Fabozzi, EDHEC Business School. Editor of The Journal of Portfolio Management "This is a welcome departure from the knowledge hoarding that plagues quantitative finance. López de Prado defines for all readers the next era of finance: industrial scale scientific research powered by machines." —John Fawcett, Founder and CEO, Quantopian "Marcos has assembled in one place an invaluable set of lessons and techniques for practitioners seeking to deploy machine learning techniques in finance. If machine learning is a new and potentially powerful weapon in the arsenal of quantitative finance, Marcos' insightful book is laden with useful advice to help keep a curious practitioner from going down any number of blind alleys, or shooting oneself in the foot." —Ross Garon, Head of Cubist Systematic Strategies. Managing Director, Point72 Asset Management "The first wave of quantitative innovation in finance was led by Markowitz optimization. Machine Learning is the second wave and it will touch every aspect of finance. López de Prado's Advances in Financial Machine Learning is essential for readers who want to be ahead of the technology rather than being replaced by it." —Prof. Campbell Harvey, Duke University. Former President of the American Finance Association "The complexity inherent to financial systems justifies the application of sophisticated mathematical techniques. Advances in Financial Machine Learning is an exciting book that unravels a complex subject in clear terms. I wholeheartedly recommend this book to anyone interested in the future of quantitative investments." —Prof. John C. Hull, University of Toronto, Author of Options, Futures, and other Derivatives "Prado's book clearly illustrates how fast this world is moving, and how deep you need to dive if you are to excel and deliver top of the range solutions and above the curve performing algorithms... Prado's book is clearly at the bleeding edge of the machine learning world." —Irish Tech News "Financial data is special for a key reason: The markets have only one past. There is no 'control group', and you have to wait for true out-of-sample data. Consequently, it is easy to fool yourself, and with the march of Moore's Law and the new machine learning, it's easier than ever. López de Prado explains how to avoid falling for these common mistakes. This is an excellent book for anyone working, or hoping to work, in computerized investment and trading." —Dr. David J. Leinweber, Former Managing Director, First Quadrant, Author of Nerds on Wall Street: Math, Machines and Wired Markets "In his new book, Dr. López de Prado demonstrates that financial machine learning is more than standard machine learning applied to financial datasets. It is an important field of research in its own right. It requires the development of new mathematical tools and approaches, needed to address the nuances of financial datasets. I strongly recommend this book to anyone who wishes to move beyond the standard Econometric toolkit." —Dr. Richard R. Lindsey, Managing Partner, Windham Capital Management, Former Chief Economist, U.S. Securities and Exchange Commission "Dr. Lopez de Prado, a well-known scholar and an accomplished portfolio manager who has made several important contributions to the literature on machine learning (ML) in finance, has produced a comprehensive and innovative book on the subject. He has illuminated numerous pitfalls awaiting anyone who wishes to use ML in earnest, and he has provided much needed blueprints for doing it successfully. This timely book, offering a good balance of theoretical and applied findings, is a must for academics and practitioners alike." —Prof. Alexander Lipton, Connection Science Fellow, Massachusetts Institute of Technology. Risk's Quant of the Year (2000) "How does one make sense of todays’ financial markets in which complex algorithms route orders, financial data is voluminous, and trading speeds are measured in nanoseconds? In this important book, Marcos López de Prado sets out a new paradigm for investment management built on machine learning. Far from being a 'black box' technique, this book clearly explains the tools and process of financial machine learning. For academics and practitioners alike, this book fills an important gap in our understanding of investment management in the machine age." —Prof. Maureen O'Hara, Cornell University. Former President of the American Finance Association "Marcos López de Prado has produced an extremely timely and important book on machine learning. The author's academic and professional first-rate credentials shine through the pages of this book - indeed, I could think of few, if any, authors better suited to explaining both the theoretical and the practical aspects of this new and (for most) unfamiliar subject. Both novices and experienced professionals will find insightful ideas, and will understand how the subject can be applied in novel and useful ways. The Python code will give the novice readers a running start, and will allow them to gain quickly a hands-on appreciation of the subject. Destined to become a classic in this rapidly burgeoning field." —Prof. Riccardo Rebonato, EDHEC Business School. Former Global Head of Rates and FX Analytics at PIMCO "A tour de force on practical aspects of machine learning in finance brimming with ideas on how to employ cutting edge techniques, such as fractional differentiation and quantum computers, to gain insight and competitive advantage. A useful volume for finance and machine learning practitioners alike." —Dr. Collin P. Williams, Head of Research, D-Wave Systems