Probabilistic methods for financial and marketing informatics

Probabilistic Methods for Financial and Marketing Informatics Richard E Neapolitan Xia Jiang Publisher Publishing Services Manager Project Manager Assistant Editor Interior printer Cover printer Diane D Cerra George Morrison Kathryn Liston Asma Palmeiro The Maple-Vail Book Manufacturing Group Phoenix Color Morgan Kaufmann Publishers is an imprint of Elsevier 500 Sansome Street, Suite 400, San Francisco, CA 94111 This book is printed on acid-free paper @ 2007 by Elsevier Inc All rights reserved Designations used by companies to distinguish their products are often claimed as trademarks or registered trademarks In all instances in which Morgan Kaufmann Publishers is aware of a claim, the product names appear in initial capital or all capital letters Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, scanning, or otherwise-without prior written permission of the publisher Permissions may be sought directly from Elsevier's Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: permissions@elsevier.com You may also complete your request online via the Elsevier homepage (http://elsevier.com), by selecting "Support Contact" then "Copyright and Permission" and then "Obtaining Permissions." Library of Congress Cataloging-in-Publication Data Application submitted ISBN 13:978-0-12-370477-1 ISBN10:0-12-370477-4 For information on all Morgan Kaufmann publications, visit our Web site at www.mkp.com or www.books.elsevier.com Printed in the United States of America 07 08 09 10 11 10987654321 Working together to grow libraries in developing countries www.elsevier.com I www.bookaid.org I www.sabre.org Preface This book is based on a course I recently developed for computer science majors at Northeastern Illinois University (NEIU) The motivation for developing this course came from guidance I obtained from the NEIU Computer Science Department Advisory Board One objective of this Board is to advise the Department concerning the maintenance of curricula that is relevant to the needs of companies in Chicagoland The Board consists of individuals in IT departments from major companies such as Walgreen's, AON Company, United Airlines, Harris Bank, and Microsoft After the dot.com bust and the introduction of outsourcing, it became evident that students, trained only in the fundamentals of computer science, programming, web design, etc., often did not have the skills to compete in the current U.S job market So I asked the Advisory Board what else the students should know The board unanimously felt the students needed business skills such as knowledge of IT project management, marketing, and finance As a result, our revised curriculum, for students who hoped to obtain employment immediately following graduation, contained a number of business courses However, several members of the board said they'd like to see students equipped with knowledge of cutting edge applications of computer science to areas such as decision analysis, risk management, data mining, and market basket analysis I realized that some of the best work in these areas was being done in my own field, namely Bayesian networks After consulting with colleagues worldwide and checking on topics taught in similar programs at other universities, I decided it was time for a course on applying probabilistic reasoning to business problems So my new course called "Informatics for MIS Students" and this book called Probabilistic Methods for Financial and Marketing Informatics were conceived Part I covers the basics of Bayesian networks and decision analysis Much of this material is based on my 2004 book Learning Bayesian Networks However, I've tried to make the material more accessible Rather than dwelling on rigor, algorithms, and proofs of theorems, I concentrate on showing examples and using the software package Netica to represent and solve problems The specific content of Part I is as follows: Chapter provides a definition of informatics and probabilistic informatics Chapter reviews the probability and statistics needed to understand the remainder of the book Chapter presents Bayesian networks and inference in Bayesian networks Chapter concerns learning Bayesian networks from data Chapter introduces decision analysis iii iv and influence diagrams, and Chapter covers further topics in decision analysis There is overlap between the material in Part I and that which would be found in a book on decision analysis However, I discuss Bayesian networks and learning Bayesian networks in more detail, whereas a decision analysis book would show more examples of solving problems using decision analysis Sections and subsections in Part I that are marked with a star ( ~ ) contain material that either requires a background in continuous mathematics or that seems to be inherently more difficult than the material in the rest of the book For the most part, these sections can be skipped without impacting one's mastery of the rest of the book The only exception is that if Section 3.6 (which covers d-separation) is omitted, it will be necessary to briefly review the faithfulness condition in order to understand Sections 4.4.1 and 4.5.1, which concern the constraint-based method for learning faithful DAGs from data I believe one can gain an intuition for this type of learning from a few simple examples, and one does not need a formal knowledge of d-separation to understand these examples I've presented constraint-based learning in this fashion at several talks and workshops worldwide and found that the audience could always understand the material Furthermore, this is how I present the material to my students Part II presents financial applications Specifically, Chapter presents the basics of investment science and develops a Bayesian network for portfolio risk analysis Sections 7.2 and 7.3 are marked with a star ('k) because the material in these sections seems inherently more difficult than most of the other material in the book However, they not require as background the material from Part I that is marked with a star ( ~ ) Chapter discusses modeling real options, which concerns decisions a company must make as to what projects it should pursue Chapter covers venture capital decision making, which is the process of deciding whether to invest money in a start-up company Chapter 10 discusses a model for bankruptcy prediction Part III contains chapters on two important areas of marketing First, Chapter 11 shows methods for doing collaborative filtering and market basket analysis These disciplines concern determining what products an individual might prefer based on how the individual feels about other products Finally, Chapter 12 presents a technique for doing targeted advertising, which is the process of identifying those customers to whom advertisements should be sent There is too much material for me to cover the entire book in a one semester course at NEIU Since the course requires discrete mathematics and business statistics as prerequisites, I only review most of the material in Chapter However, I discuss conditional independence in depth because ordinarily the students have not been exposed to this concept I then cover the following sections from the remainder of the book: Chapter 3:3.1-3.5.1 Chapter 4: 4.1, 4.2, 4.4.1, 4.5.1, 4.6 Chapter 5: 5.1-5.3.2, 5.3.4 Chapters - 12: All sections The course is titled "Informatics for MIS Students," and is a required course in the MIS (Management Information Science) concentration of NEIU's Computer Science M.S Degree Program This book should be appropriate for any similar course in an MIS, computer science, business, or MBA program It is intended for upper level undergraduate and graduate students Besides having taken one or two courses covering basic probability and statistics, it would be useful but not necessary for the student to have studied data structures Part I of the book could also be used for the first part of any course involving probabilistic reasoning using Bayesian networks That is, although many of the examples in Part I concern the stock market and applications to business problems, I've presented the material in a general way Therefore, an instructor could use Part I to cover basic concepts and then provide papers relative to a particular domain of interest For example, if the course is "Probabilistic Methods for Medical Informatics," the instructor could cover Part I of this book, and then provide papers concerning applications in the medical domain For the most part, the applications discussed in Part II were the results of research done at the School of Business of the University of Kansas, while the applications in Part III were the results of research done by the Machine Learning and Applied Statistics Group of Microsoft Research The reason is not that I have any particular affiliations with either of this institutions Rather, I did an extensive search for financial and marketing applications, and the ones I found that seemed to be most carefully designed and evaluated came from these institutions I thank Catherine Shenoy for reviewing the chapter on investment science and Dawn Homes, Francisco Javier Dfez, and Padmini Jyotishmati for reviewing the entire book They all offered many useful comments and criticisms I thank Prakash Shenoy and Edwin Burmeister for correspondence concerning some of the content of the book I thank my co-author, Xia Jiang, for giving me the idea to write this book in the first place, and for her efforts on the book itself Finally, I thank Prentice Hall for granting me permission to reprint material from my 2004 book Learning Bayesian Networks Rich Neapolitan RE-Neapolit an@neiu, ed u This Page Intentionally Left Blank Contents Preface I iii Bayesian Networks and Decision Analysis Probabilistic Informatics W h a t Is I n f o r m a t i c s ? Probabilistic Informatics 1.3 O u t l i n e of T h i s B o o k Probability and Statistics 2.1 2.2 2.3 2.4 2.5 3 1.1 1.2 P r o b a b i l i t y Basics 2.1.1 Probability Spaces 2.1.2 Conditional Probability and Independence 10 12 2.1.3 Bayes' Theorem Random Variables 2.2.1 P r o b a b i l i t y D i s t r i b u t i o n s of R a n d o m V a r i a b l e s 2.2.2 I n d e p e n d e n c e of R a n d o m V a r i a b l e s T h e M e a n i n g of P r o b a b i l i t y 2.3.1 Relative Frequency Approach to Probability 2.3.2 Subjective Approach to Probability R a n d o m V a r i a b l e s in A p p l i c a t i o n s Statistical Concepts 2.5.1 Expected Value 2.5.2 Variance and Covariance 2.5.3 Linear Regression 15 16 16 21 24 25 28 30 34 34 35 41 Bayesian Networks 53 3.1 W h a t Is a B a y e s i a n N e t w o r k ? 54 3.2 P r o p e r t i e s of B a y e s i a n N e t w o r k s 3.2.1 D e f i n i t i o n of a B a y e s i a n N e t w o r k 3.2.2 R e p r e s e n t a t i o n of a B a y e s i a n N e t w o r k 56 56 59 3.3 C a u s a l N e t w o r k s as B a y e s i a n N e t w o r k s 63 3.3.1 3.3.2 63 68 Causality Causality and the Markov Condition CONTENTS viii 3.4 3.5 3.6 3.3.3 T h e Markov Condition w i t h o u t Causality Inference in Bayesian Networks 3.4.1 Examples of Inference 3.4.2 Inference Algorithms and Packages 3.4.3 Inference Using Netica How Do We O b t a i n t h e Probabilities? 3.5.1 T h e Noisy O R - G a t e Model 3.5.2 M e t h o d s for Discretizing Continuous Variables * Entailed Conditional Independencies * 3.6.1 Examples of Entailed Conditional Independencies 3.6.2 d-Separation 3.6.3 Faithful and Unfaithful P r o b a b i l i t y Distributions 3.6.4 Markov Blankets and Boundaries 71 72 73 75 77 78 79 86 92 92 95 99 102 Learning Bayesian Networks 4.1 4.2 4.3 4.4 4.5 4.6 4.7 111 P a r a m e t e r Learning 112 4.1.1 Learning a Single P a r a m e t e r 112 4.1.2 Learning All P a r a m e t e r s in a Bayesian Network 119 Learning S t r u c t u r e (Model Selection) 126 Score-Based S t r u c t u r e Learning * 127 4.3.1 Learning S t r u c t u r e Using the Bayesian Score 127 4.3.2 Model Averaging 137 C o n s t r a i n t - B a s e d S t r u c t u r e Learning 138 4.4.1 Learning a DAG Faithful to P 138 4.4.2 Learning a DAG in Which P Is E m b e d d e d Faithfully ~ 144 Causal Learning 145 4.5.1 Causal Faithfulness A s s u m p t i o n 145 4.5.2 Causal E m b e d d e d Faithfulness A s s u m p t i o n ~ 148 Software Packages for Learning 151 E x a m p l e s of Learning 153 4.7.1 Learning Bayesian Networks 153 4.7.2 Causal Learning 162 Decision Analysis Fundamentals 5.1 5.2 5.3 Decision Trees 5.1.1 Simple E x a m p l e s 5.1.2 Solving More C o m p l e x Decision Trees Influence D i a g r a m s 5.2.1 Representing with Influence D i a g r a m s 5.2.2 Solving Influence Diagrams 5.2.3 Techniques for Solving Influence D i a g r a m s * 5.2.4 Solving Influence Diagrams Using Netica D y n a m i c Networks * 5.3.1 D y n a m i c Bayesian Networks 5.3.2 D y n a m i c Influence D i a g r a m s 177 178 178 182 195 195 202 202 207 212 212 219 Further Techniques in Decision Analysis 6.1 6.2 6.3 6.4 6.5 6.6 II 229 M o d e l i n g Risk Preferences 230 6.1.1 The Exponential Utility Function 231 6.1.2 A D e c r e a s i n g Risk-Averse U t i l i t y F u n c t i o n A n a l y z i n g Risk D i r e c t l y 6.2.1 Using t h e Variance to M e a s u r e Risk 6.2.2 Risk Profiles Dominance 235 236 236 238 240 6.3.1 Deterministic Dominance 6.3.2 Stochastic Dominance 6.3.3 G o o d Decision versus G o o d O u t c o m e 240 241 S e n s i t i v i t y Analysis 6.4.1 Simple M o d e l s 6.4.2 A More Detailed Model 243 244 244 250 Value of I n f o r m a t i o n 254 6.5.1 E x p e c t e d Value of Perfect I n f o r m a t i o n 255 6.5.2 E x p e c t e d Value of I m p e r f e c t I n f o r m a t i o n N o r m a t i v e Decision Analysis Financial Applications 257 259 265 Investment Science 267 7.1 267 7.2 7.3 Basics of I n v e s t m e n t Science 7.1.1 Interest 7.1.2 Net P r e 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Intelligent Data Mining, Springer-Verlag, New York, 1999 [Zadeh, 1995] Zadeh, L., "Probability Theory and Fuzzy Logic Are Complementary Rather Than Competitive," Technometrics, Vol 37, 1995 Index Bracket Medians Method, 87 Abstract model, Accountability, 82 Active user, 374 Algorithm heuristic, model-based, Alternative, 179 Ancestor, 57 Arbitrage, 297 Arbitrage Pricing Theory (APT), 297 Arc reversal/node reduction, 207 Asset, 272 Average absolute deviation scoring, 381 Capital Asset Pricing Model (CAPM), 289 Capital market line, 286 Cascaded naive Bayesian network, 368 Case amplification, 377 Causal DAG, 63, 68, 105 Causal embedded faithfulness condition, 148 Causal faithfulness condition, 146 Causal graph, 68 Causal inhibition, 82 Causal Markov assumption, 69, 145 Causal minimum message length (CaMML), 155 Causal network, 69, 145 Causal strength, 80 Causality, 63 and the Markov condition, 68 Bad decision/good outcome, 243 Bayes' Theorem, 15, 53 Bayesian, 33 Bayesian information criterion (BIC), 152 Bayesian network, 58 dynamic, 213 embedded, 86 inference in, 72 learning parameters of, 112 learning structure of constraint-based, 138 score-based, 127 model averaging and, 137 naive, 358 cascaded, 368 noisy OR-gate model in, 79 parameters, 111 structure, 111 Bayesian score, 127 Beliefs, 28 Beta, 287 Blocked, 96 Cause direct, 68 Chain, 57 Chain rule, 20, 47 Chance node, 179, 195 Class probability tree, 388 complete, 388 growing, 390 Cluster learning problem, 378 Coefficient of determination, 44, 293 Collaborative filtering, 6, 373 memory-based, 374 model-based, 374 Compound interest, 269 Constant risk-averse utility function, 235 409 410 Constant-Growth Dividend Discount Model, 307 Convenience sample, 66 Correlation coefficient, 38, 375 Covariance, 37 Cumulative risk profile, 239 Cycle, 57 D-separation, 97 Data, Data mining, Datum, Decision, 179 versus good/bad outcome, 243 Decision analysis, 180 normative, 259 Decision node, 179, 195 Decision tree, 179 algorithm for solving, 182 solving, 180 Decreasing risk-averse utility function, 235 Default voting, 377 Descendent, 57 Deterministic dominance, 240 Direct cause, 68 Directed acyclic graph (DAG), 57 d-separation in, 97 head-to-head meeting in, 96 head-to-tail meeting in, 96 tail-to-tail meeting in, 96 Directed edge, 57 Directed graph, 56 Discounted cash flow (DCF), 329 Discounting, 56, 66 Discretizing continuous variables, 86 Bracket Medians Method, 87 Pearson-Tukey Method, 90, 363 Dividend, 272 Dividend Discount Model (DDM), 307 Dominance deterministic, 240 stochastic, 241 Dynamic Bayesian network, 213 Dynamic influence diagram, 219 INDEX Earnings, 308 retained, 308 Earnings per share (EPS), 308 Efficient frontier, 284 Efficient market, 285 Embedded Bayesian network, 86 Embedded faithfulness condition, 143 causal, 148 Emergent behavior, 222 Entailed conditional independency, 92 Equity, 308 Equivalent sample size, 123 Event, 10 elementary, 10 Exception independence, 82 Exchangeability, 113 Expected dividend growth rate, 307 Expected lift in profit (ELP), 392 Expected utility, 179 Expected value, 34 Expected value maximizer, 230 Expected value of imperfect informarion (EVII), 258 Expected value of perfect information (EVPI), 255 Experiment, 10 Explicit voting, 374 Exponential utility function, 231 Factor model, 296 Faithfulness condition, 101 and Markov boundary, 103 causal, 146 Firm-specific risk, 288 Forward P/E ratio, 311 Frequentist, 25 Fundamental analysis, 303 Good decision/bad outcome, 243 Greedy equivalent search (GES), 152 Growth rate expected dividend, 307 Growth stocks, 301 Head-to-head meeting, 96 Head-to-tail meeting, 96 INDEX Heuristic algorithm, Holding period, 268 Holding period return (HPR) return rate, 272 Implicit voting, 373 Includes, 127 Income stocks, 301 Independence, 13 conditional, 13 of random variables, 22, 23 of random variables, 21, 23 of random vectors, 212 Influence diagram, 195 dynamic, 219 solving, 203 Informatics, bio, financial, marketing, 5, medical, Information, Initial public offering (IPO), 271 Instantiate, 66 Interest compound, 269 simple, 268 Intrinsic value, 305 Inverse-user frequency, 377 Knowledge, Leaky noisy OR-gate model, 83 general formula for, 84 Linear regression multiple, 45 simple, 42 Logistic regression, 369 Logit function, 86 Macroeconomic risk factors, 296 Maintenance margin, 275 Managerial option, 330 Manipulation, 64 bad, 105 Margin, 274 call, 276 411 maintenance, 275 Market basket analysis, 374 Market portfolio, 276 Market risk, 288 Market-value-weighted index, 277 Markov blanket, 102 Markov boundary, 103 Markov condition, 58 and causal Markov assumption, 145 and Markov blanket, 102 Markov equivalent, 122 Markov property, 214 Maximum a posterior probability (MAP) 113 Maximum likelihood estimate (MLE), 27, 112 Mean, 35 Mean-standard deviation diagram, 280 Minimum message length (MML), 155 Minimum variance portfolio, 282 Mobile target localization, 216 Model averaging, 137 Model selection, 125 Model-based algorithm, Multiple linear regression, 45 Mutually exclusive and exhaustive, 14 Naive Bayesian network, 358 Net present expected value (NPEV), 329 Net present value (NPV), 271 No arbitrage principle, 297 Node(s), 56 chance, 179, 195 decision, 179, 195 utility, 195 Noisy OR-gate model, 79 assumptions in, 82 general formula for, 82 leaky, 83 Nondescendent, 57 Nonsystematic risk, 288 Nonsystematic shock, 296 412 Normative decision analysis, 259 Odds, 29 One-Fund Theorem, 285 Outcomes, 10 P / E ratio, 311 forward, 311 trailing, 311 Parameters, 111 Parent, 57 Path, 57 Pearson-Tukey Method, 90, 363 Plowback ratio, 309 Population, 10, 26, 30 finite, 26 Price-weighted index, 277 Principal, 268 Principle of Indifference, 11 Probability conditional, 12 correlation coefficient and, 38 covariance and, 37 distribution, 17 joint, 18 marginal, 19 expected value and, 34 law of total, 14 maximum a posterior, 113 maximum likelihood estimate of, 27 odds and, 29 posterior, 32 Principle of Indifference and, 11 prior, 32 relative frequency approach to, 25 space, 11 subjective approach to, 28 variance and, 35 Prospect theory, 259 Prospectus, 271 Quality adjusted life expectancy (QALE), 191 R-squared, 44, 293 INDEX Random matrix, 212 Random process, 27 Random sample, 26 Random sequence, 27 Random variable(s), 16 chain rule for, 20, 47 conditional independence of, 22, 23 in applications, 30 independence of, 21, 23 joint probability distribution of, 18 probability distribution of, 17 marginal, 19 space of, 16 Random vector, 212 Randomized controlled experiment (RCE), 64 Ranked scoring, 381 Rate of return, 268 Real option, 330 Regression logistic, 369 multiple linear, 45 simple linear, 42 Regret theory, 259 Relative frequency, 25 Required rate of return, 304 Retained earnings, 308 Return on equity (ROE), 308 Risk exposure, 290, 296 Risk premium, 290, 298 Risk profile, 238 cumulative, 239 Risk tolerance, 231 Risky discount rate, 329 Sample convenience, 66 random, 26 Sample space, 10 Sampling, 26 with replacement, 27 Score-based structure learning, 127 Security market line, 290 Selection bias, 66 Sensitivity analysis, 244 413 INDEX two-way, 246 Share capital, 308 Shareholder's equity, 308 Short sale, 274 Sigmoid function, 86 Simple interest, 268 Simple linear regression, 42 Standard error of coefficient, 43 Stationary, 214 Stochastic dominance, 241 Stock exchange, 271 Stock market index, 277 market-value-weighted, 277 price-weighted, 277 Stocks, 271 growt h, 301 income, 301 total capitalization of, 276 Structure, 111 Subjective probability, 28 Subjectivist, 28 Systematic risk, 288 Tail-to-tail meeting, 96 Targeted advertising, 387 Time trade-off quality adjustment, 191 Time-separable, 219 Total capitalization, 276 Trailing P/E ratio, 311 Treasury shares, 308 Two-way sensitivity analysis, 246 Utility, 179 expected, 179 Utility function, 230 constant risk-averse, 235 decreasing risk-averse, 235 exponential, 231 Utility node, 195 Valuation Model, 303 Value-at-risk (VaR), 319 Variance, 35 Vector similarity, 377 Venture capital (VC), 343 Voting default, 377 explicit, 374 implicit, 373 Weight in a portfolio, 276 This Page Intentionally Left Blank ... areas of informatics, namely financial informatics and marketing informatics F i n a n c i a l i n f o r m a t i c s involves applying the methods of informatics to the management of money and other... time for a course on applying probabilistic reasoning to business problems So my new course called "Informatics for MIS Students" and this book called Probabilistic Methods for Financial and Marketing. .. States These programs go by various names, including bioinformatics, medical informatics, chemical informatics, music informatics, marketing informatics, etc What these programs have in common? To