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Bayesian Programming Bayesian Programming K13774_FM.indd 1 10/28/13 2:17 PM Chapman & Hall/CRC Machine Learning & Pattern Recognition Series SERIES EDITORS Ralf Herbrich Thore Graepel Amazon Development Center Microsoft Research Ltd. Berlin, Germany Cambridge, UK AIMS AND SCOPE This series reflects the latest advances and applications in machine learning and pat- tern recognition through the publication of a broad range of reference works, text- books, and handbooks. The inclusion of concrete examples, applications, and meth- ods is highly encouraged. The scope of the series includes, but is not limited to, titles in the areas of machine learning, pattern recognition, computational intelligence, robotics, computational/statistical learning theory, natural language processing, computer vision, game AI, game theory, neural networks, computational neurosci- ence, and other relevant topics, such as machine learning applied to bioinformatics or cognitive science, which might be proposed by potential contributors. PUBLISHED TITLES MACHINE LEARNING: An Algorithmic Perspective Stephen Marsland HANDBOOK OF NATURAL LANGUAGE PROCESSING, Second Edition Nitin Indurkhya and Fred J. Damerau UTILITY-BASED LEARNING FROM DATA Craig Friedman and Sven Sandow A FIRST COURSE IN MACHINE LEARNING Simon Rogers and Mark Girolami COST-SENSITIVE MACHINE LEARNING Balaji Krishnapuram, Shipeng Yu, and Bharat Rao ENSEMBLE METHODS: FOUNDATIONS AND ALGORITHMS Zhi-Hua Zhou MULTI-LABEL DIMENSIONALITY REDUCTION Liang Sun, Shuiwang Ji, and Jieping Ye BAYESIAN PROGRAMMING Pierre Bessière, Emmanuel Mazer, Juan-Manuel Ahuactzin, and Kamel Mekhnacha K13774_FM.indd 2 10/28/13 2:17 PM Chapman & Hall/CRC Machine Learning & Pattern Recognition Series Bayesian Programming Pierre Bessière CNRS, Paris, France Emmanuel Mazer CNRS, Grenoble, France Juan-Manuel Ahuactzin PROBAYES, Puebla, Mexico Kamel Mekhnacha PROBAYES, Grenoble, France K13774_FM.indd 3 10/28/13 2:17 PM CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20131023 International Standard Book Number-13: 978-1-4398-8033-3 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com To the late Edwin Thompson Jaynes for his doubts about certitudes and for his certitudes about probabilities This page intentionally left blank Contents Foreword xv Preface xvii 1 Introduction 1 1.1 Probability an alternative to logic . 1 1.2 Aneedforanewcomputingparadigm . 5 1.3 A need for a new modeling methodology . 5 1.4 A need for new inference algorithms . 8 1.5 A need for a new programming language and new hardware 10 1.6 Aplacefornumerouscontroversies . 11 1.7 Runningrealprogramsasexercises . 12 I Bayesian Programming Principles 15 2 Basic Concepts 17 2.1 Variable ............................. 18 2.2 Probability . 18 2.3 The normalization postulate . 19 2.4 Conditional probability . 19 2.5 Variable conjunction . 20 2.6 Theconjunctionpostulate(Bayestheorem) . 20 2.7 Syllogisms . 21 2.8 The marginalization rule . 22 2.9 Joint distribution and questions . 23 2.10 Decomposition ......................... 25 2.11 Parametricforms ........................ 26 2.12 Identification .......................... 28 2.13 Specification = Variables + Decomposition + Parametricforms ........................ 29 2.14 Description = Specification + Identification . 29 2.15 Question............................. 29 2.16 Bayesian program = Description + Question . 31 2.17 Results ............................. 32 vii viii Contents 3 Incompleteness and Uncertainty 35 3.1 Observingawatertreatmentunit . 35 3.1.1 The elementary water treatment unit . 36 3.1.2 Experimentation and uncertainty . 38 3.2 Lessons,comments,andnotes . 40 3.2.1 The effect of incompleteness . 40 3.2.2 Theeffectofinaccuracy . .. .. .. .. .. .. 41 3.2.3 Not taking into account the effect of ignored variables may lead to wrong decisions . 42 3.2.4 From incompleteness to uncertainty . 43 4 Description = Specification + Identification 47 4.1 Pushing objects and following contours . 48 4.1.1 TheKheperarobot ................... 48 4.1.2 Pushingobjects ..................... 49 4.1.3 Following contours . 53 4.2 Description of a water treatment unit . 56 4.2.1 Specification . 56 4.2.2 Identification . 59 4.2.3 Bayesianprogram.................... 59 4.2.4 Results . 60 4.3 Lessons,comments,andnotes . 60 4.3.1 Description = Specification + Identification . 60 4.3.2 Specification = Variables + Decomposition + Forms 61 4.3.3 Learning is a means to transform incompleteness into uncertainty ....................... 62 5 TheImportanceofConditionalIndependence 65 5.1 WatertreatmentcenterBayesianmodel . 65 5.2 Descriptionofthewatertreatmentcenter . 66 5.2.1 Specification . 66 5.2.2 Identification . 70 5.2.3 Bayesianprogram.................... 71 5.3 Lessons,comments,andnotes . 71 5.3.1 Independence versus conditional independence . 71 5.3.2 The importance of conditional independence . 73 6 BayesianProgram=Description+Question 75 6.1 WatertreatmentcenterBayesianmodel(end) . 76 6.2 Forward simulation of a single unit . 76 6.2.1 Question . 77 6.2.2 Results . 78 6.3 Forwardsimulationofthe water treatmentcenter . 78 6.3.1 Question . 78 6.3.2 Results . 80 Contents ix 6.4 Controlofthewatertreatmentcenter . 81 6.4.1 Question(1)....................... 81 6.4.2 Results(1)........................ 81 6.4.3 Question(2)....................... 82 6.4.4 Results(2)........................ 84 6.5 Diagnosis ............................ 85 6.5.1 Question . 86 6.5.2 Results . 86 6.6 Lessons,comments,andnotes . 87 6.6.1 Bayesian Program = Description + Question . 87 6.6.2 The essence of Bayesian inference . 88 6.6.3 No inverse or direct problem . 89 6.6.4 No ill-posed problem . 89 II Bayesian Programming Cookbook 91 7 Information Fusion 93 7.1 “Naive”Bayessensorfusion . 94 7.1.1 Statementoftheproblem . 94 7.1.2 Bayesianprogram.................... 94 7.1.3 Instanceandresults.. .. .. .. .. .. .. .. 96 7.2 Relaxing the conditional independence fundamental hypothesis ............................ 102 7.2.1 Statementoftheproblem . 102 7.2.2 Bayesianprogram. .. .. .. .. .. .. .. .. 103 7.2.3 Instanceandresults. 103 7.3 Classification . 105 7.3.1 Statementoftheproblem . 105 7.3.2 Bayesianprogram. .. .. .. .. .. .. .. .. 106 7.3.3 Instanceandresults. 106 7.4 Ancillary clues . 108 7.4.1 Statementoftheproblem . 108 7.4.2 Bayesianprogram. .. .. .. .. .. .. .. .. 108 7.4.3 Instanceandresults. 110 7.5 Sensor fusion with false alarm . 113 7.5.1 Statementoftheproblem . 113 7.5.2 Bayesianprogram. .. .. .. .. .. .. .. .. 114 7.5.3 Instanceandresults. 114 7.6 Inverseprogramming ...................... 116 7.6.1 Statementoftheproblem . 116 7.6.2 Bayesianprogram. .. .. .. .. .. .. .. .. 117 7.6.3 Instanceandresults. 118 x Contents 8 Bayesian Programming with Coherence Variables 121 8.1 Basic example with Boolean variables . 122 8.1.1 Statementoftheproblem . 122 8.1.2 Bayesianprogram. .. .. .. .. .. .. .. .. 123 8.1.3 Instanceandresults. 124 8.2 Basic example with discrete variables . 125 8.2.1 Statementoftheproblem . 125 8.2.2 Bayesianprogram. .. .. .. .. .. .. .. .. 126 8.2.3 Instanceandresults. 126 8.3 Checking the semantic of Λ .................. 130 8.3.1 Statementoftheproblem . 130 8.3.2 Bayesianprogram. .. .. .. .. .. .. .. .. 130 8.3.3 Instanceandresults. 131 8.4 Information fusion revisited using coherence variables . 132 8.4.1 Statementoftheproblems . 132 8.4.2 Bayesianprogram. .. .. .. .. .. .. .. .. 135 8.4.3 Instanceandresults. 135 8.5 Reasoning with soft evidence . 141 8.5.1 Statementoftheproblem . 141 8.5.2 Bayesianprogram. .. .. .. .. .. .. .. .. 142 8.5.3 Instanceandresults. 143 8.6 Switch .............................. 145 8.6.1 Statementoftheproblem . 145 8.6.2 Bayesianprogram.
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