Foundations of Probabilistic Logic Programming Languages, Semantics, Inference and Learning
Probabilistic Logic Programming extends Logic Programming by enabling the representation of uncertain information by means of probability theory. Probabilistic Logic Programming is at the intersection of two wider research fields: the integration of logic and probability and Probabilistic Programmin...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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United Kingdom
River Publishers
2018
Routledge |
| Vydání: | 1 |
| Edice: | River Publishers Series in Software Engineering |
| Témata: | |
| ISBN: | 100079587X, 9781000795875, 9788770220187, 8770220182 |
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- Foreword xi Preface xiii Acknowledgements xv List of Figures xvii List of Tables xxi List of Examples xxiii List of Definitions xxvii List of Theorems xxix List of Abbreviations xxxi 1 Preliminaries 1 1.1 Orders, Lattices, Ordinals 1 1.2 Mappings and Fixpoints 3 1.3 Logic Programming 4 1.4 Semantics for Normal Logic Programs 13 1.4.1 Program Completion 13 1.4.2 Well-Founded Semantics 15 1.4.3 Stable Model Semantics 21 1.5 Probability Theory 23 1.6 Probabilistic Graphical Models 32 2 Probabilistic Logic Programming Languages 41 2.1 Languages with the Distribution Semantics 41 2.1.1 Logic Programs with Annotated Disjunctions 42 2.1.2 ProbLog 43 2.1.3 Probabilistic Horn Abduction 43 2.1.4 PRISM 44 2.2 The Distribution Semantics for Programs Without Function Symbols 45 2.3 Examples of Programs 50 2.4 Equivalence of Expressive Power 56 2.5 Translation to Bayesian Networks 58 2.6 Generality of the Distribution Semantics 62 2.7 Extensions of the Distribution Semantics 64 2.8 CP-Logic 66 2.9 Semantics for Non-Sound Programs 71 2.10 KBMC Probabilistic Logic Programming Languages 76 2.10.1 Bayesian Logic Programs 76 2.10.2 CLP(BN) 76 2.10.3 The Prolog Factor Language 79 2.11 Other Semantics for Probabilistic Logic Programming 80 2.11.1 Stochastic Logic Programs 81 2.11.2 ProPPR 82 2.12 Other Semantics for Probabilistic Logics 84 2.12.1 Nilsson’s Probabilistic Logic 84 2.12.2 Markov Logic Networks 84 2.12.2.1 Encoding Markov Logic Networks with Probabilistic Logic Programming 85 2.12.3 Annotated Probabilistic Logic Programs 88 3 Semantics with Function Symbols 91 3.1 The Distribution Semantics for Programs with Function Symbols 92 3.2 Infinite Covering Set of Explanations 97 3.3 Comparison with Sato and Kameya’s Definition 110 4 Semantics for Hybrid Programs 115 4.1 Hybrid ProbLog 115 4.2 Distributional Clauses 118 4.3 Extended PRISM 124 4.4 cplint Hybrid Programs 126 4.5 Probabilistic Constraint Logic Programming 130 4.5.1 Dealing with Imprecise Probability Distributions 135 5 Exact Inference 145 5.1 PRISM 146 5.2 Knowledge Compilation 150 5.3 ProbLog1 151 5.4 cplint 155 5.5 SLGAD 157 5.6 PITA 158 5.7 ProbLog2 163 5.8 TP Compilation 176 5.9 Modeling Assumptions in PITA 178 5.9.1 PITA(OPT) 181 5.9.2 MPE with PITA 186 5.10 Inference for Queries with an Infinite Number of Explanations 186 5.11 Inference for Hybrid Programs 187 6 Lifted Inference 195 6.1 Preliminaries on Lifted Inference 195 6.1.1 Variable Elimination 197 6.1.2 GC-FOVE 201 6.2 LP2 202 6.2.1 Translating ProbLog into PFL 202 6.3 Lifted Inference with Aggregation Parfactors 205 6.4 Weighted First-Order Model Counting 207 6.5 Cyclic Logic Programs 210 6.6 Comparison of the Approaches 210 7 Approximate Inference 213 7.1 ProbLog1 213 7.1.1 Iterative Deepening 213 7.1.2 k-best 215 7.1.3 Monte Carlo 216 7.2 MCINTYRE 218 7.3 Approximate Inference for Queries with an Infinite Number of Explanations 221 7.4 Conditional Approximate Inference 222 7.5 Approximate Inference by Sampling for Hybrid Programs 223 7.6 Approximate Inference with Bounded Error for Hybrid Programs 226 7.7 k-Optimal 229 7.8 Explanation-Based Approximate Weighted Model Counting 231 7.9 Approximate Inference with TP -compilation 233 7.10 DISTR and EXP Tasks 234 8 Non-Standard Inference 239 8.1 Possibilistic Logic Programming 239 8.2 Decision-Theoretic ProbLog 241 8.3 Algebraic ProbLog 250 9 Parameter Learning 259 9.1 PRISM Parameter Learning 259 9.2 LLPAD and ALLPAD Parameter Learning 265 9.3 LeProbLog 267 9.4 EMBLEM 270 9.5 ProbLog2 Parameter Learning 280 9.6 Parameter Learning for Hybrid Programs 282 10 Structure Learning 283 10.1 Inductive Logic Programming 283 10.2 LLPAD and ALLPAD Structure Learning 287 10.3 ProbLog Theory Compression 289 10.4 ProbFOIL and ProbFOIL+ 290 10.5 SLIPCOVER 296 10.5.1 The Language Bias 296 10.5.2 Description of the Algorithm 296 10.5.2.1 Function INITIALBEAMS 298 10.5.2.2 Beam Search with Clause Refinements 300 10.5.3 Execution Example 301 10.6 Examples of Datasets 304 11 cplint Examples 305 11.1 cplint Commands 305 11.2 Natural Language Processing 309 11.2.1 Probabilistic Context-Free Grammars 309 11.2.2 Probabilistic Left Corner Grammars 310 11.2.3 Hidden Markov Models 311 11.3 Drawing Binary Decision Diagrams 313 11.4 Gaussian Processes 314 11.5 Dirichlet Processes 318 11.5.1 The Stick-Breaking Process 319 11.5.2 The Chinese Restaurant Process 322 11.5.3 Mixture Model 324 11.6 Bayesian Estimation 326 11.7 Kalman Filter 327 11.8 Stochastic Logic Programs 330 11.9 Tile Map Generation 332 11.10 Markov Logic Networks 334 11.11 Truel 335 11.12 Coupon Collector Problem 339 11.13 One-Dimensional Random Walk 341 11.14 Latent Dirichlet Allocation 342 11.15 The Indian GPA Problem 346 11.16 Bongard Problems 348 12 Conclusions 351 References 353 Index 375 About the Author 387
- 4.1 Hybrid ProbLog -- 4.2 Distributional Clauses -- 4.3 Extended PRISM -- 4.4 cplint Hybrid Programs -- 4.5 Probabilistic Constraint Logic Programming -- 4.5.1 Dealing with Imprecise Probability Distributions -- 5: Exact Inference -- 5.1 PRISM -- 5.2 Knowledge Compilation -- 5.3 ProbLog1 -- 5.4 cplint -- 5.5 SLGAD -- 5.6 PITA -- 5.7 ProbLog2 -- 5.8 TP Compilation -- 5.9 Modeling Assumptions in PITA -- 5.9.1 PITA(OPT) -- 5.9.2 MPE with PITA -- 5.10 Inference for Queries with an Infinite Number of Explanations -- 5.11 Inference for Hybrid Programs -- 6: Lifted Inference -- 6.1 Preliminaries on Lifted Inference -- 6.1.1 Variable Elimination -- 6.1.2 GC-FOVE -- 6.2 LP2 -- 6.2.1 Translating ProbLog into PFL -- 6.3 Lifted Inference with Aggregation Parfactors -- 6.4 Weighted First-Order Model Counting -- 6.5 Cyclic Logic Programs -- 6.6 Comparison of the Approaches -- 7: Approximate Inference -- 7.1 ProbLog1 -- 7.1.1 Iterative Deepening -- 7.1.2 k-best -- 7.1.3 Monte Carlo -- 7.2 MCINTYRE -- 7.3 Approximate Inference for Queries with an Infinite Number of Explanations -- 7.4 Conditional Approximate Inference -- 7.5 Approximate Inference by Sampling for Hybrid Programs -- 7.6 Approximate Inference with Bounded Error for Hybrid Programs -- 7.7 k-Optimal -- 7.8 Explanation-Based Approximate Weighted Model Counting -- 7.9 Approximate Inference with TP-compilation -- 7.10 DISTR and EXP Tasks -- 8: Non-Standard Inference -- 8.1 Possibilistic Logic Programming -- 8.2 Decision-Theoretic ProbLog -- 8.3 Algebraic ProbLog -- 9: Parameter Learning -- 9.1 PRISM Parameter Learning -- 9.2 LLPAD and ALLPAD Parameter Learning -- 9.3 LeProbLog -- 9.4 EMBLEM -- 9.5 ProbLog2 Parameter Learning -- 9.6 Parameter Learning for Hybrid Programs -- 10: Structure Learning -- 10.1 Inductive Logic Programming -- 10.2 LLPAD and ALLPAD Structure Learning
- Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Table of Contents -- Foreword -- Preface -- Acknowledgments -- List of Figures -- List of Tables -- List of Examples -- List of Definitions -- List of Theorems -- List of Abbreviations -- 1: Preliminaries -- 1.1 Orders, Lattices, Ordinals -- 1.2 Mappings and Fixpoints -- 1.3 Logic Programming -- 1.4 Semantics for Normal Logic Programs -- 1.4.1 Program Completion -- 1.4.2 Well-Founded Semantics -- 1.4.3 Stable Model Semantics -- 1.5 Probability Theory -- 1.6 Probabilistic Graphical Models -- 2: Probabilistic Logic Programming Languages -- 2.1 Languages with the Distribution Semantics -- 2.1.1 Logic Programs with Annotated Disjunctions -- 2.1.2 ProbLog -- 2.1.3 Probabilistic Horn Abduction -- 2.1.4 PRISM -- 2.2 The Distribution Semantics for Programs Without Function Symbols -- 2.3 Examples of Programs -- 2.4 Equivalence of Expressive Power -- 2.5 Translation to Bayesian Networks -- 2.6 Generality of the Distribution Semantics -- 2.7 Extensions of the Distribution Semantics -- 2.8 CP-Logic -- 2.9 Semantics for Non-Sound Programs -- 2.10 KBMC Probabilistic Logic Programming Languages -- 2.10.1 Bayesian Logic Programs -- 2.10.2 CLP(BN) -- 2.10.3 The Prolog Factor Language -- 2.11 Other Semantics for Probabilistic Logic Programming -- 2.11.1 Stochastic Logic Programs -- 2.11.2 ProPPR -- 2.12 Other Semantics for Probabilistic Logics -- 2.12.1 Nilsson's Probabilistic Logic -- 2.12.2 Markov Logic Networks -- 2.12.2.1 Encoding Markov Logic Networks with Probabilistic Logic Programming -- 2.12.3 Annotated Probabilistic Logic Programs -- 3: Semantics with Function Symbols -- 3.1 The Distribution Semantics for Programs with Function Symbols -- 3.2 Infinite Covering Set of Explanations -- 3.3 Comparison with Sato and Kameya's Definition -- 4: Semantics for Hybrid Programs
- 10.3 ProbLog Theory Compression -- 10.4 ProbFOIL and ProbFOIL+ -- 10.5 SLIPCOVER -- 10.5.1 The Language Bias -- 10.5.2 Description of the Algorithm -- 10.5.2.1 Function INITIALBEAMS -- 10.5.2.2 Beam Search with Clause Refinements -- 10.5.3 Execution Example -- 10.6 Examples of Datasets -- 11: cplint Examples -- 11.1 cplint Commands -- 11.2 Natural Language Processing -- 11.2.1 Probabilistic Context-Free Grammars -- 11.2.2 Probabilistic Left Corner Grammars -- 11.2.3 Hidden Markov Models -- 11.3 Drawing Binary Decision Diagrams -- 11.4 Gaussian Processes -- 11.5 Dirichlet Processes -- 11.5.1 The Stick-Breaking Process -- 11.5.2 The Chinese Restaurant Process -- 11.5.3 Mixture Model -- 11.6 Bayesian Estimation -- 11.7 Kalman Filter -- 11.8 Stochastic Logic Programs -- 11.9 Tile Map Generation -- 11.10 Markov Logic Networks -- 11.11 Truel -- 11.12 Coupon Collector Problem -- 11.13 One-Dimensional Random Walk -- 11.14 Latent Dirichlet Allocation -- 11.15 The Indian GPA Problem -- 11.16 Bongard Problems -- 12: Conclusions -- References -- Index -- About the Author