An introduction to lifted probabilistic inference:
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| Format: | Book |
| Language: | English |
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Cambridge, Massachusetts ; London, England
The MIT Press
[2021]
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| Series: | Neural information processing series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxii, 429 Seiten Illustrationen |
| ISBN: | 9780262542593 |
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MARC
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| 245 | 1 | 0 | |a An introduction to lifted probabilistic inference |c edited by Guy van den Broeck, Kristian Kersting, Sriraam Natarajan, and David Poole |
| 264 | 1 | |a Cambridge, Massachusetts ; London, England |b The MIT Press |c [2021] | |
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| adam_text | Contents List of Figures Contributors Preface I OVERVIEW 1 Statistical Relational AI: Representation, Inference and Learning xv xxi xxiii 3 Guy Van den Broeck, Kristian Kersting, Sriraam Natarajan, and David Poole 1.1 1.2 1.3 1.4 2 Representations 1.1.1 First-order Logic and Logic Programs 1.1.2 Probability and Graphical Models 1.1.3 Relational Probabilistic Models 1.1.4 Weighted First-order Model Counting 1.1.5 Observations and Queries Inference Learning Book Details Modeling and Reasoning with Statistical Relational Representations 4 5 6 8 11 11 12 14 14 15 Angelika Kimmig and David Poole 2.1 2.2 2.3 Preliminaries: First-order Logic Lifted Graphical Models and Probabilistic Logic Programs 2.2.1 Parameterized Factors: Markov Logic Networks 2.2.2 Probabilistic Logic Programs: ProbLog 2.2.3 Inference Tasks Statistical Relational Representations 2.3.1 Desirable Properties of Representation Languages 16 17 17 21 26 28 28
Contents VI 2.3.2 2.4 3 Design Choices Conclusions Statistical Relational Learning 29 38 39 Sriraam Natarajan, Jesse Davis, Kristian Kersting, Daniel Lowd, Pedro Domingos, and Raymond Mooney 3.1 3.2 3.3 Introduction Statistical Relational Learning Models Parameter Learning of SRL models 39 40 41 3.4 3.5 Markov Logic Networks Parameter and Structure Learning of Markov Logic Networks 3.5.1 Parameter Learning 41 42 42 3.5.2 Structure Learning Boosting-based Learning of SRL Models Deep Transfer Learning Using SRL Models 3.7.1 TAMAR 3.7.2 DTM 3.7.3 TODTLER 3.7.4 LTL Conclusion 44 45 47 48 48 49 51 53 3.6 3.7 3.8 П EXACT INFERENCE 4 Lifted Variable Elimination 57 Nima Taghipour, Daan Fierens, Jesse Davis, Hendrik Blockeel, and Rodrigo de Salvo Braz 4.1 4.2 4.3 4.4 Introduction Lifted Variable Elimination by Example 4.2.1 The Workshop Example 4.2.2 Variable Elimination 4.2.3 Lifted Inference: ExploitingSymmetries among Factors 4.2.4 Lifted Inference: ExploitingSymmetries within Factors 4.2.5 Splitting Overlapping Groups and Its Relation to Unification Representation 4.3.1 A Constraint-based Representation Formalism 4.3.2 Counting Formulas The GC-FOVE Algorithm: Outline 57 58 58 59 62 62 64 66 66 68 70
vii Contents 4.5 5 GC-FOVE’s Operators 4.5.1 Lifted Multiplication 4.5.2 Lifted Summing-out 4.5.3 Counting Conversion 4.5.4 Splitting and Shattering 4.5.5 Expansion of Counting Formulas 71 71 73 76 79 82 4.5.6 4.5.7 85 85 Count Normalization Grounding a Logvar Search-Based Exact Lifted Inference 89 Seyed Mehran Kazemi, Guy Van den Broeck, and David Poole 5.1 5.2 5.3 6 Background and Notation 5.1.1 Random Variables, Independence, and Symmetry 5.1.2 Finite-domain Function-free First-order Logic 5.1.3 Log-linear Models 5.1.4 Graphical Notation of Dependencies in Log-linear Models 5.1.5 Markov Logic Networks 5.1.6 From Normalization Constant to Probabilistic Inference Weighted Model Count 5.2.1 Formal Definition 5.2.2 Converting Inference into Calculating WMCs 5.2.3 Efficiently Finding the WMC of a Theory 90 90 91 92 93 93 94 94 95 96 96 5.2.4 Order of Applying Rules Lifting Search-Based Inference 5.3.1 Weighted Model Counting for First-order Theories 5.3.2 Converting Inference for Relational Models into Calculating WMCs of First-order Theories 5.3.3 Efficiently Calculating the WMC of a First-order Theory 99 100 101 5.3.4 5.3.5 110 110 Order of Applying Rules Bounding the Complexity of Lifted Inference Lifted Aggregation and Skolemization for Directed Models 103 103 113 Wannes Meert, Jaesik Choi, Jacek Kisyñski, Hung Bui, Guy Van den Broeck, Adnan Darwiche, Rodrigo de Salvo Brąz, and David Poole 6.1 6.2 Introduction Lifted Aggregation in Directed First-order Probabilistic Models 6.2.1 Parameterized Random Variables and Parametric Factors ИЗ 114 114
viii Contents 6.2.2 6.2.3 6.2.4 6.3 6.4 6.5 7 Aggregation in Directed First-order Probabilistic Models Existing Algorithm Incorporating Aggregation in C-FOVE 116 118 119 6.2.5 Experiments Efficient Methods for Lifted Inference with Aggregation Parfactors 6.3.1 Efficient Methods for AFM Problems 125 127 129 6.3.2 Aggregation Factors with Multiple Atoms 6.3.3 Efficient Lifted Belief Propagation with Aggregation Parfactors 6.3.4 Ernår Analysis 6.3.5 Experiments 134 135 136 Lifted Aggregation through Skolemization for Weighted Firstorder Model Counting 6.4.1 Normal Forms 137 137 6.4.2 Skolemization for WFOMC 137 6.4.3 6.4.4 Skolemization of Markov Logic Networks Skolemization of Probabilistic Logic Programs 139 141 135 6.4.5 Negative Probabilities 6.4.6 Experiments 143 144 Conclusions 144 First-order Knowledge Compilation 147 Seyed Mehran Kazemi, Guy Van den Broeck, and David Poole 7.1 7.2 7.3 8 Calculating WMC of Propositional Theories through Knowledge Compilation Knowledge Compilation for First-order Theories 148 149 7.2.1 7.2.2 151 151 Compilation Example Pruning Why Compile to Low-level Programs? Domain Liftability 152 155 Seyed Mehran Kazemi, Angelika Kimmig, Guy Van den Broeck, and David Poole 9 8.1 Domain-liftable Classes 155 8.2 8.1.1 Membership Checking Negative Results 158 158 Tractability through Exchangeability: The Statistics of Lifting Mathias Niepert and Guy Van den Broeck 161
Contents 9.1 9.2 9.3 9.4 9.5 9.6 ix Introduction A Case Study: Markov Logic 9.2.1 Markov Logic Networks Review 161 162 163 9.2.2 Inference without Independence Finite Exchangeability 163 164 9.3.1 9.3.2 165 166 Finite Partial Exchangeability Partial Exchangeability and Probabilistic Inference 9.3.3 Markov Logic Case Study Exchangeable Decompositions 166 167 9.4.1 9.4.2 Variable Decompositions Tractable Variable Decompositions 167 168 9.4.3 Markov Logic Case Study Marginal and Conditional Exchangeability 169 170 9.5.1 170 Marginal and Conditional Decomposition 9.5.2 Markov Lògic Case Study Discussion and Conclusion Ш APPROXIMATE INFERENCE 10 Lifted Markov Chain Monte Carlo 172 173 181 Mathias Niepert and Guy Van den Broeck 10.1 Introduction 181 10.2 Background 10.2.1 Group Theory 10.2.2 Finite Markov Chains 10.2.3 Markov Chain Monte Carlo 10.3 Symmetries of Probabilistic Models 10.3.1 Graphical Model Symmetries 182 182 183 183 184 184 10.3.2 Relational Model Symmetries 10.4 Lifted MCMC for Symmetric Models 10.4.1 Lumping 185 186 187 10.4.2 Orbital Markov Chains 10.5 Lifted MCMC for Asymmetric Models 10.5.1 Mixing 188 190 190 10.5.2 Metropolis-Hastings Chains 10.5.3 Orbital Metropolis Chains 190 191
x Contents 10.5.4 Lifted Metropolis-Hastings 10.6 Approximate Symmetries 10.6.1 Relational Symmetrization 10.6.2 Propositional Symmetrization 10.6.3 From OSAs to Automorphisms 10.7 Empirical Evaluation 10.7.1 Symmetric Model Experiments 10.8 Asymmetric Model Experiments 10.9 Conclusions *· 10.10 Acknowledgments 10.11 Appendix: Proof of Theorem 10.3 11 Lifted Message Passing for Probabilistic and Combinatorial Problems 192 193 194 194 195 195 195 196 198 198 198 203 Kristian Kersting, Fabian Hadiji, Babak Ahmadi, Martin Mladenov, and Sriraam Natarajan 11.1 Introduction 11.2 Loopy Belief Propagation (LBP) 11.3 Lifted Message Passing for Probabilistic Inference: Lifted (Loopy) BP 11.3.1 Step 1 - Compressing the Factor Graph 11.3.2 Step 2 - BP on the Compressed Factor Graph 206 206 208 11.4 Lifted Message Passing for SAT Problems 11.4.1 Lifted Satisfiability 11.4.2 CNFs and Factor Graphs 11.4.3 Belief Propagation for Satisfiability 11.4.4 Decimation-based SAT Solving 11.4.5 Lifted Warning Propagation 11.4.6 Lifted Survey Propagation 11.4.7 Lifted Decimation 11.4.8 Experimental Evaluation 11.4.9 Summary: Lifted Satisfiability 11.5 Lifted Sequential Clamping for SAT Problems and Sampling 11.5.1 Lifted Sequential Inference 211 212 214 216 216 217 220 223 224 225 227 228 11.5.2 Experimental Evaluation 11.5.3 Summary Lifted Sequential Clamping 11.6 Lifted Message Passing for MAP via Likelihood Maximization 11.6.1 Lifted Likelihood Maximization (LM) 203 205 233 237 238 239
xi Contents 11.6.2 Bootstrapped Likelihood Maximization (LM) 11.6.3 Bootstrapped Lifted Likelihood Maximization (LM) 242 243 11.6.4 Experimental Evaluation 249 11.6.5 Summary of Lifted Likelihood Maximization for MAP Inference 11.7 Conclusions 12 254 256 Lifted Generalized Belief Propagation: Relax, Compensate and Recover 259 Guy Van den Broeck, Arthur Choi, and Adnan Darwiche 12.1 Introduction 12.2 RCR for Ground MLNs 12.2.1 Ground Relaxation 12.2.2 Ground Compensation 12.2.3 Ground Recovery 12.3 Lifted RCR 12.3.1 First-order Relaxation 13 259 260 261 261 262 263 263 12.3.2 First-order Compensation 265 12.3.3 Count-Normalization 12.3.4 The Compensation Scheme 268 269 12.3.5 First-order Recovery 12.4 Partitioning Equivalences 12.4.1 Partitioning Atoms by Preemptive Shattering 12.4.2 Partitioning Equivalences by Preemptive Shattering 269 270 270 271 12.4.3 Dynamic Equivalence Partitioning 12.5 Related and Future Work 12.5.1 Relation to Propositional Algorithms 12.5.2 Relation to Lifted Algorithms 12.5.3 Opportunities for Equivalence Partitioning 272 273 273 274 274 12.6 Experiments 12.6.1 Implementation 12.6.2 Results 12.7 Conclusions 275 275 276 280 Liftability Theory of Variational Inference 281 Martin Mladenov, Hung Bui, and Kristian Kersting 13.1 Introduction 13.2 Lifted Variational Inference 281 282
xii Contents 13.2.1 Symmetry: Groups and Partitions 13.2.2 Exponential Families and the Variational Principle 283 285 13.2.3 Lifting the Variational Principle 286 13.3 Exact Lifted Variational Inference: Automorphisms of T 13.3.1 Automorphisms of Exponential Family 288 13.3.2 Parameter Tying and Lifting Partitions 13.3.3 Computing Automorphisms of Ţ 291 292 13.3.4 The Lifted Marginal Polytope 13.4 BeyonďOrbits of T: Approximate Lifted Variational Inference 13.4.1 Approximate Variational Inference 293 295 296 13.4.2 Equitable Partitions of the Exponential Family 13.4.3 Equitable Partitions of Concave Energies 297 299 13.4.4 Lifted Counting Numbers 302 13.4.5 Computing Equitable Partitions of Exponential Families 13.5 Unfolding Variational Inference Algorithms via Reparametrization 13.5.1 The Lifted Approximate Variational Problem 14 288 304 305 306 13.5.2 Energy Equivalence of Exponential Families 308 13.5.3 Finding Partition-Equivalent Exponential Families 311 13.6 Symmetries of Markov Logic Networks (MLNs) 13.7 Conclusions 315 316 Lifted Inference for Hybrid Relational Models 317 Jaesik Choi, Kristian Kersting, and Yuqiao Chen 14.1 Introduction 14.2 Relational Continuous Models 317 318 14.2.1 Inference Algorithms for RCMs 321 14.2.2 Exact Lifted Inference with RCMs 14.2.3 Conditions for Exact Lifted Inference 324 325 14.3 Relational Kalman Filtering 327 14.3.1 Model and Problem Definitions 328 14.3.2 Lifted Relational Kalman Filter 332 14.3.3 Algorithms and Computational Complexity 335 14.4 Lifted Message Passing for Hybrid Relational Models 14.4.1 Lifted Gaussian Belief
Propagation 14.4.2 Multi-evidence Lifting 337 337 340
Contents 14.4.3 Sequential Multi-Evidence Lifting 14.5 Approximate Lifted Inference for General RCMs 14.6 Conclusions xiii 341 343 344 IV BEYOND PROBABILISTIC INFERENCE 15 Color Refinement and Its Applications 349 Martin Grohe, Kristian Kersting, Martin Mladenov, and Pascal Schweitzer 16 15.1 Introduction 15.1.1 Applications 15.1.2 Variants 15.1.3 A Logical Characterization of Color Refinement 15.2 Color Refinement in Quasilinear Time 15.3 Application: Graph Isomorphism Testing 15.4 The Weisfeiler-Leman Algorithm 15.5 Fractional Isomorphism 349 350 351 352 353 355 358 360 15.5.1 Color Refinement and Fractional Isomorphism of Matrices 15.6 Application: Linear Programming 15.7 Application: Weisfeiler-Leman Graph Kernels 15.8 Conclusions 364 366 368 370 Stochastic Planning and Lifted Inference 373 Roni Khardon and Scott Sanner 16.1 Introduction 16.1.1 Stochastic Planning and Inference 16.1.2 Stochastic Planning and Generalized Lifted Inference 16.2 Preliminaries 16.2.1 Relational Expressions and Their Calculus of Operations 16.2.2 Relational MDPs 16.3 Symbolic Dynamic Programming 16.4 Discussion and Related Work 16.4.1 Deductive Lifted Stochastic Planning 16.4.2 Inductive Lifted Stochastic Planning 16.5 Conclusions Bibliography Index 373 375 378 381 381 384 386 392 392 394 395 397 425
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Contents List of Figures Contributors Preface I OVERVIEW 1 Statistical Relational AI: Representation, Inference and Learning xv xxi xxiii 3 Guy Van den Broeck, Kristian Kersting, Sriraam Natarajan, and David Poole 1.1 1.2 1.3 1.4 2 Representations 1.1.1 First-order Logic and Logic Programs 1.1.2 Probability and Graphical Models 1.1.3 Relational Probabilistic Models 1.1.4 Weighted First-order Model Counting 1.1.5 Observations and Queries Inference Learning Book Details Modeling and Reasoning with Statistical Relational Representations 4 5 6 8 11 11 12 14 14 15 Angelika Kimmig and David Poole 2.1 2.2 2.3 Preliminaries: First-order Logic Lifted Graphical Models and Probabilistic Logic Programs 2.2.1 Parameterized Factors: Markov Logic Networks 2.2.2 Probabilistic Logic Programs: ProbLog 2.2.3 Inference Tasks Statistical Relational Representations 2.3.1 Desirable Properties of Representation Languages 16 17 17 21 26 28 28
Contents VI 2.3.2 2.4 3 Design Choices Conclusions Statistical Relational Learning 29 38 39 Sriraam Natarajan, Jesse Davis, Kristian Kersting, Daniel Lowd, Pedro Domingos, and Raymond Mooney 3.1 3.2 3.3 Introduction Statistical Relational Learning Models Parameter Learning of SRL models 39 40 41 3.4 3.5 Markov Logic Networks Parameter and Structure Learning of Markov Logic Networks 3.5.1 Parameter Learning 41 42 42 3.5.2 Structure Learning Boosting-based Learning of SRL Models Deep Transfer Learning Using SRL Models 3.7.1 TAMAR 3.7.2 DTM 3.7.3 TODTLER 3.7.4 LTL Conclusion 44 45 47 48 48 49 51 53 3.6 3.7 3.8 П EXACT INFERENCE 4 Lifted Variable Elimination 57 Nima Taghipour, Daan Fierens, Jesse Davis, Hendrik Blockeel, and Rodrigo de Salvo Braz 4.1 4.2 4.3 4.4 Introduction Lifted Variable Elimination by Example 4.2.1 The Workshop Example 4.2.2 Variable Elimination 4.2.3 Lifted Inference: ExploitingSymmetries among Factors 4.2.4 Lifted Inference: ExploitingSymmetries within Factors 4.2.5 Splitting Overlapping Groups and Its Relation to Unification Representation 4.3.1 A Constraint-based Representation Formalism 4.3.2 Counting Formulas The GC-FOVE Algorithm: Outline 57 58 58 59 62 62 64 66 66 68 70
vii Contents 4.5 5 GC-FOVE’s Operators 4.5.1 Lifted Multiplication 4.5.2 Lifted Summing-out 4.5.3 Counting Conversion 4.5.4 Splitting and Shattering 4.5.5 Expansion of Counting Formulas 71 71 73 76 79 82 4.5.6 4.5.7 85 85 Count Normalization Grounding a Logvar Search-Based Exact Lifted Inference 89 Seyed Mehran Kazemi, Guy Van den Broeck, and David Poole 5.1 5.2 5.3 6 Background and Notation 5.1.1 Random Variables, Independence, and Symmetry 5.1.2 Finite-domain Function-free First-order Logic 5.1.3 Log-linear Models 5.1.4 Graphical Notation of Dependencies in Log-linear Models 5.1.5 Markov Logic Networks 5.1.6 From Normalization Constant to Probabilistic Inference Weighted Model Count 5.2.1 Formal Definition 5.2.2 Converting Inference into Calculating WMCs 5.2.3 Efficiently Finding the WMC of a Theory 90 90 91 92 93 93 94 94 95 96 96 5.2.4 Order of Applying Rules Lifting Search-Based Inference 5.3.1 Weighted Model Counting for First-order Theories 5.3.2 Converting Inference for Relational Models into Calculating WMCs of First-order Theories 5.3.3 Efficiently Calculating the WMC of a First-order Theory 99 100 101 5.3.4 5.3.5 110 110 Order of Applying Rules Bounding the Complexity of Lifted Inference Lifted Aggregation and Skolemization for Directed Models 103 103 113 Wannes Meert, Jaesik Choi, Jacek Kisyñski, Hung Bui, Guy Van den Broeck, Adnan Darwiche, Rodrigo de Salvo Brąz, and David Poole 6.1 6.2 Introduction Lifted Aggregation in Directed First-order Probabilistic Models 6.2.1 Parameterized Random Variables and Parametric Factors ИЗ 114 114
viii Contents 6.2.2 6.2.3 6.2.4 6.3 6.4 6.5 7 Aggregation in Directed First-order Probabilistic Models Existing Algorithm Incorporating Aggregation in C-FOVE 116 118 119 6.2.5 Experiments Efficient Methods for Lifted Inference with Aggregation Parfactors 6.3.1 Efficient Methods for AFM Problems 125 127 129 6.3.2 Aggregation Factors with Multiple Atoms 6.3.3 Efficient Lifted Belief Propagation with Aggregation Parfactors 6.3.4 Ernår Analysis 6.3.5 Experiments 134 135 136 Lifted Aggregation through Skolemization for Weighted Firstorder Model Counting 6.4.1 Normal Forms 137 137 6.4.2 Skolemization for WFOMC 137 6.4.3 6.4.4 Skolemization of Markov Logic Networks Skolemization of Probabilistic Logic Programs 139 141 135 6.4.5 Negative Probabilities 6.4.6 Experiments 143 144 Conclusions 144 First-order Knowledge Compilation 147 Seyed Mehran Kazemi, Guy Van den Broeck, and David Poole 7.1 7.2 7.3 8 Calculating WMC of Propositional Theories through Knowledge Compilation Knowledge Compilation for First-order Theories 148 149 7.2.1 7.2.2 151 151 Compilation Example Pruning Why Compile to Low-level Programs? Domain Liftability 152 155 Seyed Mehran Kazemi, Angelika Kimmig, Guy Van den Broeck, and David Poole 9 8.1 Domain-liftable Classes 155 8.2 8.1.1 Membership Checking Negative Results 158 158 Tractability through Exchangeability: The Statistics of Lifting Mathias Niepert and Guy Van den Broeck 161
Contents 9.1 9.2 9.3 9.4 9.5 9.6 ix Introduction A Case Study: Markov Logic 9.2.1 Markov Logic Networks Review 161 162 163 9.2.2 Inference without Independence Finite Exchangeability 163 164 9.3.1 9.3.2 165 166 Finite Partial Exchangeability Partial Exchangeability and Probabilistic Inference 9.3.3 Markov Logic Case Study Exchangeable Decompositions 166 167 9.4.1 9.4.2 Variable Decompositions Tractable Variable Decompositions 167 168 9.4.3 Markov Logic Case Study Marginal and Conditional Exchangeability 169 170 9.5.1 170 Marginal and Conditional Decomposition 9.5.2 Markov Lògic Case Study Discussion and Conclusion Ш APPROXIMATE INFERENCE 10 Lifted Markov Chain Monte Carlo 172 173 181 Mathias Niepert and Guy Van den Broeck 10.1 Introduction 181 10.2 Background 10.2.1 Group Theory 10.2.2 Finite Markov Chains 10.2.3 Markov Chain Monte Carlo 10.3 Symmetries of Probabilistic Models 10.3.1 Graphical Model Symmetries 182 182 183 183 184 184 10.3.2 Relational Model Symmetries 10.4 Lifted MCMC for Symmetric Models 10.4.1 Lumping 185 186 187 10.4.2 Orbital Markov Chains 10.5 Lifted MCMC for Asymmetric Models 10.5.1 Mixing 188 190 190 10.5.2 Metropolis-Hastings Chains 10.5.3 Orbital Metropolis Chains 190 191
x Contents 10.5.4 Lifted Metropolis-Hastings 10.6 Approximate Symmetries 10.6.1 Relational Symmetrization 10.6.2 Propositional Symmetrization 10.6.3 From OSAs to Automorphisms 10.7 Empirical Evaluation 10.7.1 Symmetric Model Experiments 10.8 Asymmetric Model Experiments 10.9 Conclusions *· 10.10 Acknowledgments 10.11 Appendix: Proof of Theorem 10.3 11 Lifted Message Passing for Probabilistic and Combinatorial Problems 192 193 194 194 195 195 195 196 198 198 198 203 Kristian Kersting, Fabian Hadiji, Babak Ahmadi, Martin Mladenov, and Sriraam Natarajan 11.1 Introduction 11.2 Loopy Belief Propagation (LBP) 11.3 Lifted Message Passing for Probabilistic Inference: Lifted (Loopy) BP 11.3.1 Step 1 - Compressing the Factor Graph 11.3.2 Step 2 - BP on the Compressed Factor Graph 206 206 208 11.4 Lifted Message Passing for SAT Problems 11.4.1 Lifted Satisfiability 11.4.2 CNFs and Factor Graphs 11.4.3 Belief Propagation for Satisfiability 11.4.4 Decimation-based SAT Solving 11.4.5 Lifted Warning Propagation 11.4.6 Lifted Survey Propagation 11.4.7 Lifted Decimation 11.4.8 Experimental Evaluation 11.4.9 Summary: Lifted Satisfiability 11.5 Lifted Sequential Clamping for SAT Problems and Sampling 11.5.1 Lifted Sequential Inference 211 212 214 216 216 217 220 223 224 225 227 228 11.5.2 Experimental Evaluation 11.5.3 Summary Lifted Sequential Clamping 11.6 Lifted Message Passing for MAP via Likelihood Maximization 11.6.1 Lifted Likelihood Maximization (LM) 203 205 233 237 238 239
xi Contents 11.6.2 Bootstrapped Likelihood Maximization (LM) 11.6.3 Bootstrapped Lifted Likelihood Maximization (LM) 242 243 11.6.4 Experimental Evaluation 249 11.6.5 Summary of Lifted Likelihood Maximization for MAP Inference 11.7 Conclusions 12 254 256 Lifted Generalized Belief Propagation: Relax, Compensate and Recover 259 Guy Van den Broeck, Arthur Choi, and Adnan Darwiche 12.1 Introduction 12.2 RCR for Ground MLNs 12.2.1 Ground Relaxation 12.2.2 Ground Compensation 12.2.3 Ground Recovery 12.3 Lifted RCR 12.3.1 First-order Relaxation 13 259 260 261 261 262 263 263 12.3.2 First-order Compensation 265 12.3.3 Count-Normalization 12.3.4 The Compensation Scheme 268 269 12.3.5 First-order Recovery 12.4 Partitioning Equivalences 12.4.1 Partitioning Atoms by Preemptive Shattering 12.4.2 Partitioning Equivalences by Preemptive Shattering 269 270 270 271 12.4.3 Dynamic Equivalence Partitioning 12.5 Related and Future Work 12.5.1 Relation to Propositional Algorithms 12.5.2 Relation to Lifted Algorithms 12.5.3 Opportunities for Equivalence Partitioning 272 273 273 274 274 12.6 Experiments 12.6.1 Implementation 12.6.2 Results 12.7 Conclusions 275 275 276 280 Liftability Theory of Variational Inference 281 Martin Mladenov, Hung Bui, and Kristian Kersting 13.1 Introduction 13.2 Lifted Variational Inference 281 282
xii Contents 13.2.1 Symmetry: Groups and Partitions 13.2.2 Exponential Families and the Variational Principle 283 285 13.2.3 Lifting the Variational Principle 286 13.3 Exact Lifted Variational Inference: Automorphisms of T 13.3.1 Automorphisms of Exponential Family 288 13.3.2 Parameter Tying and Lifting Partitions 13.3.3 Computing Automorphisms of Ţ 291 292 13.3.4 The Lifted Marginal Polytope 13.4 BeyonďOrbits of T: Approximate Lifted Variational Inference 13.4.1 Approximate Variational Inference 293 295 296 13.4.2 Equitable Partitions of the Exponential Family 13.4.3 Equitable Partitions of Concave Energies 297 299 13.4.4 Lifted Counting Numbers 302 13.4.5 Computing Equitable Partitions of Exponential Families 13.5 Unfolding Variational Inference Algorithms via Reparametrization 13.5.1 The Lifted Approximate Variational Problem 14 288 304 305 306 13.5.2 Energy Equivalence of Exponential Families 308 13.5.3 Finding Partition-Equivalent Exponential Families 311 13.6 Symmetries of Markov Logic Networks (MLNs) 13.7 Conclusions 315 316 Lifted Inference for Hybrid Relational Models 317 Jaesik Choi, Kristian Kersting, and Yuqiao Chen 14.1 Introduction 14.2 Relational Continuous Models 317 318 14.2.1 Inference Algorithms for RCMs 321 14.2.2 Exact Lifted Inference with RCMs 14.2.3 Conditions for Exact Lifted Inference 324 325 14.3 Relational Kalman Filtering 327 14.3.1 Model and Problem Definitions 328 14.3.2 Lifted Relational Kalman Filter 332 14.3.3 Algorithms and Computational Complexity 335 14.4 Lifted Message Passing for Hybrid Relational Models 14.4.1 Lifted Gaussian Belief
Propagation 14.4.2 Multi-evidence Lifting 337 337 340
Contents 14.4.3 Sequential Multi-Evidence Lifting 14.5 Approximate Lifted Inference for General RCMs 14.6 Conclusions xiii 341 343 344 IV BEYOND PROBABILISTIC INFERENCE 15 Color Refinement and Its Applications 349 Martin Grohe, Kristian Kersting, Martin Mladenov, and Pascal Schweitzer 16 15.1 Introduction 15.1.1 Applications 15.1.2 Variants 15.1.3 A Logical Characterization of Color Refinement 15.2 Color Refinement in Quasilinear Time 15.3 Application: Graph Isomorphism Testing 15.4 The Weisfeiler-Leman Algorithm 15.5 Fractional Isomorphism 349 350 351 352 353 355 358 360 15.5.1 Color Refinement and Fractional Isomorphism of Matrices 15.6 Application: Linear Programming 15.7 Application: Weisfeiler-Leman Graph Kernels 15.8 Conclusions 364 366 368 370 Stochastic Planning and Lifted Inference 373 Roni Khardon and Scott Sanner 16.1 Introduction 16.1.1 Stochastic Planning and Inference 16.1.2 Stochastic Planning and Generalized Lifted Inference 16.2 Preliminaries 16.2.1 Relational Expressions and Their Calculus of Operations 16.2.2 Relational MDPs 16.3 Symbolic Dynamic Programming 16.4 Discussion and Related Work 16.4.1 Deductive Lifted Stochastic Planning 16.4.2 Inductive Lifted Stochastic Planning 16.5 Conclusions Bibliography Index 373 375 378 381 381 384 386 392 392 394 395 397 425 |
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| author2 | Broeck, Guy van den Kersting, Kristian 1973- Natarajan, Sriraam Poole, David L. 1958- |
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| author_facet | Broeck, Guy van den Kersting, Kristian 1973- Natarajan, Sriraam Poole, David L. 1958- |
| building | Verbundindex |
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| ctrlnum | (OCoLC)1261046243 (DE-599)BVBBV047486137 |
| discipline | Informatik |
| discipline_str_mv | Informatik |
| format | Book |
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| id | DE-604.BV047486137 |
| illustrated | Illustrated |
| index_date | 2024-07-03T18:14:15Z |
| indexdate | 2024-07-10T09:13:26Z |
| institution | BVB |
| isbn | 9780262542593 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032887521 |
| oclc_num | 1261046243 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | xxii, 429 Seiten Illustrationen |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | The MIT Press |
| record_format | marc |
| series2 | Neural information processing series |
| spelling | An introduction to lifted probabilistic inference edited by Guy van den Broeck, Kristian Kersting, Sriraam Natarajan, and David Poole Cambridge, Massachusetts ; London, England The MIT Press [2021] © 2021 xxii, 429 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Neural information processing series Statistik (DE-588)4056995-0 gnd rswk-swf Künstliche Intelligenz (DE-588)4033447-8 gnd rswk-swf Künstliche Intelligenz (DE-588)4033447-8 s Statistik (DE-588)4056995-0 s DE-604 Broeck, Guy van den (DE-588)1244879339 edt Kersting, Kristian 1973- (DE-588)173912001 edt Natarajan, Sriraam (DE-588)1105668657 edt Poole, David L. 1958- (DE-588)141818018 edt Erscheint auch als Online-Ausgabe 978-0-262-36559-8 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032887521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | An introduction to lifted probabilistic inference Statistik (DE-588)4056995-0 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4033447-8 |
| title | An introduction to lifted probabilistic inference |
| title_auth | An introduction to lifted probabilistic inference |
| title_exact_search | An introduction to lifted probabilistic inference |
| title_exact_search_txtP | An introduction to lifted probabilistic inference |
| title_full | An introduction to lifted probabilistic inference edited by Guy van den Broeck, Kristian Kersting, Sriraam Natarajan, and David Poole |
| title_fullStr | An introduction to lifted probabilistic inference edited by Guy van den Broeck, Kristian Kersting, Sriraam Natarajan, and David Poole |
| title_full_unstemmed | An introduction to lifted probabilistic inference edited by Guy van den Broeck, Kristian Kersting, Sriraam Natarajan, and David Poole |
| title_short | An introduction to lifted probabilistic inference |
| title_sort | an introduction to lifted probabilistic inference |
| topic | Statistik (DE-588)4056995-0 gnd Künstliche Intelligenz (DE-588)4033447-8 gnd |
| topic_facet | Statistik Künstliche Intelligenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032887521&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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