دانلود کتاب Probabilistic and Causal Inference: The Works of Judea Pearl

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Probabilistic and Causal Inference: The Works of Judea Pearl Contents Preface Credits I INTRODUCTION 1 Biography of Judea Pearl by Stuart J. Russell References 2 Turing Award Lecture References 3 Interview by Martin Ford References 4 An Interview with Ron Wassertein on How The Book of Why Transforms Statistics 5 Selected Annotated Bibliography by Judea Pearl Search and Heuristics Bayesian Networks Causality Causal, Casual, and Curious II HEURISTICS 6 Introduction by Judea Pearl References 7 Asymptotic Properties of Minimax Trees and Game-Searching Procedures Abstract 7.1 The Probability of Winning a Standard h-level Game Tree with Random WIN Positions 7.2 Game Trees with an Arbitrary Distribution of Terminal Values 7.3 The Mean Complexity of Solving (h, d, P0)-game 7.4 Solving, Testing, and Evaluating Game Trees 7.5 Test and, if Necessary, Evaluate—The SCOUT Algorithm 7.6 Analysis of SCOUT's Expected Performance 7.7 On the Branching Factor of the ALPHA–BETA (α–β) procedure References 8 The Solution for the Branching Factor of the Alpha–Beta Pruning Algorithm and its Optimality 8.1 Introduction 8.1.1 Informal Description of the α-β Procedure 8.1.2 Previous Analytical Results 8.2 Analysis 8.2.1 An Integral Formula for Nn,d 8.2.2 Evaluation of Rα-β 8.3 Conclusions References 9 On the Discovery and Generation of Certain Heuristics Abstract 9.1 Introduction: Typical Uses of Heuristics 9.1.1 The Traveling Salesman Problem (TSP) 9.1.2 Some Properties of Heuristics 9.1.3 Where do these Heuristics Come from? 9.2 Mechanical Generation of Admissible Heuristics 9.3 Can a Program Tell an Easy Problem When It Sees One? 9.4 Conclusions 9.4.1 Bibliographical and Historical Remarks References III PROBABILITIES 10 Introduction by Judea Pearl References 11 Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach Abstract 11.1 Introduction 11.2 Definitions and Nomenclature 11.3 Structural Assumptions 11.4 Combining Top and Bottom Evidences 11.5 Propagation of Information Through the Network 11.6 A Token Game Illustration 11.7 Properties of the Updating Scheme 11.8 A Summary of Proofs 11.9 Conclusions References 12 Fusion, Propagation, and Structuring in Belief Networks Abstract 12.1 Introduction 12.1.1 Belief Networks 12.1.2 Conditional Independence and Graph Separability 12.1.3 An Outline and Summary of Results 12.2 Fusion and Propagation 12.2.1 Autonomous Propagation as a Computational Paradigm 12.2.2 Belief Propagation in Trees 12.2.2.1 Data Fusion 12.2.2.2 Propagation Mechanism 12.2.2.3 Illustrating the Flow of Belief 12.2.2.4 Properties of the Updating Scheme 12.2.3 Propagation in Singly Connected Networks 12.2.3.1 Fusion Equations 12.2.3.2 Propagation Equation 12.2.4 Summary and Extensions for Multiply Connected Networks 12.3 Structuring Causal Trees 12.3.1 Causality, Conditional Independence, and Tree Architecture 12.3.2 Problem Definition and Nomenclature 12.3.3 Star-Decomposable Triplets 12.3.4 A Tree-Reconstruction Procedure 12.3.5 Conclusions and Open Questions 12.A Appendix A. Derivation of the Updating Rules for Singly Connected Networks 12.A.1 Updating BEL 12.A.2 Updating π 12.A.3 Updating λ 12.B Appendix B. Conditions for Star-decomposability Acknowledgments References 13 GRAPHOIDS: Graph-Based Logic for Reasoning about Relevance Relations Or When Would x Tell You More about y If You Already Know z? Abstract 13.1 Introduction 13.2 Probabilistic Dependencies and their Graphical Representation 13.3 GRAPHOIDS 13.4 Special Graphoids and Open Problems 13.4.1 Graph-induced Graphoids 13.4.2 Probabilistic Graphoids 13.4.3 Correlational Graphoids 13.5 Conclusions References 14 System Z: A Natural Ordering of Defaults with Tractable Applications to Nonmonotonic Reasoning Abstract 14.1 Description 14.2 Consequence Relations 14.3 Illustrations 14.4 The Maximum Entropy Approach 14.5 Conditional Entailment 14.6 Conclusions Acknowledgments 14.I Appendix I: Uniqueness of The Minimal Ranking Function 14.II Appendix II: Rational Monotony of Admissible Rankings References IV CAUSALITY 1988–2001 15 Introduction by Judea Pearl References 16 Equivalence and Synthesis of Causal Models Abstract 16.1 Introduction 16.2 Patterns of Causal Models 16.3 Embedded Causal Models 16.4 Applications to the Synthesis of Causal Models IC-Algorithm (Inductive Causation) Acknowledgments References 17 Probabilistic Evaluation of Counterfactual Queries Abstract 17.1 Introduction 17.2 Notation 17.3 Party Example 17.4 Probabilistic vs. Functional Specification 17.5 Evaluating Counterfactual Queries 17.6 Party Again 17.7 Special Case: Linear-Normal Models 17.8 Conclusion Acknowledgments References 18 Causal Diagrams for Empirical Research (With Discussions) Summary Some key words 18.1 Introduction 18.2 Graphical Models and the Manipulative Account of Causation 18.2.1 Graphs and Conditional Independence 18.2.2 Graphs as Models of Interventions 18.3 Controlling Confounding Bias 18.3.1 The Back-Door Criterion 18.3.2 The Front-Door Criteria 18.4 A Calculus of Intervention 18.4.1 General 18.4.2 Preliminary Notation 18.4.3 Inference Rules 18.4.4 Symbolic Derivation of Causal Effects: An Example 18.4.5 Causal Inference by Surrogate Experiments 18.5 Graphical Tests of Identifiability 18.5.1 General 18.5.2 Identifying Models 18.5.3 Nonidentifying Models 18.6 Discussion Acknowledgments 18.A Appendix Proof of Theorem 18.3 References 18.I Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.II Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.III Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.IV Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.V Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.VI Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.VI.A Introduction 18.VI.B Task 1 18.VI.B.1 General 18.VI.B.2 A Causal Model 18.VI.B.3 Relationship with Pearl's Work 18.VI.C Task 2 18.VII Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.VII.A Successful and Unsuccessful Causal Inference: Some Examples 18.VII.B Warranted Inferences 18.VIII Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.IX Discussion of ‘Causal Diagrams for Empirical Research’ by J. Pearl 18.IX.A Introduction 18.IX.B Ignorability and the Back-Door Criterion 18.X Rejoinder to Discussions of ‘Causal Diagrams for Empirical Research’ 18.X.A General 18.X.B Graphs, Structural Equations and Counterfactuals 18.X.C The Equivalence of Counterfactual and Structural Analyses 18.X.D Practical Versus Hypothetical Interventions 18.X.E Intervention as Conditionalisation 18.X.F Testing Versus using Assumptions 18.X.G Causation Versus Dependence 18.X.H Exemplifying Modelling Errors 18.X.I The Myth of Dangerous Graphs Additional References 19 Probabilities of Causation: Three Counterfactual Interpretations and Their Identification Abstract 19.1 Introduction 19.2 Structural Model Semantics (A Review) 19.2.1 Definitions: Causal Models, Actions and Counterfactuals 19.2.2 Examples 19.2.3 Relation to Lewis' Counterfactuals 19.2.4 Relation to Probabilistic Causality 19.2.5 Relation to Neyman–Rubin Model 19.3 Necessary and Sufficient Causes: Conditions of Identification 19.3.1 Definitions, Notations, and Basic Relationships 19.3.2 Bounds and Basic Relationships under Exogeneity 19.3.3 Identifiability under Monotonicity and Exogeneity 19.3.4 Identifiability under Monotonicity and Non-Exogeneity 19.4 Examples and Applications 19.4.1 Example 1: Betting against a Fair Coin 19.4.2 Example 2: The Firing Squad 19.4.3 Example 3: The Effect of Radiation on Leukemia 19.4.4 Example 4: Legal Responsibility from Experimental and Nonexperimental Data 19.5 Identification in Non-Monotonic Models 19.6 From Necessity and Sufficiency to “Actual Cause” 19.6.1 The Role of Structural Information 19.6.2 Singular Sufficient Causes 19.6.3 Example: The Desert Traveler (after P. Suppes) 19.6.3.1 Necessity and Sufficiency Ignoring Internal Structure 19.6.3.2 Sufficiency and Necessity given Forensic Reports 19.6.3.3 Necessity Given Forensic Reports 19.7 Conclusion 19.A Appendix: The Empirical Content of Counterfactuals References 20 Direct and Indirect Effects Abstract 20.1 Introduction 20.2 Conceptual Analysis 20.2.1 Direct versus Total Effects 20.2.2 Descriptive versus Prescriptive Interpretation 20.2.3 Policy Implications of the Descriptive Interpretation 20.2.4 Descriptive Interpretation of Indirect Effects 20.3 Formal Analysis 20.3.1 Notation 20.3.2 Controlled Direct Effects (review) 20.3.3 Natural Direct Effects: Formulation 20.3.4 Natural Direct Effects: Identification 20.3.5 Natural Indirect Effects: Formulation 20.3.6 Natural Indirect Effects: Identification 20.3.7 General Path-specific Effects 20.4 Conclusions Acknowledgments References V CAUSALITY 2002–2020 21 Introduction by Judea Pearl References 22 Comment: Understanding Simpson's Paradox 22.1 The History 22.2 A Paradox Resolved 22.2.1 Simpson's Surprise 22.2.2 Which Scenarios Invite Reversals? 22.2.3 Making the Correct Decision 22.3 Armistead's Critique 22.4 Conclusions References 23 Graphical Models for Recovering Probabilistic and Causal Queries from Missing Data Abstract 23.1 Introduction 23.2 Missingness Graph and Recoverability 23.2.1 Recoverability 23.3 Recovering Probabilistic Queries by Sequential Factorization 23.4 Recoverability in the Absence of an Admissible Sequence 23.5 Non-recoverability Criteria for Joint and Conditional Distributions 23.6 Recovering Causal Queries 23.6.1 Recovering P(y|do(z)) when Y and Ry are inseparable 23.7 Attrition 23.7.1 Recovering Joint Distributions under Simple Attrition 23.7.2 Recovering Causal Effects under Simple Attrition 23.8 Related Work 23.9 Conclusion Acknowledgments References 23.A Appendix 23.A.1 Missingness Process in Figure 23.1 23.A.2 Testing Compatibility between Underlying and Manifest Distributions 23.A.3 Proof of Theorem 23.1 23.A.4 Recovering P(V) when Parents of R belong to Vo U Vm 23.A.5 Proof of Theorem 23.2 23.A.6 Example: Recoverability by Theorem 23.2 23.A.7 Proof of Corollary 23.1 23.A.8 Proof of Theorem 23.3 23.A.9 Proof of Corollary 23.2 23.A.10 Proof of Theorem 23.4 23.A.11 Proof of Theorem 23.5 23.A.12 Proof of Theorem 23.6 24 Recovering from Selection Bias in Causal and Statistical Inference Abstract 24.1 Introduction 24.1.1 Related Work and Our Contributions 24.2 Recoverability without External Data 24.3 Recoverability with External Data 24.4 Recoverability of Causal Effects 24.5 Conclusions Acknowledgments References 25 External Validity: From Do-Calculus to Transportability Across Populations Abstract Key words and phrases 25.1 Introduction: Threats vs. Assumptions 25.2 Preliminaries: The Logical Foundations of Causal Inference 25.2.1 Causal Models as Inference Engines 25.2.2 Assumptions in Nonparametric Models 25.2.3 Representing Interventions, Counterfactuals and Causal Effects 25.2.4 Identification, d-Separation and Causal Calculus 25.2.5 The Rules of do-Calculus 25.3 Inference Across Populations: Motivating Examples 25.4 Formalizing Transportability 25.4.1 Selection Diagrams and Selection Variables 25.4.2 Transportability: Definitions and Examples 25.5 Transportability of Causal Effects—A Graphical Criterion 25.6 Conclusions 25.A Appendix Acknowledgments References 26 Detecting Latent Heterogeneity Abstract Keywords 26.1 Introduction 26.2 Covariate-Induced Heterogeneity 26.2.1 Assessing Covariate-Induced Heterogeneity 26.2.2 Special Cases 26.3 Latent Heterogeneity between the Treated and Untreated 26.3.1 Two Types of Confounding 26.3.2 Separating Fixed-Effect from Variable-Effect Bias 26.4 Three Ways of Detecting Heterogeneity 26.4.1 Detecting Heterogeneity in Randomized Trials 26.4.2 Detecting Heterogeneity Through Adjustment 26.4.3 Detecting Heterogeneity Through Mediating Instruments 26.5 Example: Heterogeneity in Recruitment 26.6 Conclusions Acknowledgments Declaration of Conflicting Interests Funding References Author Biography 26.A Appendix A (An Extreme Case of Latent Heterogeneity) 26.B Appendix B (Assessing Heterogeneity in Structural Equation Models) 26.B.1 The Structural Origin of Counterfactuals 26.B.2 Illustration VI CONTRIBUTED ARTICLES 27 On Pearl's Hierarchy and the Foundations of Causal Inference Abstract 27.1 Introduction 27.1.1 Roadmap of the Chapter 27.1.2 Notation 27.2 Structural Causal Models and the Causal Hierarchy 27.2.1 Pearl Hierarchy, Layer 1—Seeing 27.2.2 Pearl Hierarchy, Layer 2—Doing 27.2.3 Pearl Hierarchy, Layer 3—Imagining Counterfactual Worlds 27.3 Pearl Hierarchy—A Logical Perspective 27.4 Pearl Hierarchy—A Graphical Perspective 27.4.1 Causal Inference via L2-constraints—Markovian Causal Bayesian Networks 27.4.2 Causal Inference via L2-constraints—Semi-Markovian Causal Bayes Networks 27.4.2.1 Revisiting Locality in Semi-Markovian Models 27.4.2.2 CBNs with Latent Variables—Putting All the Pieces Together 27.4.2.3 Cross-layer Inferences through CBNs with Latent Variables 27.5 Conclusions Acknowledgments References 28 The Tale Wags the DAG Abstract 28.1 Introduction 28.2 The Ladder of Causation 28.3 Ground Level: Syntax 28.4 Rung 1: Seeing 28.4.1 Qualitative Structure 28.4.2 Quantitative Structure 28.4.3 Empirical Assessment 28.4.4 Functional DAGs 28.4.5 Downsizing and Upsizing 28.4.6 Empirical Assessment 28.5 Rung 2: Doing 28.5.1 Intervention DAGs 28.5.2 Augmented DAGs 28.5.3 Empirical Assessment 28.5.4 Downsizing and Upsizing 28.5.5 Functional Intervention DAGs 28.6 Rung 3: Imagining 28.7 Conclusion References 29 Instrumental Variables with Treatment-induced Selection: Exact Bias Results 29.1 Introduction 29.2 Causal Graphs 29.3 Instrumental Variables 29.4 Selection Bias in IV: Qualitative Analysis 29.5 Selection Bias in IV: Quantitative Analysis 29.5.1 Selection as a Function of Treatment Alone 29.5.2 Selection as a Function of a Mediator 29.5.3 Selection on Treatment and the Unobserved Confounder 29.6 Conclusion 29.A Appendix 29.A.1 Proof of Truncation Bias Expressions 29.A.2 Proof of Adjustment as Point Truncation (Proposition 29.3) References 30 Causal Models and Cognitive Development References 31 The Causal Foundations of Applied Probability and Statistics Abstract 31.1 Introduction: Scientific Inference is a Branch of Causality Theory 31.2 Causality is Central Even for Purely Descriptive Goals 31.3 The Strength of Probabilistic Independence Demands Physical Independence 31.4 The Superconducting Supercollider of Selection 31.5 Data and Algorithms are Causes of Reported Results 31.6 Getting Causality into Statistics by Putting Statistics into Causal Terms from the Start 31.7 Causation in 20th-century Statistics 31.8 Causal Analysis versus Traditional Statistical Analysis 31.9 Relating Causality to Traditional Statistical Philosophies and “Objective” Statistics 31.10 Discussion 31.11 Conclusion 31.A Appendix 31.A.1 A Counting Measure for the Logical Content of a Finite Exchangeability Assumption Acknowledgments References 32 Pearl on Actual Causation Abstract 32.1 Introduction 32.2 Actual Causation 32.3 Causal Models and But-for Causation 32.4 Pre-emption and Lewis 32.5 Intransitivity and Overdetermination 32.6 Pearl's Definitions of Actual Causation 32.7 Pearl's Achievement References 33 Causal Diagram and Social Science Research 33.1 Graphical Causal Models and Social Science Research 33.2 Two Applications of Graphical Causal Models 33.2.1 Causal Inference with Panel Data 33.2.2 Causal Inference with Interference between Units 33.3 The Future of Causal Research in the Social Sciences References 34 Causal Graphs for Missing Data: A Gentle Introduction 34.1 Introduction 34.2 Missingness Graphs 34.2.1 Graphical Representation of Missingness Categories 34.3 Recoverability 34.3.1 Recoverability in MAR and MCAR Problems 34.3.1.1 Recoverability of Joint Distribution in MCAR and MAR Models 34.3.1.2 Recoverability as a Guide for Estimation 34.3.2 Recoverability in MNAR Problems 34.3.2.1 Recovering P(X, Y) Given the m-graph G in Figure 34.2(a) 34.3.2.2 Recovering P(X, Y) Given the m-graph in Figure 34.2(b) 34.3.2.3 Recovering P(X, Y) Given the m-graph in Figure 34.2(c) 34.3.2.4 Recovering P(X, Y) Given the m-graph in Figure 34.2(d) 34.3.2.5 Recovering P(X) Given the m-graph in Figure 34.2(e) 34.3.3 Non-recoverability 34.4 Testability References 35 A Note of Appreciation 35.1 A Magic Square 35.2 A Magic Shield of David 36 Causal Models for Dynamical Systems Abstract 36.1 Introduction 36.1.1 Structural Causal Models with Measurement Noise 36.1.2 Structural Causal Models with Driving Noise 36.1.3 Interventions 36.1.4 Time-dependent Data 36.2 Chemical Reaction Networks and ODEs 36.3 Causal Kinetic Models 36.3.1 Causal Kinetic Models with Measurement Noise 36.3.2 Causal Kinetic Models with Driving Noise 36.3.3 Interventions 36.3.4 Other Causal Models for Dynamical Systems and Related Work 36.4 Challenges in Causal Inference for ODE-based Systems 36.5 From Invariance to Causality and Generalizability 36.6 Conclusions Acknowledgments References 37 Probabilistic Programming Languages: Independent Choices and Deterministic Systems 37.1 Probabilistic Models and Deterministic Systems 37.2 Possible Worlds Semantics 37.3 Inference 37.4 Learning 37.5 Other Issues 37.6 Causal Models 37.7 Some Pivotal References 37.8 Conclusion References 38 An Interventionist Approach to Mediation Analysis 38.1 Introduction 38.2 Approaches to Mediation Based on Counterfactuals Defined in Terms of the Mediator: The CDE and PDE 38.2.1 Two Hypothetical River Blindness Treatment Studies 38.2.2 The PDE and CDE in the River Blindness Studies 38.2.3 Identification of the PDE via the Mediation Formula under the NPSEM-IE for Figure 38.3(a) 38.2.4 Partial Identification of the PDE Under the FFRCISTG for Figure 38.3(a) 38.2.5 An Example in Which an FFRCISTG Model Holds, but an NPSEM-IE Does Not 38.2.6 Testable Versus Untestable Assumptions and Identifiability 38.3 Interventionist Theory of Mediation 38.3.1 Interventional Interpretation of the PDE Under an Expanded Graph 38.3.2 Direct and Indirect Effects via the Expanded Graph 38.3.3 Expanded Graphs for a Single Treatment 38.3.4 On the Substantive Relationship between Different Gex Graphs and Gex 38.3.5 Generalizations 38.3.6 Identification of Cross-world Nested Counterfactuals of DAG G under an FFRCISTG Model for its Expanded Graph Gex 38.4 Path-Specific Counterfactuals 38.4.1 Conditional Path-specific Distributions 38.5 Conclusion Acknowledgments 38.A Appendix 38.A.1 Proof of PDE Bounds under the FFRCISTG Model 38.A.2 Proof that the PDE is Not Identified in the River Blindness Study 38.A.3 Detecting Confounding via Interventions on A and S 38.A.4 Proof of Proposition 38.3 References 39 Causality for Machine Learning Abstract 39.1 Introduction 39.2 The Mechanization of Information Processing 39.3 From Statistical to Causal Models 39.3.1 Methods Driven by Independent and Identically Distributed Data 39.3.2 Structural Causal Models 39.4 Levels of Causal Modeling 39.5 Independent Causal Mechanisms 39.6 Cause–Effect Discovery 39.7 Half-sibling Regression and Exoplanet Detection 39.8 Invariance, Robustness, and Semi-supervised Learning 39.8.1 Semi-supervised Learning 39.8.2 Adversarial Vulnerability 39.8.3 Multi-task Learning 39.8.4 Reinforcement Learning 39.9 Causal Representation Learning 39.9.1 Learning Transferable Mechanisms 39.9.2 Learning Disentangled Representations 39.9.3 Learning Interventional World Models and Reasoning 39.10 Personal Notes and Conclusion Acknowledgments References 40 Why Did They Do That? Abstract 40.1 Introduction 40.2 Some Examples 40.3 Back to the Garden of Eden 40.4 Decision Theory and Decision Analysis 40.5 Back Again in the Garden of Eden 40.6 Conclusion: God's Decision References 41 Multivariate Counterfactual Systems and Causal Graphical Models 41.1 Introduction 41.2 Graphs, Non-parametric Structural Equation Models, and the g-/do Operator 41.2.1 Graphical Models 41.2.2 Causal Models Associated with DAGs 41.2.2.1 Non-parametric Structural Equations with Independent Errors 41.2.2.2 A Less Restrictive Model: Non-parametric Structural Equations with Single-World (FFRCISTG) Independences 41.2.3 Single-World Intervention Graphs 41.2.4 Factorization Associated with the SWIG Global Markov Property 41.2.5 SWIG Representation of the Defining FFRCISTG Assumptions 41.3 The Potential Outcomes Calculus and Identification 41.4 Identification in Hidden Variable Causal Models 41.4.1 Latent Projection ADMGs 41.4.2 The Identified Splitting Operation in a SWIG 41.4.3 The Extended ID Algorithm 41.4.4 Identification of Conditional Interventional Distributions 41.4.5 Representing Context-specific Independence using SWIGs 41.5 Conclusion Acknowledgments 41.A Appendix 41.A.1 Incompleteness of d-Separation in Twin Networks due to Deterministic Relations 41.A.2 Weaker Causal Models to Which the po-Calculus Also Applies 41.A.3 Completeness Proofs References 42 Causal Bayes Nets as Psychological Theory Abstract 42.1 The Human Conception of Causality 42.2 Core Properties 42.3 The Broader Perspective: The Community of Knowledge 42.4 Collective Causal Models 42.5 Conclusion Acknowledgments References 43 Causation: Objective or Subjective? Abstract 43.1 Causation: A Bunch of Attitudes 43.2 The Model Relativity of Causation 43.3 Laws 43.4 Probability Acknowledgments References Editors' Biographies Index