دانلود کتاب Handbook of graphical models

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Cover......Page 1
Half Title......Page 2
Chapman & Hall/CRCHandbooks of Modern Statistical Methods......Page 3
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 16
Contributors......Page 18
Part I Conditional independencies andMarkov properties......Page 20
Chapter 1 Conditional Independence and Basic Markov Properties Milan Studený......Page 22
1.1.2 Graphs and local computation method......Page 23
1.1.4 Geometric approach and methods of modern algebra......Page 24
1.1.5 A motivational example......Page 25
1.2.1 Discrete probability measures......Page 27
1.2.2 Continuous distributions......Page 29
1.3.1 Conditional independence in the discrete case......Page 30
1.3.2 More general CI concepts......Page 33
1.4.1 Conditional independence structure......Page 34
1.4.2 Statistical model of a CI structure......Page 36
1.5 Semi-graphoids, Graphoids, and Separoids......Page 37
1.5.1 Elementary and dominant triplets......Page 38
1.6 Elementary Graphical Concepts......Page 40
1.7.1 Global Markov property for an UG......Page 41
1.7.2 Local and pairwise Markov properties for an UG......Page 42
1.8.1 Directional separation criteria......Page 43
1.8.3 Local Markov property for a DAG......Page 48
1.8.5 Markov equivalence for DAGs......Page 49
1.9 Remarks on Chordal Graphs......Page 50
1.10.1 The concept of a structural imset......Page 51
1.11 CI Inference......Page 52
2.1 Introduction......Page 58
2.1.1 Decomposable graphs......Page 59
2.1.3 Marginalizing and conditioning......Page 60
2.1.4 Outline of the chapter......Page 61
2.2 Chain Graphs......Page 62
2.2.1 Factorization......Page 63
2.2.2 Local Markov property......Page 64
2.2.4 Other Markov properties for chain graphs......Page 65
2.3.1 ADMGs......Page 66
2.3.2 Ancestral sets......Page 67
2.3.3 Districts......Page 68
2.3.4 A conditional independence model......Page 69
2.4 Non-Independence Constraints......Page 70
2.4.1 Verma constraints......Page 71
2.4.3 mDAGs......Page 73
2.5.1 Other models......Page 74
2.5.2 Ancestral graphs......Page 75
2.5.3 Quantum states......Page 76
2.6 Summary......Page 77
3.1 Introduction......Page 80
3.2.1 Polynomials, ideals and varieties......Page 82
3.2.2 Irreducible and primary decomposition......Page 84
3.2.4 Real algebraic geometry......Page 86
3.3.1 Discrete random variables......Page 87
3.3.2 Gaussian random variables......Page 90
3.3.3 The contraction axiom......Page 91
3.4.1 The intersection axiom......Page 92
3.4.2 The four-cycle......Page 93
3.5 The Vanishing Ideal of a Graphical Model......Page 94
3.6 Further Reading......Page 97
Part II Computing with factorizing distributions......Page 100
Chapter 4 Algorithms and Data Structures for Exact Computation of Marginals Jeffrey A. Bilmes......Page 102
4.1.1 Graphical models......Page 103
4.1.2 Probabilistic inference......Page 104
4.2 Inference on Trees......Page 105
4.2.1 Trees and tree structured factorization......Page 106
4.2.2 Eliminating variables via marginalization......Page 107
4.2.3 The variable elimination process on graphs......Page 109
4.3 Triangulated Graphs and Fill-in Free Elimination Orders......Page 110
4.3.2 Triangulated graphs......Page 111
4.3.3 Good heuristics for choosing an elimination order......Page 114
4.3.4 The running intersection property and junction trees......Page 115
4.3.5 Entanglement......Page 119
4.4.1 Benefits of junction trees......Page 120
4.4.2 Factorization......Page 121
4.4.4 Message initialization......Page 122
4.4.5 Necessary condition for true marginals......Page 124
4.4.6 Achieving true marginals via message passing......Page 125
4.4.7 Message schedules......Page 129
4.5 Discussion......Page 130
Chapter 5 Approximate Methods for Calculating Marginals and Likelihoods Nicholas Ruozzi......Page 136
5.1.1 The Kullback-Leibler divergence......Page 137
5.1.2 The Gibbs free energy......Page 138
5.2 The Bethe Free Energy......Page 139
5.2.1 Convex and reweighted free energies......Page 141
5.2.2 A combinatorial characterization of the Bethe free energy......Page 142
5.3.1 Loopy belief propagation......Page 144
5.3.2 Reweighted message-passing algorithms......Page 145
5.3.4 Naive mean field......Page 146
5.3.5 Sampling methods......Page 147
5.4.1 Log-linear models......Page 148
5.4.2 Maximum likelihood estimation (MLE)......Page 149
5.4.3 Maximum entropy......Page 153
5.4.4 Pseudolikelihood learning......Page 154
Appendix: Marginal Reparameterization of a Tree-Structured Distribution......Page 155
6.1 Introduction......Page 160
6.2 The MAP Estimation Problem......Page 161
6.3.3 Local search methods......Page 163
6.4 Integer Programming and LP Relaxations......Page 164
6.4.1 LP relaxations......Page 165
6.4.2 Tight LP relaxations......Page 166
6.5.2 Subgradient descent......Page 167
6.5.3 Block coordinate minimization......Page 168
6.5.4 -descent......Page 169
6.5.5 The smoothed dual......Page 170
6.5.6 The strongly-convex dual......Page 172
6.6 Relation to Message-Passing Algorithms......Page 175
6.7 Rounding Schemes......Page 176
Appendix: The Dual LP Relaxation......Page 177
7.1 Introduction......Page 184
7.2 Hidden Markov Models......Page 185
7.3 Particle Filtering and Smoothing......Page 188
7.4.1 A general construction......Page 191
7.4.2 Convergence results......Page 192
7.4.3 Variance estimation......Page 194
7.5.1 Resampling schemes......Page 195
7.5.2 Auxiliary particle filters......Page 196
7.5.3 Reducing interaction for distributed implementation......Page 197
7.5.4 SMC samplers......Page 198
7.6 Particle MCMC......Page 199
7.7 Discussion......Page 202
Part III Statistical inference......Page 208
8.1 Introduction......Page 210
8.2 Notation and Terminology......Page 211
8.3 Overview of Discrete Graphical Models......Page 213
8.4.1 Establishing independence relationships......Page 216
8.4.2 Two properties of Möbius inversion......Page 217
8.5 Undirected Graph Models......Page 219
8.6 Bidirected Graph Models......Page 222
8.7 Regression Graph Models......Page 225
8.8 Non-binary Variables and Likelihood Inference......Page 229
Chapter 9 Gaussian Graphical Models Caroline Uhler......Page 236
9.1 The Gaussian Distribution and Conditional Independence......Page 238
9.2 The Gaussian Likelihood and Convex Optimization......Page 239
9.3 The MLE as a Positive Definite Completion Problem......Page 242
9.4 ML Estimation and Convex Geometry......Page 243
9.5 Existence of the MLE for Various Classes of Graphs......Page 246
9.6 Algorithms for Computing the MLE......Page 249
9.7 Learning the Underlying Graph......Page 252
9.8 Other Gaussian Models with Linear Constraints......Page 253
10.1 Introduction......Page 258
10.2.1 Graphs and Markov properties......Page 260
10.2.2 The Wishart distribution......Page 261
10.3.1 The graphical Gaussian (or concentration graph) model......Page 263
10.3.2 The hyper inverse Wishart prior......Page 264
10.3.3 Priors with several shape parameters......Page 267
10.3.4 Covariance graph models......Page 269
10.4.1 Computing the normalizing constant of the G-Wishart......Page 270
10.4.2 Sampling from the G-Wishart......Page 271
10.4.3 Moving away from Bayes factors......Page 272
10.4.4 Moving away from Bayes factors and the G-Wishart......Page 273
10.5 Matrix Variate Graphical Gaussian Models......Page 275
10.6 Fractional Bayes Factors......Page 277
10.7 Two Interesting Questions......Page 279
Chapter 11 Latent Tree Models Piotr Zwiernik......Page 284
11.1.1 Definitions......Page 285
11.1.2 Motivation and applications......Page 286
11.1.3 Parsimonious latent tree models......Page 288
11.1.4 Gaussian and general Markov models......Page 289
11.2.1 Gaussian latent tree model......Page 290
11.2.2 General Markov models......Page 292
11.2.3 Linear models......Page 293
11.2.4 Distance based methods......Page 294
11.3.1 Identifiability......Page 295
11.3.2 Guarantees for tree reconstruction......Page 296
11.3.3 Model selection......Page 297
11.4.2 The structural EM algorithm......Page 298
11.4.3 Phylogenetic invariants......Page 299
11.5 Discussion......Page 300
12.1 Introduction......Page 308
12.3 Gaussian Graphical Models......Page 309
12.3.2 Edge recovery via matrix estimation......Page 310
12.3.3 Edge recovery via linear regression......Page 311
12.3.4 Statistical theory......Page 312
12.4 Ising Models......Page 315
12.4.1 Logistic regression......Page 316
12.4.2 Other methods......Page 317
12.5.1 Nonparanormal distributions......Page 318
12.5.2 Augmented inverse covariance matrices......Page 319
12.5.3 Other exponential families......Page 320
12.6 Robustness......Page 321
12.6.3 Latent variables......Page 322
12.7 Further Reading......Page 323
13.1 Introduction......Page 328
13.2 Semiparametric Exponential Family Graphical Models......Page 330
13.2.1 Examples......Page 331
13.3 Tree and Forest Graphical Models......Page 332
13.3.1 Tree estimation......Page 333
13.4 Gaussian Copulas and Variants......Page 334
13.4.1 Estimation......Page 336
13.4.3 Trees and copulas......Page 337
13.5 Tensor Product Smoothing Spline ANOVA Models......Page 338
13.5.2 Fisher-Hyvärinen scoring......Page 339
13.6 Summary and Extensions......Page 341
14.1.1 Introduction......Page 344
14.1.2 De-biasing regularized estimators......Page 346
14.1.3 Graphical Lasso......Page 347
14.1.4 Nodewise square-root Lasso......Page 352
14.1.6 Simulation results......Page 354
14.1.7 Discussion......Page 356
14.2 Directed Acyclic Graphs......Page 357
14.2.1 Maximum likelihood estimator with `0-penalization......Page 358
14.2.2 Inference for edge weights......Page 359
14.3 Conclusion......Page 360
14.4.1 Proofs for undirected graphical models......Page 361
14.4.2 Proofs for directed acyclic graphs......Page 365
Part IV Causal inference......Page 370
15.1 Introduction......Page 372
15.2 Association versus Causation: Seeing versus Doing......Page 374
15.3.1 Intervention graphs......Page 377
15.3.2 Causal DAGs......Page 379
15.3.3 Comparison......Page 382
15.4.1 The Back-Door Theorem......Page 383
15.4.2 The Front-Door Theorem......Page 386
15.5.1 Confounding......Page 388
15.5.2 Selection bias......Page 392
15.6 Discussion and Outlook......Page 394
16.1 Introduction......Page 400
16.2 Causal Models of a DAG......Page 401
16.2.1 Causal, direct, indirect, and path-specific effects......Page 403
16.2.2 Responses to dynamic treatment regimes......Page 404
16.2.4 Identification of causal effects......Page 405
16.2.5 Identification of path-specific effects......Page 406
16.3 Causal Models of a DAG with Hidden Variables......Page 407
16.3.2 Conditional mixed graphs and kernels......Page 408
16.3.3 The fixing operation......Page 409
16.3.4 The ID algorithm......Page 410
16.3.7 Path-specific effects......Page 413
16.3.8 Responses to dynamic treatment regimes......Page 414
16.4 Linear Structural Equation Models......Page 415
16.4.1 Global identification of linear SEMs......Page 416
16.4.2 Generic identification of linear SEMs......Page 417
16.5 Summary......Page 419
Chapter 17 Mediation Analysis Johan Steen and Stijn Vansteelandt......Page 424
17.1 Introduction......Page 425
17.2.1 Natural direct and indirect effects......Page 426
17.2.2 Path-specific effects......Page 427
17.3 Cross-World Quantities Call for Cross-World Assumptions......Page 428
17.3.1 Imposing cross-world independence......Page 429
17.3.3 Single world versus multiple worlds models......Page 430
17.4.1 Unmeasured mediator-outcome confounding......Page 431
17.4.2 Adjusting for mediator-outcome confounding......Page 432
17.4.3 Treatment-induced mediator-outcome confounding......Page 433
17.4.5 Sufficient conditions to recover natural effects from experimental data......Page 434
17.4.6 Sufficient conditions to recover natural effects from observational data......Page 435
17.5 Identification 2.0......Page 438
17.5.1 Building blocks for complete graphical identification criteria......Page 439
17.5.2 The central notion of recantation......Page 442
17.6.2 Two types of auxiliary variables......Page 445
17.6.3 Mediating instruments — some reasons for skepticism......Page 446
17.7.2 Deterministic expanded graphs......Page 447
17.7.3 Some examples......Page 448
17.8 Path-Specific Effects for Multiple Mediators......Page 449
17.9 Discussion and Further Challenges......Page 451
18.1 Introduction......Page 458
18.2 Why Causal Search Is Difficult......Page 459
18.3 Assumptions and Terminology......Page 460
18.4 Types of Search......Page 463
18.5.1 Acyclicity, no latent confounders, no selection bias......Page 464
18.5.2 Acyclicity, latent confounders, selection bias......Page 471
18.5.3 Cycles, no latent confounders, no selection bias......Page 473
18.5.4 Cycles, latent confounders, overlapping data sets, experimental and observational data......Page 474
18.6.1 Score-based DAG search......Page 475
18.6.2 Score-based equivalence class search......Page 476
18.6.3 Functional causal discovery......Page 477
18.7 Conclusion and Discussions......Page 481
Part V Applications......Page 490
19.1 Introduction......Page 492
19.2 Bayesian Networks for the Analysis of Evidence......Page 493
19.3.1 Generic modules......Page 497
19.4 Quantitative Analysis......Page 499
19.5 Bayesian Networks for Forensic Genetics......Page 500
19.5.2 Bayesian network for simple paternity cases......Page 501
19.6 Bayesian Networks for DNA Mixtures......Page 503
19.6.1 Qualitative data......Page 504
19.6.2 Quantitative data......Page 505
19.6.3 Further developments on DNA mixtures......Page 507
19.7.1 Uncertainty in allele frequencies......Page 508
19.7.2 Heterogeneous reference population......Page 509
Appendix: Genetic Background......Page 511
Chapter 20 Graphical Models in Molecular Systems Biology Sach Mukherjee and Chris Oates......Page 516
20.1.2 Biological networks......Page 517
20.1.4 Notation......Page 518
20.2.1 Gaussian graphical models......Page 519
20.2.2 Directed acyclic graphs......Page 521
20.2.3 Heterogeneous data and biological context......Page 522
20.3.2 Towards linear models......Page 523
20.3.4 Nonlinear models......Page 524
20.4.2 Empirical assessment of causal discovery......Page 526
20.5 Perspective and Outlook......Page 527
21.1 Introduction......Page 532
21.1.2 Publicly available databases......Page 533
21.2.1 Network-assisted analysis in genome-wide association studies......Page 534
21.2.2 Co-expression network-based association analysis of rare variants .......Page 535
21.3 Network-Based eQTL and Integrative Genomic Analysis......Page 536
21.3.1 Detection of trans acting genetic effects......Page 537
21.3.2 A causal mediation framework for integration of GWAS and eQTL studies......Page 538
21.4.1 Covariance based on compositional data......Page 541
21.4.2 Microbial community dynamics......Page 542
21.5 Future Directions and Topics......Page 543
Index......Page 548