本章目录
26 Graphical model structure learning 907
26.1 Introduction 907
26.2 Structure learning for knowledge discovery 908
26.2.1 Relevance networks 908
26.2.2 Dependency networks 909
26.3 Learning tree structures 910
26.3.1 Directed or undirected tree? 911
26.3.2 Chow-Liu algorithm for finding the ML tree structure 912
26.3.3 Finding the MAP forest 912
26.3.4 Mixtures of trees 914
26.4 Learning DAG structures 914
26.4.1 Markov equivalence 914
26.4.2 Exact structural inference 916
26.4.3 Scaling up to larger graphs 920
26.5 Learning DAG structure with latent variables 922
26.5.1 Approximating the marginal likelihood when we have missing data 922
26.5.2 Structural EM 925
26.5.3 Discovering hidden variables 926
26.5.4 Case study: Google’s Rephil 928
26.5.5 Structural equation models * 929
26.6 Learning causal DAGs 931
26.6.1 Causal interpretation of DAGs 931
26.6.2 Using causal DAGs to resolve Simpson’s paradox 933
26.6.3 Learning causal DAG structures 935
26.7 Learning undirected Gaussian graphical models 938
26.7.1 MLE for a GGM 938
26.7.2 Graphical lasso 939
26.7.3 Bayesian inference for GGM structure * 941
26.7.4 Handling non-Gaussian data using copulas * 942
26.8 Learning undirected discrete graphical models 942
26.8.1 Graphical lasso for MRFs/CRFs 942
26.8.2 Thin junction trees 944