Parameter identifiability of discrete Bayesian networks with hidden\n variables

2014/06/02 by Elizabeth S. Allman, Allman, Elizabeth S., John A. Rhodes +5 · 2 citations
Computer Science · #Bayesian Modeling and Causal Inference

paper · pdf · doi:10.48550/arxiv.1406.0541

Abstract

Identifiability of parameters is an essential property for a statistical\nmodel to be useful in most settings. However, establishing parameter\nidentifiability for Bayesian networks with hidden variables remains\nchallenging. In the context of finite state spaces, we give algebraic arguments\nestablishing identifiability of some special models on small DAGs. We also\nestablish that, for fixed state spaces, generic identifiability of parameters\ndepends only on the Markov equivalence class of the DAG. To illustrate the use\nof these results, we investigate identifiability for all binary Bayesian\nnetworks with up to five variables, one of which is hidden and parental to all\nobservable ones. Surprisingly, some of these models have parameterizations that\nare generically 4-to-one, and not 2-to-one as label swapping of the hidden\nstates would suggest. This leads to interesting difficulties in interpreting\ncausal effects.\n

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