Learning decomposable markov networks in pseudo-independent domains with local evaluation

Abstract

We consider learning probabilistic graphical models in a problem domain of unknown dependence structure. Common learning algorithms rely on single-link lookahead search, which assumes the underlying domain is not pseudo-independent. Since the dependence structure of the domain is unknown, such assumption is fallible. We study learning algorithms that make no such assumption and return an approximate dependence structure no matter whether the domain is pseudo-independent or not. The focus of this paper is on learning decomposable Markov networks, which can directly be used for model-based inference or as the intermediate step for further learning of directed graphical models. We identify a small subset of domain variables, termed crux, in the graphical models currently being examined during search. We prove that crux is sufficient for computing the incremental change of both model description length as well as data description length given the model. Based on crux, we propose algorithms that reduce evaluation of alternative graphical models to local computation, improve efficiency significantly, and introduce no error to the selection of alternative models.

Corrected score methods for estimating Bayesian networks with error‐prone nodes

“…Many existing works follow the theme of search-and-score. [28][29][30][31][32][33][34][35] Following this theme, one formulates a scoring criterion, and searches for a directed graph, or an equivalent class of directed graphs, 36 that optimizes the score. The score can be constructed based on a likelihood function of observed data in the frequentist framework; 11,37 it can also originate from a posterior distribution of a graph in the Bayesian framework.…”

“…There is a large collection of works on inferring Bayesian networks. Many existing works follow the theme of search‐and‐score 28‐35 . Following this theme, one formulates a scoring criterion, and searches for a directed graph, or an equivalent class of directed graphs, 36 that optimizes the score.…”

Incremental Compilation of Bayesian Networks Based on Maximal Prime Subgraphs

“…Thus, Xiang and Lee propose its use when learning undirected structures from data, in particular Decomposable Markov Networks. 41 The idea is to identify the subgraphs involved in an incremental operation, e.g. adding a link, and restrict score computations only to those subgraphs Currently, there exist several studies which use our preliminarily proposed MPDbased Incremental Compilation technique or which cite it as an important approach to the modularity problem when compiling or learning BNs.…”