Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independencies, but different DAGs may encode the same set of relations and are indistinguishable using observational data. Equivalent DAGs can be collected into classes, each represented by a partially directed graph known as essential graph (EG). Structure learning directly conducted on the EG space, rather than on the allied space of DAGs, leads to theoretical and computational benefits. Still, the majority of efforts has been dedicated to Gaussian data, with less attention to methods designed for multivariate categorical data. A Bayesian methodology for structure learning of categorical EGs is then proposed. Combining a constructive parameter prior elicitation with a graph-driven likelihood decomposition, a closed-form expression for the marginal likelihood of a categorical EG model is derived. Asymptotic properties are studied, and an MCMC sampler scheme developed for approximate posterior inference. The methodology is evaluated on both simulated scenarios and real data, with appreciable performance in comparison with state-of-the-art methods.

Castelletti, F., Peluso, S. (2021). Equivalence class selection of categorical graphical models. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 164(December 2021) [10.1016/j.csda.2021.107304].

Equivalence class selection of categorical graphical models

Castelletti F.
;
Peluso S.
2021

Abstract

Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independencies, but different DAGs may encode the same set of relations and are indistinguishable using observational data. Equivalent DAGs can be collected into classes, each represented by a partially directed graph known as essential graph (EG). Structure learning directly conducted on the EG space, rather than on the allied space of DAGs, leads to theoretical and computational benefits. Still, the majority of efforts has been dedicated to Gaussian data, with less attention to methods designed for multivariate categorical data. A Bayesian methodology for structure learning of categorical EGs is then proposed. Combining a constructive parameter prior elicitation with a graph-driven likelihood decomposition, a closed-form expression for the marginal likelihood of a categorical EG model is derived. Asymptotic properties are studied, and an MCMC sampler scheme developed for approximate posterior inference. The methodology is evaluated on both simulated scenarios and real data, with appreciable performance in comparison with state-of-the-art methods.
Articolo in rivista - Articolo scientifico
Bayesian model selection; Categorical data; Graphical model; Markov equivalence;
English
18-giu-2021
2021
164
December 2021
107304
none
Castelletti, F., Peluso, S. (2021). Equivalence class selection of categorical graphical models. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 164(December 2021) [10.1016/j.csda.2021.107304].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/319382
Citazioni
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
Social impact