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2019 Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods
Jimmy Olsson, Tatjana Pavlenko, Felix L. Rios
Electron. J. Statist. 13(2): 2865-2897 (2019). DOI: 10.1214/19-EJS1585

Abstract

We present a sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models. As a key component of our suggested approach, we show that the problem of graph estimation, which in general lacks natural sequential interpretation, can be recast into a sequential setting by proposing a recursive Feynman-Kac model that generates a flow of junction tree distributions over a space of increasing dimensions. We focus on particle McMC methods to provide samples on this space, in particular on particle Gibbs (PG), as it allows for generating McMC chains with global moves on an underlying space of decomposable graphs. To further improve the PG mixing properties, we incorporate a systematic refreshment step implemented through direct sampling from a backward kernel. The theoretical properties of the algorithm are investigated, showing that the proposed refreshment step improves the performance in terms of asymptotic variance of the estimated distribution. The suggested sampling methodology is illustrated through a collection of numerical examples demonstrating high accuracy in Bayesian graph structure learning in both discrete and continuous graphical models.

Citation

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Jimmy Olsson. Tatjana Pavlenko. Felix L. Rios. "Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods." Electron. J. Statist. 13 (2) 2865 - 2897, 2019. https://doi.org/10.1214/19-EJS1585

Information

Received: 1 June 2018; Published: 2019
First available in Project Euclid: 29 August 2019

zbMATH: 07104732
MathSciNet: MR3998930
Digital Object Identifier: 10.1214/19-EJS1585

Subjects:
Primary: 62L20, 62L20
Secondary: 62-09

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Vol.13 • No. 2 • 2019
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