Electronic Journal of Statistics

Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods

Jimmy Olsson, Tatjana Pavlenko, and Felix L. Rios

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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.

Article information

Electron. J. Statist., Volume 13, Number 2 (2019), 2865-2897.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62L20: Stochastic approximation 62L20: Stochastic approximation
Secondary: 62-09: Graphical methods

Structure learning sequential sampling decomposable graphical models particle Gibbs

Creative Commons Attribution 4.0 International License.


Olsson, Jimmy; Pavlenko, Tatjana; Rios, Felix L. Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods. Electron. J. Statist. 13 (2019), no. 2, 2865--2897. doi:10.1214/19-EJS1585. https://projecteuclid.org/euclid.ejs/1567065622

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