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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

   
 
 

 

Graphical posterior predictive classification: Bayesian model averaging with particle Gibbs


Authors: Tatjana Pavlenko and Felix L. Rios
Journal: Theor. Probability and Math. Statist. 109 (2023), 81-99
MSC (2020): Primary 54C40, 14E20; Secondary 46E25, 20C20
DOI: https://doi.org/10.1090/tpms/1198
Published electronically: October 3, 2023
MathSciNet review: 4652995
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Abstract: In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. An explicit evaluation of the model probabilities is well known to be infeasible. To address this issue, we consider the particle Gibbs strategy of J. Olsson, T. Pavlenko, and F. L. Rios [Electron. J. Statist. 13 (2019), no. 2, 2865–2897] for posterior sampling from decomposable graphical models which utilizes the so-called Christmas tree algorithm of J. Olsson, T. Pavlenko, and F. L. Rios [Stat. Comput. 32 (2022), no. 5, Paper No. 80, 18] as proposal kernel. We also derive a strong hyper Markov law which we call the hyper normal Wishart law that allows to perform the resultant Bayesian calculations locally. The proposed predictive graphical classifier reveals superior performance compared to the ordinary Bayesian predictive rule that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers.


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Additional Information

Tatjana Pavlenko
Affiliation: Department of Statistics, Uppsala University, Box 513, 751 20 Uppsala, Sweden
Email: tatjana.pavlenko@statistik.uu.se

Felix L. Rios
Affiliation: Department of Mathematics, KTH Royal Institute of Technology SE-100 44 Stockholm, Sweden
Email: flrios@kth.se

Keywords: Decomposable graphical models, strong hyper Markov law, particle Markov chain Monte Carlo
Received by editor(s): March 31, 2022
Accepted for publication: February 3, 2023
Published electronically: October 3, 2023
Additional Notes: The first author was supported in part by AI4Reseach Grant, Uppsala University.
Article copyright: © Copyright 2023 Taras Shevchenko National University of Kyiv