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Closed-form Bayesian inference of graphical model structures by averaging over trees

Abstract : We consider the inference of the structure of an undirected graphical model in a Bayesian framework. To avoid convergence issues and highly demanding Monte Carlo sampling, we focus on exact inference. More specifically we aim at achieving the inference with closed-form posteriors, avoiding any sampling step. To this aim, we restrict the set of considered graphs to mixtures of spanning trees. We investigate under which conditions on the priors - on both tree structures and parameters - closed-form Bayesian inference can be achieved. Under these conditions, we derive a fast an exact algorithm to compute the posterior probability for an edge to belong to the tree model using an algebraic result called the Matrix-Tree theorem. We show that the assumption we have made does not prevent our approach to perform well on synthetic and flow cytometry data.
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https://hal.inrae.fr/hal-03111633
Contributor : Sandrine Fouché Connect in order to contact the contributor
Submitted on : Friday, January 15, 2021 - 2:28:00 PM
Last modification on : Tuesday, January 18, 2022 - 2:26:07 PM

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  • HAL Id : hal-03111633, version 1
  • WOS : 000476599100001

Citation

Loïc Schwaller, Stephane S. Robin, Michael Stumpf. Closed-form Bayesian inference of graphical model structures by averaging over trees. Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2019, 160 (2), pp.1-23. ⟨hal-03111633⟩

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