Machine Learning Coffee seminar "Learning Markov Equivalence Classes of Directed Acyclic Graphs: an Objective Bayes Approach"

Guido Consonni, Professor of Statistics, Universita Cattolica del Sacro Cuore

Learning Markov Equivalence Classes of Directed Acyclic Graphs: an Objective Bayes Approach

Abstract: A Markov equivalence class contains all the Directed Acyclic Graphs (DAGs) encoding the same conditional independencies, and is represented by a Completed Partially Directed DAG (CPDAG), also named Essential Graph (EG). We approach the problem of model selection among noncausal sparse Gaussian DAGs by directly scoring EGs, using an objective Bayes method. Specifically, we construct objective priors for model selection based on the Fractional Bayes Factor, leading to a closed form expression for the marginal likelihood of an EG. Next we propose an MCMC strategy to explore the space of EGs, possibly accounting for sparsity constraints, and illustrate the performance of our method on simulation studies, as well as on a real dataset. Our method is fully Bayesian and thus provides a coherent quantification of inferential uncertainty, requires minimal prior specification, and shows to be competitive in learning the structure of the data-generating EG when compared to alternative state-of-the-art algorithms.

Machine Learning Coffee seminars are weekly seminars held jointly by the Aalto University and the University of Helsinki. The seminars aim to gather people from different fields of science with interest in machine learning. Talks will begin at 9:15 am and porridge and coffee will be served from 9:00 am.

Next talks:

Nov 6, Otaniemi: Pekka Marttinen "Efficient and accurate approximate Bayesian computation"

Nov 13, Kumpula: Jukka Corander "Learning of Ultra High-Dimensional Potts Models for Bacterial Population Genomics"

Nov 20, Otaniemi: Perttu Hämäläinen "Towards Intelligent Exergames"

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