AUEB STATS SEMINARS 21/3/2018: Learning Markov Equivalence Classes of Directed Acyclic Graphs: an Objective Bayes Approach by Prof. Guido Consonni
Mon 12 Mar 2018 - 12:31
ΚΥΚΛΟΣ ΣΕΜΙΝΑΡΙΩΝ ΣΤΑΤΙΣΤΙΚΗΣ ΜΑΡΤΙΟΣ 2018
Universita' Cattolica del Sacro Cuore, Milan, Italy
Learning Markov Equivalence Classes of Directed Acyclic Graphs: an Objective Bayes Approach
ΑΙΘΟΥΣΑ T201, 2ος ΟΡΟΦΟΣ,
ΝΕΟ ΚΤΙΡΙΟ Ο.Π.Α. (ΤΡΟΙΑΣ 2)
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.
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