[Statlist] Next talk: Friday, 04.05.2018, with Guido Consonni, Università Cattolica del Sacro Cuore, Milano

[Maurer Letizia]

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ETH and University of Zurich

Organisers:

Proff. P. Bühlmann - L. Held - T. Hothorn - M. Maathuis -
N. Meinshausen - S. van de Geer - M. Wolf

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We are glad to announce the following talk:

Friday, 04.05.2018, at 16.15h  ETH Zurich HG G19.1
with Guido Consonni, Università Cattolica del Sacro Cuore, Milano
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Title:

Objective Bayes Model Selection of Gaussian Essential Graphs with Observational and Interventional Data<https://www.math.ethz.ch/sfs/news-and-events/research-seminar.html?s=fs18#e_12136>

Abstract:

Graphical models based on Directed Acyclic Graphs (DAGs) represent a powerful tool for investigating dependencies among variables. It is well known that one cannot distinguish between DAGs encoding the same set of conditional independencies (Markov equivalent DAGs) using only observational data. However, the space of all DAGs can be partitioned into Markov equivalence classes, each being represented by a unique Essential Graph (EG), also called Completed Partially Directed Graph (CPDAG). In some fields, in particular genomics, one can have both observational and interventional data, the latter being produced after an exogenous perturbation of some variables in the system, or from randomized intervention experiments. Interventions destroy the original causal structure, and modify the Markov property of theunderlying DAG, leading to a finer partition of DAGs into equivalence classes, each one being represented by an Interventional Essential Graph (I-EG) (Hauser and Buehlmann). In this talk we consider Bayesian model selection of EGs under the assumption that the variables are jointly Gaussian. In particular, we adopt an objective Bayes approach, based on the notion of fractional Bayes factor, and obtain a closed form expression for the marginal likelihood of an EG. Next we construct a Markov chain to explore the EG space under a sparsity constraint, and propose an MCMC algorithm to approximate the posterior distribution over the space of EGs. Our methodology, which we name Objective Bayes Essential graph Search (OBES), allows to evaluate the inferential uncertainty associated to any features of interest, for instance the posterior probability of edge inclusion. An extension of OBES to deal simultaneously with observational and interventional data is also presented: this involves suitable modifications of the likelihood and prior, as well as of the MCMC algorithm. We conclude by presenting results for simulated and real experiments (protein-signaling data).
This is joint work with Federico Castelletti, Stefano Peluso and Marco Della Vedova (Universita' Cattolica del Sacro Cuore).


This abstract is also to be found under the following link: http://stat.ethz.ch/events/research_seminar

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