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Hyper and structural Markov laws for graphical models

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If you have a question about this talk, please contact Konstantina Palla.

My talk will be based on the concept of hyper Markov laws, introduced by Dawid and Lauritzen (1993):

The general idea is to use distributions on the parameters (termed “laws” in the paper) that have analogous conditional independence properties to those of the Markov distributions. These commonly arise in two circumstances: as the sampling distributions of estimators (e.g. maximum likelihood estimators), and as priors and posteriors for Bayesian inference. As with message passing algorithms for marginalisation, we can exploit the conditional independence properties to perform calculations locally at certain points of the graph.

Secondly, I’ll introduce my own work on extending these ideas to the case where the structure of the graph itself is unknown (commonly called structural learning), by defining what I term structural Markov properties. These characterise an exponential family over the set of graphs, and form a conjugate prior allowing convenient prior to posterior updating.

This talk is part of the Machine Learning Reading Group @ CUED series.

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