Computing Junction Forests from Filtrations of Simplicial Complexes

Stochastics Seminar
Friday, November 14, 2008 - 14:00
1 hour (actually 50 minutes)
Skiles 255
Department of Statistical Science, Duke University
Let X=(X_1,\ldots,X_n) be a n-dimensional random vector for which the distribution has Markov structure corresponding to a junction forest, assuming functional forms for the marginal distributions associated with the cliques of the underlying graph. We propose a latent variable approach based on computing junction forests from filtrations. This methodology establishes connections between efficient algorithms from Computational Topology and Graphical Models, which lead to parametrizations for the space of decomposable graphs so that: i) the dimension grows linearly with respect to n, ii) they are convenient for MCMC sampling.