Abstract

Directed mixed graphs are graphical representations that include directed and bidirected edges. Such a class is motivated by dependencies that arise when hidden common causes are marginalized out of a distribution. In previous work, we introduced an efficient Monte Carlo algorithm for sampling from Gaussian mixed graph models. An analogous model for discrete distributions is likely to be doubly-intractable, in the sense that even a single Markov Chain Monte Carlo step might have a computational cost that scales exponentially with the number of variables. Instead, we built upon our results on Gaussian distributions to describe algorithms and priors for discrete binary and ordinal modeling. The models we describe are based on link functions, where a multivariate Gaussian distribution encoded by a mixed graph is projected into a discrete space. In order to account for flexible discrete distributions, we embed this model within a Dirichlet process mixture of Gaussians. 1

Citations