Bozhena Bidyuk

Cutset sampling for Bayesian networks

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the networks graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks.

Cycle-cutset sampling for Bayesian networks

The paper presents a new sampling methodology for Bayesian networks called cutset sampling that samples only a subset of the variables and applies exact inference for the others. We show that this approach can be implemented efficiently when the sampled variables constitute a cycle-cutset for the Bayesian network and otherwise it is exponential in the induced-width of the networks graph, whose sampled variables are removed. Cutset sampling is an instance of the well known Rao-Blakwellisation technique for variance reduction investigated in [5, 2, 16]. Moreover, the proposed scheme extends standard sampling methods to non-ergodic networks with ergodic subspaces. Our empirical results confirm those expectations and show that cycle cutset sampling is superior to Gibbs sampling for a variety of benchmarks, yielding a simple, yet powerful sampling scheme.

Active tuples-based scheme for bounding posterior beliefs

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or posterior marginals and enhance its performance in an anytime manner. The scheme uses the cutset conditioning principle to tighten existing bounding schemes and to facilitate anytime behavior, utilizing a fixed number of cutset tuples. The accuracy of the bounds improves as the number of used cutset tuples increases and so does the computation time. We demonstrate empirically the value of our scheme for bounding posterior marginals and probability of evidence using a variant of the bound propagation algorithm as a plug-in scheme.