The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity where instantiated variables are removed. If the assigned variables constitute a cycle-cutset, the rest of the network is singly-connected and therefore can be ...

The k-partition problem is as follows: Given a graph G and a positive integer k, partition the vertices of G into at most k parts A1, A2, . . . , Ak, where it may be specified that Ai induces a stable set, a clique, or an arbitrary subgraph, and pairs Ai, Aj (i = j) be completely nonadjacent, completely adjacent, or arbitrarily adjacent. The list k-partition problem generalizes the k-partition ...

The paper extends the principle of cutset sampling over Bayesian networks, presented previously for Gibbs sampling, to likelihood weighting (LW). Cutset sampling is motivated by the Rao-Blackwell theorem which implies that sampling over a subset of variables requires fewer samples for convergence due to the reduction in sampling variance. The scheme exploits the network structure in selecting c...

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 appro...

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 appro...

We prove that in grids of any size there exists a minimal cycle-cutset that its complement induces a single connected tree. More generally, any cycle-cutset in a grid can be transformed to a tree-inducing cycle-cutset, no bigger than the original one. We use this result to improve the known lower bounds on the size of a minimal cycle-cutset in some cases of grids, thus equating the lower bound ...

We show how to find a small loop cutset in a Bayesian network. Finding such a loop cutset is the first :itep in the method of conditioning for inference. Our algorithm for finding a loop cutset, called MGA, finds a loop cutset which is guaranteed in the worst case to contain less than twice the number of variables contained in a minimum loop cutset. The algorithm is based on a reduction to the ...

BPLS: Cutset-Driven Local Search For MPE and Improved Bounds for Minimal Cutsets in Grids by Alon Milchgrub Master of Science in Computer Science The problem of finding an optimum of a multivariate function described as a sum of potentials over (small) subsets of variables is one of fundamental interest both in probabilistic inference and other fields. In this thesis we present a cycle-cutset d...

A cutset in the poset 2, of subsets of {1, . . . , n} ordered by inclusion, is a subset of 2 that intersects every maximal chain. Let 0 ≤ α ≤ 1 be a real number. Is it possible to find a cutset in 2 that, for each 0 ≤ i ≤ n, contains at most α ( n i ) subsets of size i? Let α(n) be the greatest lower bound of all real numbers for which the answer is positive. In this note we prove the rather su...