We show how to nd a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the rst step in the method of conditioning for inference. Our randomized algorithm for nding a loop cutset outputs a minimum loop cutset after O(c 6kn) steps with probability at least 1 (1 1 6k ) k , where c > 1 is a constant speci ed by the user, k is the minimal size of a ...

We show how to nd a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the rst step in the method of conditioning for inference. Our randomized algorithm for nding a loop cutset outputs a minimum loop cutset after O(c 6 k kn) steps with probability at least 1 ? (1 ? 1 6 k) c6 k , where c > 1 is a constant speciied by the user, k is the minimal ...

We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called REPEATEDWGUESSI, outputs a minimum loop cutset, after O(c.6"n) steps, with probability a t least 1 (1 $ ) c ~ * , where c > 1 is a constant specified by the user...

We show how to find a small loop cutset in a Bayesian network. Finding such a loop cutset is the first step in the method of conditioi~ing 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. We test MGA on randomly generated graphs and ...

In this paper, we present cutset networks, a new tractable probabilistic model for representing multi-dimensional discrete distributions. Cutset networks are rooted OR search trees, in which each OR node represents conditioning of a variable in the model, with tree Bayesian networks (Chow-Liu trees) at the leaves. From an inference point of view, cutset networks model the mechanics of Pearl’s c...

The method of conditioning permits probabilistic inference in multiply connected belief networks using an algorithm by Pearl. This method uses a select set of nodes, the loop cutset, to render the multiply connected network singly connected. We discuss the function of the nodes of the loop cutset and a condition that must be met by the nodes of the loop cutset. We show that the problem of findi...

The paper investigates the behavior of iterative belief propagation algorithm (IBP) in Bayesian networks with loops. In multiply-connected network, IBP is only guaranteed to converge in linear time to the correct posterior marginals when evidence nodes form a loop-cutset. We propose an -cutset criteria that IBP will converge and compute posterior marginals close to correct when a single value i...

The Multicut problem, given a graph G, a set of terminal pairs T = {(si, ti) | 1 ≤ i ≤ r} and an integer p, asks whether one can find a cutset consisting of at most p non-terminal vertices that separates all the terminal pairs, i.e., after removing the cutset, ti is not reachable from si for each 1 ≤ i ≤ r. The fixed-parameter tractability of Multicut in undirected graphs, parameterized by the ...

Cutset conditioning and clique-tree propagation are two popular methods for exact probabilistic inference in Bayesian belief networks. Cutset conditioning is based on decomposition of a subset of network nodes, whereas clique-tree propagation depends on aggregation of nodes. We characterize network structures in which the performances of these methods differ. We describe a means to combine cuts...

We consider the problem of finding a cutset in a directed graph G = (V, E), i.e. a set of vertices that cuts all cycles in G. Finding a cutset of minimum cardinality is NP-hard. There exist several approximate and exact algorithms, most of them using graph reduction techniques. In this paper we propose a constraint programming approach to cutset problems and design a global constraint for compu...