The paper presents a parameterized approximation scheme for probabilistic inference. The scheme, called MiniClustering (MC), extends the partition-based approximation offered by mini-bucket elimination, to tree decompositions.

The paper presents a method for generating solutions of a constraint satisfaction problem (CSP) uniformly at random. The main

The paper presents a parameterized approximation scheme for probabilistic inference. The scheme, called Mini-Clustering (MC) extends the partition-based approximation offered by mini-bucket elimination, to tree decompositions. The benefit of this extension is that all single variable beliefs are computed (approximately) at once, using a twophase message-passing process along the cluster tree. The resulting approximation scheme is governed by a controlling parameter, "z" that allows adjustable levels of accuracy and efficiency, in "anytime" style. Empirical evaluation against competing algorithms such as iterative belief propagation and stochastic simulation, demonstrate the superiority of the MC approximation scheme for several classes of problems. 1

Introduction In this abstract we present a method of generating solutions to a constraint satisfaction problem according to an arbitrary probability distribution. If S is the set of solutions, and P is a probability density function, solution x should be generated with probability P (x)= y2S P (y). We allow P to be speci ed directly, in the form of a Bayesian network, or indirectly, as a set of probabilistic biases. Biases are judgments on the probability of certain events. They delimit a set of consistent probability distributions. For example, if the bias P (:X 1 ) = 1=2 is given, then one consistent distribution on the three binary variables fX 1 ; X 2 ; X 3 g might give equal probability to each of the 2 3 = 8 possible assignments. Another consistent distribution might give probability 1/2 to the event in which all variables are true and 1/2 to the event in which they are all false. In general, many distributions may be consistent with a given set of biases. So given a fu