Inference in graphical models consists of repeatedly multiplying and summing out potentials. It is generally intractable because the derived potentials obtained in this way can be exponentially large. Approximate inference techniques such as belief propagation and variational methods combat this by simplifying the derived potentials, typically by dropping variables from them. We propose an alternate method for simplifying potentials: quantizing their values. Quantization causes different states of a potential to have the same value, and therefore introduces contextspecific independencies that can be exploited to represent the potential more compactly. We use algebraic decision diagrams (ADDs) to do this efficiently. We apply quantization and ADD reduction to variable elimination and junction tree propagation, yielding a family of bounded approximate inference schemes. Our experimental tests show that our new schemes significantly outperform state-of-the-art approaches on many benchmark instances. 1

In this paper, we consider two variance reduction schemes that exploit the structure of the primal graph of the graphical model: Rao-Blackwellised w-cutset sampling and AND/OR sampling. We show that the two schemes are orthogonal and can be combined to further reduce the variance. Our combination yields a new family of estimators which trade time and space with variance. We demonstrate experimentally that the new estimators are superior, often yielding an order of magnitude improvement over previous schemes on several benchmarks. 1

Itiswellknownthatcomputingrelativeapproximationsofweightedcountingqueries such as the probability of evidence in a Bayesian network, the partition function of a Markov network, and the number of solutions of a constraint satisfaction problem is NP-hard. In this paper, we settle therefore on an easier problem of computing highconfidence lower bounds and propose an algorithm based on importance sampling and Markov inequality for it. However, a straight-forward application of Markov inequality often yields poor lower bounds because it uses only one sample. We therefore propose several new schemes that extend it to multiple samples. Empirically, we show that our new schemes are quite powerful, often yielding substantially higher (better) lower bounds than state-of-the-art schemes. 1

Variational inference algorithms such as belief propagation have had tremendous impact on our ability to learn and use graphical models, and give many insights for developing or understanding exact and approximate inference. However, variational approaches have not been widely adoped for decision making in graphical models, often formulated through influence diagrams and including both centralized and decentralized (or multi-agent) decisions. In this work, we present a general variational framework for solving structured cooperative decisionmaking problems, use it to propose several belief propagation-like algorithms, and analyze them both theoretically and empirically. 1

The paper introduces a family of approximate schemes that extend the process of computing sample mean in importance sampling from the conventional OR space to the AND/OR search space for graphical models. All the sample means are defined on the same set of samples and trade time with variance. At one end is the AND/OR sample tree mean which has the same time complexity as the conventional OR sample tree mean but has lower variance. At the other end is the AND/OR sample graph mean which requires more time to compute but has the lowest variance. The paper provides theoretical analysis as well as empirical evaluation demonstrating that the AND/OR sample tree and graph means are far closer to the true mean than the OR sample tree mean.