Randomized Algorithms for the Loop Cutset Problem

We show how to find a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in the method of conditioning for inference. Our randomized algorithm for finding 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 specified by the user, k is the minimal size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm often finds a loop cutset that is closer to the minimum weight loop cutset than the ones found by the best deterministic algorithms known

A Comparison of Algorithms for Learning Hidden Variables in Normal Graphs

A Bayesian factor graph reduced to normal form consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived from a constrained maximum likelihood (ML) formulation and from a minimum KL-divergence criterion using KKT conditions. The learning algorithms are compared with two other updating equations based on a Viterbi-like and on a variational approximation respectively. The performance of the various algorithm is verified on synthetic data sets for various architectures. The objective of this paper is to provide the programmer with explicit algorithms for rapid deployment of Bayesian graphs in the applications.Comment: Submitted for journal publicatio

Technology Adoption in Poorly Specified Environments

This article extends the characteristics-based choice framework of technology adoption to account for decisions taken by boundedly-rational individuals in environments where traits are not fully observed. It is applied to an agricultural setting and introduces the concept of ambiguity in the agricultural technology adoption literature by relaxing strict informational and cognition related assumptions that are implied by traditional Bayesian analysis. The main results confirm that ambiguity increases as local conditions become less homogeneous and as computational ability, own experience and nearby adoption rates decrease. Measurement biases associated with full rationality assumptions are found to increase when decision makers have low computational ability, low experience and when their farming conditions differ widely from average adopter ones. A complementary empirical paper (Useche 2006) finds that models assuming low confidence in observed data, ambiguity and pessimistic expectations about traits predict sample shares better than models which assume that farmers do not face ambiguity or are optimistic about the traits of new varieties.Research and Development/Tech Change/Emerging Technologies,

Beliefs in Decision-Making Cascades

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality.Comment: final version, to appear in IEEE Transactions on Signal Processin

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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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