Wide-angle sonar mapping of the environment by mobile robot is nontrivial due to several sources of uncertainty: dropouts due to "specular" reflections, obstacle location uncertainty due to the wide beam, and distance measurement error. Earlier papers address the latter problems, but dropouts remain a problem in many environments. We present an approach that lifts the overoptimistic independence assumption used in earlier work, and use Bayes nets to represent the dependencies between objects of the model. Objects of the model consist of readings, and of regions in which "quasi location invariance" of the (possible) obstacles exists, with respect to the readings. Simulation supports the method's feasibility. The model is readily extensible to allow for prior distributions, as well as other types of sensing operations.

Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of distributions. Two approaches for combination of local models are considered. The first approach takes the largest set of joint distributions that is compatible with the local sets of distributions; we show how to reduce this type of robust inference to a linear programming problem. The second approach takes the convex hull of joint distributions generated from the local sets of distributions; we demonstrate how to apply interior-point optimization methods to generate posterior bounds and how to generate approximations that are guaranteed to converge to correct posterior bounds. We also discuss calculation of bounds for expected utilities and variances, and global perturbation models.

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective computational procedures are represented by sequences possessing a special property; we shall call them perfect sequences. The paper lays down the elementary foundation necessary for further study of iterative application of operators of composition. We believe to develop a technique describing several graph models in a unifying way. We are convinced that practically all theoretical results and procedures connected with decomposable models and Bayesian networks can be translated into the terminology introduced in this paper. For example, complexity of computational procedures in these models is closely dependent on possibility to change the ordering of oligo-dimensional measures defining the model. Therefore, in this paper, lot of attention is paid to possibility to change ordering of the operators of composition.

This paper proposes a novel, algorithm-independent approach to optimizing belief network inference. rather than designing optimizations on an algorithm by algorithm basis, we argue that one should use an unoptimized algorithm to generate a Q-DAG, a compiled graphical representation of the belief network, and then optimize the Q-DAG and its evaluator instead. We present a set of Q-DAG optimizations that supplant optimizations designed for traditional inference algorithms, including zero compression, network pruning and caching. We show that our Q-DAG optimizations require time linear in the Q-DAG size, and significantly simplify the process of designing algorithms for optimizing belief network inference.

This paper introduces a computational framework for reasoning in Bayesian belief networks that derives significant advantages from focused inference and relevance reasoning. This framework is based on d -separation and other simple and computationally efficient techniques for pruning irrelevant parts of a network. Our main contribution is a technique that we call relevance-based decomposition. Relevance-based decomposition approaches belief updating in large networks by focusing on their parts and decomposing them into partially overlapping subnetworks. This makes reasoning in some intractable networks possible and, in addition, often results in significant speedup, as the total time taken to update all subnetworks is in practice often considerably less than the time taken to update the network as a whole. We report results of empirical tests that demonstrate practical significance of our approach.

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribution, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the "ground-truth'' tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50% and 15% of missing entries respectively, resulting in recovery errors at -10dB and -15dB.

I present a parallel algorithm for exact probabilistic inference in Bayesian networks. For polytree networks with n variables, the worst-case time complexity is O(log n) on a CREW PRAM (concurrent-read, exclusive-write parallel random-access machine) with n processors, for any constant number of evidence variables. For arbitrary networks, the time complexity is O(r^{3w}*log n) for n processors, or O(w*log n) for r^{3w}*n processors, where r is the maximum range of any variable, and w is the induced width (the maximum clique size), after moralizing and triangulating the network.

The process of diagnosis involves learning about the state of a system from various observations of symptoms or findings about the system. Sophisticated Bayesian (and other) algorithms have been developed to revise and maintain beliefs about the system as observations are made. Nonetheless, diagnostic models have tended to ignore some common sense reasoning exploited by human diagnosticians; In particular, one can learn from which observations have not been made, in the spirit of conversational implicature. There are two concepts that we describe to extract information from the observations not made. First, some symptoms, if present, are more likely to be reported before others. Second, most human diagnosticians and expert systems are economical in their data-gathering, searching first where they are more likely to find symptoms present. Thus, there is a desirable bias toward reporting symptoms that are present. We develop a simple model for these concepts that can significantly improve diagnostic inference.

Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states. They have been widely studied in the neural computing literature, although their practical applicability has been limited by the difficulty of finding an effective learning algorithm. One well-established approach, known as mean field theory, represents the stochastic distribution using a factorized approximation. However, the corresponding learning algorithm often fails to find a good solution. We conjecture that this is due to the implicit uni-modality of the mean field approximation which is therefore unable to capture multi-modality in the true distribution. In this paper we use variational methods to approximate the stochastic distribution using multi-modal mixtures of factorized distributions. We present results for both inference and learning to demonstrate the effectiveness of this approach.

We analyze differences between two information-theoretically motivated approaches to statistical inference and model selection: the Minimum Description Length (MDL) principle, and the Minimum Message Length (MML) principle. Based on this analysis, we present two revised versions of MML: a pointwise estimator which gives the MML-optimal single parameter model, and a volumewise estimator which gives the MML-optimal region in the parameter space. Our empirical results suggest that with small data sets, the MDL approach yields more accurate predictions than the MML estimators. The empirical results also demonstrate that the revised MML estimators introduced here perform better than the original MML estimator suggested by Wallace and Freeman.