Exact inference in large, richly connected noisy-OR networks is intractable, and most approximate inference algorithms tend to concentrate on a small number of most probable configurations of the hidden variables under the posterior. We presented an "inclusive" variational method for bipartite noisy-OR networks that favors including all probable configurations, at the cost of including some improbable configurations. The method fits a tree to the posterior distribution sequentially, i.e., one observation at a time. Results on an ensemble of QMR-DT type networks show that the method performs better than local probability propagation and a variational upper bound for ranking most probable diseases.

Jensen's inequality is a powerful mathematical tool and one of the workhorses in statistical learning. Its applications therein include the EM algorithm, Bayesian estimation and Bayesian inference. Jensen computes simple lower bounds on otherwise intractable quantities such as products of sums and latent log-likelihoods. This simplification then permits operations like integration and maximization. Quite often (i.e. in discriminative learning) upper bounds are needed as well. We derive and prove an efficient analytic inequality that provides such variational upper bounds. This inequality holds for latent variable mixtures of exponential family distributions and thus spans a wide range of contemporary statistical models. We also discuss applications of the upper bounds including maximum conditional likelihood, large margin discriminative models and conditional Bayesian inference. Convergence, efficiency and prediction results are shown.

When trying to recover 3D structure from a set of images, the most difficult problem is establishing the correspondence between the measurements. Most existing approaches assume that features can be tracked across frames, whereas methods that exploit rigidity constraints to facilitate matching do so only under restricted camera motion. In this paper we propose a Bayesian approach that avoids the brittleness associated with singling out one "best" correspondence, and instead consider the distribution over all possible correspondences. We treat both a fully Bayesian approach that yields a posterior distribution, and a MAP approach that makes use of EM to maximize this posterior. We show how Markov chain Monte Carlo methods can be used to implement these techniques in practice, and present experimental results on real data.

Antarctica contains the most fertile meteorite hunting grounds on Earth. The pristine, dry and cold environment ensures that meteorites deposited there are preserved for long periods. Subsequent glacial flow of the ice sheets where they land concentrates them in particular areas. To date, most meteorites recovered throughout history have been done so in Antarctica in the last 20 years. Furthermore, they are less likely to be contaminated by terrestrial compounds.

The human figure exhibits complex and rich dynamic behavior that is both nonlinear and time-varying. Effective models of human dynamics can be learned from motion capture data using switching linear dynamic system (SLDS) models. We present results for human motion synthesis, classification, and visual tracking using learned SLDS models. Since exact inference in SLDS is intractable, we present three approximate inference algorithms and compare their performance. In particular, a new variational inference algorithm is obtained by casting the SLDS model as a Dynamic Bayesian Network. Classification experiments show the superiority of SLDS over conventional HMM's for our problem domain.

We propose a method of approximate dynamic programming for Markov decision processes (MDPs) using algebraic decision diagrams (ADDs). We produce near-optimal value functions and policies with much lower time and space requirements than exact dynamic programming. Our method reduces the sizes of the intermediate value functions generated during value iteration by replacing the values at the terminals of the ADD with ranges of values. Our method is demonstrated on a class of large MDPs (with up to 34 billion states), and we compare the results with the optimal value functions.

We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m.

One way to approximate inference in richly-connected graphical models is to apply the sum-product algorithm (a.k.a. The sum-product algorithm can be directly applied in Gaussian networks and in graphs for coding, but for many conditional probability functions - including the sigmoid function - direct application of the sum-product algorithm is not possible. We introduce "accumulator networks" that have low local complexity (but exponential global complexity) so the sum-product algorithm can be directly applied. In an accumulator network, the probability of a child given its parents is computed by accumulating the inputs from the parents in a Markov chain or more generally a tree. After giving expressions for inference and learning in accumulator networks, we give results on the "bars problem" and on the problem of extracting translated, overlapping faces from an image. 1 Introduction Graphical probability models with hidden variables are capable of representing complex dependencies between variables, filling in missing data and making Bayesoptimal decisions using probabilistic inferences (Hinton and Sejnowski 1986; Pearl 1988; Neal 1992).

How should we decide among competing explanations of a cognitive process given limited observations? The problem of model selection is at the heart of progress in cognitive science. In this paper, Minimum Description Length (MDL) is introduced as a method for selecting among computational models of cognition. We also show that differential geometry provides an intuitive understanding of what drives model selection in MDL. Finally, adequacy of MDL is demonstrated in two areas of cognitive modeling.

We introduce the mixture of Gaussian processes (MGP) model which is useful for applications in which the optimal bandwidth of a map is input dependent. The MGP is derived from the mixture of experts model and can also be used for modeling general conditional probability densities. We discuss how Gaussian processes -in particular in form of Gaussian process classification, the support vector machine and the MGP modelcan be used for quantifying the dependencies in graphical models. 1 Introduction Gaussian processes are typically used for regression where it is assumed that the underlying function is generated by one infinite-dimensional Gaussian distribution (i.e.