It has been noted by several authors that Belief Propagation can can also give impressive results for graphs that are not trees [2]. The Cluster Variation Method (CVM), is a method that has been developed in the physics community for approximate inference in the Ising model [3]. The CVM approximates the joint probability distribution by a number of (overlapping) marginal distributions (clusters). The quality of the approximation is determined by the size and number of clusters. When the clusters consist of only two variables, the method is known as the Bethe approximation.

The mutual information of two random variables z and J with joint probabilities {7rij} is commonly used in learning Bayesian nets as well as in many other fields. The chances 7rij are usually estimated by the empirical sampling frequency nij In leading to a point estimate J(nij In) for the mutual information. To answer questions like "is J (nij In) consistent with zero?" or "what is the probability that the true mutual information is much larger than the point estimate?"

Statistical learning and probabilistic inference techniques are used to infer the hand position of a subject from multi-electrode recordings of neural activity in motor cortex. First, an array of electrodes provides training data of neural firing conditioned on hand kinematics. We learn a nonparametric representation of this firing activity using a Bayesian model and rigorously compare it with previous models using cross-validation. Second, we infer a posterior probability distribution over hand motion conditioned on a sequence of neural test data using Bayesian inference. The learned firing models of multiple cells are used to define a non-Gaussian likelihood term which is combined with a prior probability for the kinematics. A particle filtering method is used to represent, update, and propagate the posterior distribution over time. The approach is compared with traditional linear filtering methods; the results suggest that it may be appropriate for neural prosthetic applications.

Reaching movements require the brain to generate motor commands that rely on an internal model of the task's dynamics. Here we consider the errors that subjects make early in their reaching trajectories to various targets as they learn an internal model. Using a framework from function approximation, we argue that the sequence of errors should reflect the process of gradient descent. If so, then the sequence of errors should obey hidden state transitions of a simple dynamical system. Fitting the system to human data, we find a surprisingly good fit accounting for 98% of the variance. This allows us to draw tentative conclusions about the basis elements used by the brain in transforming sensory space to motor commands. To test the robustness of the results, we estimate the shape of the basis elements under two conditions: in a traditional learning paradigm with a consistent force field, and in a random sequence of force fields where learning is not possible. Remarkably, we find that the basis remains invariant.

Multisensory response enhancement (MRE) is the augmentation of the response of a neuron to sensory input of one modality by simultaneous input from another modality. The maximum likelihood (ML) model presented here modifies the Bayesian model for MRE (Anastasio et al.) by incorporating a decision strategy to maximize the number of correct decisions. Thus the ML model can also deal with the important tasks of stimulus discrimination and identification in the presence of incongruent visual and auditory cues. It accounts for the inverse effectiveness observed in neurophysiological recording data, and it predicts a functional relation between uni-and bimodal levels of discriminability that is testable both in neurophysiological and behavioral experiments.

In this paper we explore two quantitative approaches to the modelling of counterfactual reasoning - a linear and a noisy-OR model - based on information contained in conceptual dependency networks. Empirical data is acquired in a study and the fit of the models compared to it. We conclude by considering the appropriateness of nonparametric approaches to counterfactual reasoning, and examining the prospects for other parametric approaches in the future.

A theory of categorization is presented in which knowledge of causal relationships between category features is represented as a Bayesian network. Referred to as causal-model theory, this theory predicts that objects are classified as category members to the extent they are likely to have been produced by a categorys causal model. On this view, people have models of the world that lead them to expect a certain distribution of features in category members (e.g., correlations between feature pairs that are directly connected by causal relationships), and consider exemplars good category members when they manifest those expectations. These expectations include sensitivity to higher-order feature interactions that emerge from the asymmetries inherent in causal relationships. Research on the topic of categorization has traditionally focused on the problem of learning new categories given observations of category members.

Narayanan and Jurafsky (1998) proposed that human language comprehension can be modeled by treating human comprehenders as Bayesian reasoners, and modeling the comprehension process with Bayesian decision trees. In this paper we extend the Narayanan and Jurafsky model to make further predictions about reading time given the probability of difference parses or interpretations, and test the model against reading time data from a psycholinguistic experiment.

To find out how the representations of structured visual objects depend on the co-occurrence statistics of their constituents, we exposed subjects to a set of composite images with tight control exerted over (1) the conditional probabilities of the constituent fragments, and (2) the value of Barlow's criterion of "suspicious coincidence" (the ratio of joint probability to the product of marginals). We then compared the part verification response times for various probe/target combinations before and after the exposure. For composite probes, the speedup was much larger for targets that contained pairs of fragments perfectly predictive of each other, compared to those that did not. This effect was modulated by the significance of their co-occurrence as estimated by Barlow's criterion. For lone-fragment probes, the speedup in all conditions was generally lower than for composites. These results shed light on the brain's strategies for unsupervised acquisition of structural information in vision.

Probabilistic mixture models are used for a broad range of data analysis tasks such as clustering, classification, predictive modeling, etc. Due to their inherent probabilistic nature, mixture models can easily be combined with other probabilistic or non-probabilistic techniques thus forming more complex data analysis systems. In the case of online data (where there is a stream of data available) models can be constantly updated to reflect the most current distribution of the incoming data. However, in many business applications the models themselves represent a parsimonious summary of the data and therefore it is not desirable to change models frequently, much less with every new data point. In such a framework it becomes crucial to track the applicability of the mixture model and detect the point in time when the model fails to adequately represent the data. In this paper we formulate the problem of change detection and propose a principled solution. Empirical results over both synthetic and real-life data sets are presented.