There is a growing body of experimental evidence to suggest that the brain is capable of approximating optimal Bayesian inference in the face of noisy input stimuli. Despite this progress, the neural underpinnings of this computation are still poorly understood. In this paper we focus on the problem of Bayesian filtering of stochastic time series. In particular we introduce a novel neural network, derived from a line attractor architecture, whose dynamics map directly onto those of the Kalman Filter in the limit where the prediction error is small. When the prediction error is large we show that the network responds robustly to change-points in a way that is qualitatively compatible with the optimal Bayesian model.

Everyday social interactions are heavily influenced by our snap judgments about others goals. Even young infants can infer the goals of intentional agents from observing how they interact with objects and other agents in their environment: e.g., that one agent is helping orhindering anothers attempt to get up a hill or open a box. We propose a model for how people can infer these social goals from actions, based on inverse planning in multiagent Markov decision problems (MDPs). The model infers the goal most likely to be driving an agents behavior by assuming the agent acts approximately rationally given environmental constraints and its model of other agents present.

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. In the clustering case, we associate to each data point a latent allocation variable. These latent variables can share the same value and this induces a partition of the data set. The CRP is a prior distribution on such partitions. In latent feature models, we associate to each data point a potentially infinite number of binary latent variables indicating the possession of some features and the IBP is a prior distribution on the associated infinite binary matrix.

We present a general Bayesian approach to probabilistic matrix factorization subject to linear constraints. The approach is based on a Gaussian observation model and Gaussian priors with bilinear equality and inequality constraints. We present an efficient Markov chain Monte Carlo inference procedure based on Gibbs sampling. Special cases of the proposed model are Bayesian formulations of non-negative matrix factorization and factor analysis. The method is evaluated on a blind source separation problem.

Situations in which people with opposing prior beliefs observe the same evidence and then strengthen those existing beliefs are frequently offered as evidence of human irrationality. This phenomenon, termed belief polarization, is typically assumed to be non-normative. We demonstrate, however, that a variety of cases of belief polarization are consistent with a Bayesian approach to belief revision. Simulation results indicate that belief polarization is not only possible but relatively common within the class of Bayesian models that we consider.

Nonparametric Bayesian models provide a framework for flexible probabilistic modelling of complex datasets. Unfortunately, Bayesian inference methods often require high-dimensional averages and can be slow to compute, especially with the potentially unbounded representations associated with nonparametric models. We address the challenge of scaling nonparametric Bayesian inference to the increasingly large datasets found in real-world applications, focusing on the case of parallelising inference in the Indian Buffet Process (IBP). Our approach divides a large data set between multiple processors. The processors use message passing to compute likelihoods in an asynchronous, distributed fashion and to propagate statistics about the global Bayesian posterior.

We present a sequence of unsupervised, nonparametric Bayesian models for clustering complex linguistic objects. In this approach, we consider a potentially infinite number of features and categorical outcomes. We evaluate these models for the task of within- and cross-document event coreference on two corpora. All the models we investigated show significant improvements when compared against an existing baseline for this task.

Optimal coding provides a guiding principle for understanding the representation of sensory variables in neural populations. Here we consider the influence of a prior probability distribution over sensory variables on the optimal allocation of cells and spikes in a neural population. We model the spikes of each cell as samples from an independent Poisson process with rate governed by an associated tuning curve. For this response model, we approximate the Fisher information in terms of the density and amplitude of the tuning curves, under the assumption that tuning width varies inversely with cell density. We consider a family of objective functions based on the expected value, over the sensory prior, of a functional of the Fisher information.

To cope with concept drift, we placed a probability distribution over the location of the most-recent drift point. We used Bayesian model comparison to update this distribution from the predictions of models trained on blocks of consecutive observations and pruned potential drift points with low probability. We compare our approach to a non-probabilistic method for drift and a probabilistic method for change-point detection. In our experiments, our approach generally yielded improved accuracy and/or speed over these other methods.

Figure/ground assignment, in which the visual image is divided into nearer (figural) and farther (ground) surfaces, is an essential step in visual processing, but its underlying computational mechanisms are poorly understood. Figural assignment (often referred to as border ownership) can vary along a contour, suggesting a spatially distributed process whereby local and global cues are combined to yield local estimates of border ownership. In this paper we model figure/ground estimation in a Bayesian belief network, attempting to capture the propagation of border ownership across the image as local cues (contour curvature and T-junctions) interact with more global cues to yield a figure/ground assignment. Our network includes as a nonlocal factor skeletal (medial axis) structure, under the hypothesis that medial structure draws'' border ownership so that borders are owned by their interiors. We also briefly present a psychophysical experiment in which we measured local border ownership along a contour at various distances from an inducing cue (a T-junction).