In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the difficult problem of finding the "right" number of mixture components. Inference in the model is done using an efficient parameter-free Markov Chain that relies entirely on Gibbs sampling.

We propose a new Markov Chain Monte Carlo algorithm which is a generalization of the stochastic dynamics method. The algorithm performs exploration of the state space using its intrinsic geometric structure, facilitating efficient sampling of complex distributions. Applied to Bayesian learning in neural networks, our algorithm was found to perform at least as well as the best state-of-the-art method while consuming considerably less time. 1 Introduction

We consider the problem of learning a grid-based map using a robot with noisy sensors and actuators. We compare two approaches: online EM, where the map is treated as a fixed parameter, and Bayesian inference, where the map is a (matrix-valued) random variable. We show that even on a very simple example, online EM can get stuck in local minima, which causes the robot to get "lost" and the resulting map to be useless. By contrast, the Bayesian approach, by maintaining multiple hypotheses, is much more robust. We then introduce a method for approximating the Bayesian solution, called Rao-Blackwellised particle filtering. We show that this approximation, when coupled with an active learning strategy, is fast but accurate.

The three-dimensional motion of humans is underdetermined when the observation is limited to a single camera, due to the inherent 3D ambiguity of 2D video. We present a system that reconstructs the 3D motion of human subjects from single-camera video, relying on prior knowledge about human motion, learned from training data, to resolve those ambiguities. After initialization in 2D, the tracking and 3D reconstruction is automatic; we show results for several video sequences. The results show the power of treating 3D body tracking as an inference problem.

This paper argues that two apparently distinct modes of generalizing concepts - abstracting rules and computing similarity to exemplars - should both be seen as special cases of a more general Bayesian learning framework. Bayes explains the specific workings of these two modes - which rules are abstracted, how similarity is measured - as well as why generalization should appear rule-or similarity-based in different situations. This analysis also suggests why the rules/similarity distinction, even if not computationally fundamental, may still be useful at the algorithmic level as part of a principled approximation to fully Bayesian learning.

We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial tMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte Carlo (MCMC) sampling techniques. The advantage of this method is that detection of short time learning effects between repeated trials is possible since inference is based only on single trial experiments.

In recent years, Bayesian networks have become highly successful tool for diagnosis, analysis, and decision making in real-world domains. We present an efficient algorithm for learning Bayes networks from data.

The first two methods are related to mean field ideas known in Statistical Physics. The third approach is based on Bayesian online approach which was motivated by recent results in the Statistical Mechanics of Neural Networks. We present simulation results showing: 1. that the mean field Bayesian evidence may be used for hyperparameter tuning and 2. that the online approach may achieve a low training error fast. 1 Introduction Gaussian processes provide promising nonparametric Bayesian approaches to regression and classification [2, 1].

We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into conditional distributions of feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To fix this, we introduce hidden class labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters can be found with maximum likelihood estimation using the EM algorithm. We have obtained encouraging preliminary results on the problems of detecting various objects in SAR images and target recognition in optical aerial images. 1 Introduction

Although one can derive the Gaussian noise assumption based on a maximum entropy approach, the main reason for this assumption is practicability: under the Gaussian noise assumption the maximum likelihood parameter estimate can simply be found by minimization of the squared error. Despite its common use it is far from clear that the Gaussian noise assumption is a good choice for many practical problems. A reasonable approach therefore would be a noise distribution which contains the Gaussian as a special case but which has a tunable parameter that allows for more flexible distributions.