We introduce NashProp, an iterative and local message-passing algorithm for computing Nash equilibria in multi-player games represented by arbitrary undirected graphs. We provide a formal analysis and experimental evidence demonstrating that NashProp performs well on large graphical games with many loops, often converging in just a dozen iterations on graphs with hundreds of nodes. NashProp generalizes the tree algorithm of (Kearns et al. 2001), and can be viewed as similar in spirit to belief propagation in probabilistic inference, and thus complements the recent work of (Vickrey and Koller 2002), who explored a junction tree approach. Thus, as for probabilistic inference, we have at least two promising general-purpose approaches to equilibria computation in graphs.

We propose a model for natural images in which the probability of an image is proportional to the product of the probabilities of some filter outputs. We encourage the system to find sparse features by using a Studentt distribution to model each filter output. If the t-distribution is used to model the combined outputs of sets of neurally adjacent filters, the system learns a topographic map in which the orientation, spatial frequency and location of the filters change smoothly across the map. Even though maximum likelihood learning is intractable in our model, the product form allows a relatively efficient learning procedure that works well even for highly overcomplete sets of filters. Once the model has been learned it can be used as a prior to derive the "iterated Wiener filter" for the purpose of denoising images.

We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation of prior knowledge, such as smoothness of the integrand, into the estimation. In a simple problem we show that this outperforms any classical importance sampling method. We also attempt more challenging multidimensional integrals involved in computing marginal likelihoods of statistical models (a.k.a.

In recent years variational methods have become a popular tool for approximate inference and learning in a wide variety of probabilistic models. For each new application, however, it is currently necessary first to derive the variational update equations, and then to implement them in application-specific code. Each of these steps is both time consuming and error prone. In this paper we describe a general purpose inference engine called VIBES ('Variational Inference for Bayesian Networks') which allows a wide variety of probabilistic models to be implemented and solved variationally without recourse to coding. New models are specified either through a simple script or via a graphical interface analogous to a drawing package. VIBES then automatically generates and solves the variational equations. We illustrate the power and flexibility of VIBES using examples from Bayesian mixture modelling.

We propose in this paper a probabilistic approach for adaptive inference of generalized nonlinear classification that combines the computational advantage of a parametric solution with the flexibility of sequential sampling techniques. We regard the parameters of the classifier as latent states in a first order Markov process and propose an algorithm which can be regarded as variational generalization of standard Kalman filtering. The variational Kalman filter is based on two novel lower bounds that enable us to use a non-degenerate distribution over the adaptation rate. An extensive empirical evaluation demonstrates that the proposed method is capable of infering competitive classifiers both in stationary and non-stationary environments. Although we focus on classification, the algorithm is easily extended to other generalized nonlinear models.

The extraction of a single high-quality image from a set of lowresolution images is an important problem which arises in fields such as remote sensing, surveillance, medical imaging and the extraction of still images from video. Typical approaches are based on the use of cross-correlation to register the images followed by the inversion of the transformation from the unknown high resolution image to the observed low resolution images, using regularization to resolve the ill-posed nature of the inversion process. In this paper we develop a Bayesian treatment of the super-resolution problem in which the likelihood function for the image registration parameters is based on a marginalization over the unknown high-resolution image. This approach allows us to estimate the unknown point spread function, and is rendered tractable through the introduction of a Gaussian process prior over images. Results indicate a significant improvement over techniques based on MAP (maximum a-posteriori) point optimization of the high resolution image and associated registration parameters. 1 Introduction The task in super-resolution is to combine a set of low resolution images of the same scene in order to obtain a single image of higher resolution. Provided the individual low resolution images have sub-pixel displacements relative to each other, it is possible to extract high frequency details of the scene well beyond the Nyquist limit of the individual source images.

Several authors have suggested viewing boosting as a gradient descent search for a good fit in function space. We apply gradient-based boosting methodology to the unsupervised learning problem of density estimation. We show convergence properties of the algorithm and prove that a strength of weak learnability property applies to this problem as well. We illustrate the potential of this approach through experiments with boosting Bayesian networks to learn density models.

The responses of cortical sensory neurons are notoriously variable, with the number of spikes evoked by identical stimuli varying significantly from trial to trial. This variability is most often interpreted as'noise', purely detrimental to the sensory system. In this paper, we propose an alternative view in which the variability is related to the uncertainty, about world parameters, which is inherent in the sensory stimulus. Specifically, the responses of a population of neurons are interpreted as stochastic samples from the posterior distribution in a latent variable model. In addition to giving theoretical arguments supporting such a representational scheme, we provide simulations suggesting how some aspects of response variability might be understood in this framework.

We present a novel, flexible statistical approach for modelling music and text jointly. The approach is based on multi-modal mixture models and maximum a posteriori estimation using EM. The learned models can be used to browse databases with documents containing music and text, to search for music using queries consisting of music and text (lyrics and other contextual information), to annotate text documents with music, and to automatically recommend or identify similar songs.

The application of latent/hidden variable Dynamic Bayesian Networks is constrained by the complexity of marginalising over latent variables. For this reason either small latent dimensions or Gaussian latent conditional tables linearly dependent on past states are typically considered in order that inference is tractable. We suggest an alternative approach in which the latent variables are modelled using deterministic conditional probability tables. This specialisation has the advantage of tractable inference even for highly complex nonlinear/non-Gaussian visible conditional probability tables. This approach enables the consideration of highly complex latent dynamics whilst retaining the benefits of a tractable probabilistic model.