The detection and pose estimation of people in images and video is made challenging by the variability of human appearance, the complexity of natural scenes, and the high dimensionality of articulated body mod- els. To cope with these problems we represent the 3D human body as a graphical model in which the relationships between the body parts are represented by conditional probability distributions. We formulate the pose estimation problem as one of probabilistic inference over a graphi- cal model where the random variables correspond to the individual limb parameters (position and orientation). Because the limbs are described by 6-dimensional vectors encoding pose in 3-space, discretization is im- practical and the random variables in our model must be continuous- valued. To approximate belief propagation in such a graph we exploit a recently introduced generalization of the particle filter.

We present a Bayesian approach to color constancy which utilizes a non- Gaussian probabilistic model of the image formation process. The pa- rameters of this model are estimated directly from an uncalibrated image set and a small number of additional algorithmic parameters are chosen using cross validation. The algorithm is empirically shown to exhibit RMS error lower than other color constancy algorithms based on the Lambertian surface reflectance model when estimating the illuminants of a set of test images. This is demonstrated via a direct performance comparison utilizing a publicly available set of real world test images and code base.

Principal components analysis (PCA) is one of the most widely used techniques in machine learning and data mining. Minor components analysis (MCA) is less well known, but can also play an important role in the presence of constraints on the data distribution. In this paper we present a probabilistic model for "extreme components analysis" (XCA) which at the maximum likelihood solution extracts an optimal combina- tion of principal and minor components. For a given number of compo- nents, the log-likelihood of the XCA model is guaranteed to be larger or equal than that of the probabilistic models for PCA and MCA. We de- scribe an efficient algorithm to solve for the globally optimal solution.

We introduce an information theoretic method for nonparametric, non- linear dimensionality reduction, based on the infinite cluster limit of rate distortion theory. By constraining the information available to manifold coordinates, a natural probabilistic map emerges that assigns original data to corresponding points on a lower dimensional manifold. With only the information-distortion trade off as a parameter, our method de- termines the shape of the manifold, its dimensionality, the probabilistic map and the prior that provide optimal description of the data. Some data sets may not be as complicated as they appear. Consider the set of points on a plane in Figure 1.

When we learn a new motor skill, we have to contend with both the vari- ability inherent in our sensors and the task. The sensory uncertainty can be reduced by using information about the distribution of previously ex- perienced tasks. Here we impose a distribution on a novel sensorimotor task and manipulate the variability of the sensory feedback. We show that subjects internally represent both the distribution of the task as well as their sensory uncertainty. Moreover, they combine these two sources of information in a way that is qualitatively predicted by optimal Bayesian processing.

The barn owl is a nocturnal hunter, capable of capturing prey using au- ditory information alone [1]. The neural basis for this localization be- havior is the existence of auditory neurons with spatial receptive fields [2]. We provide a mathematical description of the operations performed on auditory input signals by the barn owl that facilitate the creation of a representation of auditory space. To develop our model, we first formu- late the sound localization problem solved by the barn owl as a statistical estimation problem. The implementation of the solution is constrained by the known neurobiology.

We discuss the integration of the expectation-maximization (EM) algorithm for maximum likelihood learning of Bayesian networks with belief propagation algorithms for approximate inference. Specifically we propose to combine the outer-loop step of convergent belief propagation algorithms with the M-step of the EM algorithm. This then yields an approximate EM algorithm that is essentially still double loop, with the important advantage of an inner loop that is guaranteed to converge. Simulations illustrate the merits of such an approach.

We present a novel method for approximate inference in Bayesian mod- els and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of condi- tional probabilities in factorizing distributions, much akin to Minka's Expectation Propagation. In the jointly normal case, it coincides with the latter and belief propagation, whereas in the general case, it provides an optimization strategy containing Support Vector chunking, the Bayes Committee Machine, and Gaussian Process chunking as special cases.

Rao–Blackwellization is an approximation technique for probabilistic in- ference that flexibly combines exact inference with sampling. It is useful in models where conditioning on some of the variables leaves a sim- pler inference problem that can be solved tractably. This paper presents Sample Propagation, an efficient implementation of Rao–Blackwellized approximate inference for a large class of models. Sample Propagation tightly integrates sampling with message passing in a junction tree, and is named for its simple, appealing structure: it walks the clusters of a junction tree, sampling some of the current cluster's variables and then passing a message to one of its neighbors. We discuss the application of Sample Propagation to conditional Gaussian inference problems such as switching linear dynamical systems.

Recently, relevance vector machines (RVM) have been fashioned from a sparse Bayesian learning (SBL) framework to perform supervised learn- ing using a weight prior that encourages sparsity of representation. The methodology incorporates an additional set of hyperparameters govern- ing the prior, one for each weight, and then adopts a specific approxi- mation to the full marginalization over all weights and hyperparameters. Despite its empirical success however, no rigorous motivation for this particular approximation is currently available. To address this issue, we demonstrate that SBL can be recast as the application of a rigorous vari- ational approximation to the full model by expressing the prior in a dual form. This formulation obviates the necessity of assuming any hyperpri- ors and leads to natural, intuitive explanations of why sparsity is achieved in practice.