Accurate representation of articulated motion is a challenging problem for machine perception. Several successful tracking algorithms have been developed that model human body as an articulated tree. We propose a learning-based method for creating such articulated models from observations of multiple rigid motions. This paper is concerned with recovering topology of the articulated model, when the rigid motion of constituent segments is known. Our approach is based on finding the Maximum Likelihood tree shaped factorization of the joint probability density function (PDF) of rigid segment motions. The topology of graphical model formed from this factorization corresponds to topology of the underlying articulated body. We demonstrate the performance of our algorithm on both synthetic and real motion capture data.

They are very well suited to handle discrete of continuous sequences of varying sizes. Moreover, an efficient training algorithm (EM) is available, as well as an efficient decoding algorithm (Viterbi), which provides the optimal sequence of states (and the corresponding sequence of high level events) associated with a given sequence of low-level data. On the other hand, multimodal information processing is currently a very challenging framework of applications including multimodal person authentication, multimodal speech recognition, multimodal event analyzers, etc. In that framework, the same sequence of events is represented not only by a single sequence of data but by a series of sequences of data, each of them coming eventually from a different modality: video streams with various viewpoints, audio stream(s), etc. One such task, which will be presented in this paper, is multimodal speech recognition using both a microphone and a camera recording a speaker simultaneously while he (she) speaks.

This paper extends our earlier analysis on approximate linear programming as an approach to approximating the cost-to-go function in a discounted-cost dynamic program [6]. In this paper, we consider the average-cost criterion and a version of approximate linear programming that generates approximations to the optimal average cost and differential cost function. We demonstrate that a naive version of approximate linear programming prioritizes approximation of the optimal average cost and that this may not be well-aligned with the objective of deriving a policy with low average cost. For that, the algorithm should aim at producing a good approximation of the differential cost function. We propose a twophase variant of approximate linear programming that allows for external control of the relative accuracy of the approximation of the differential cost function over different portions of the state space via state-relevance weights. Performance bounds suggest that the new algorithm is compatible with the objective of optimizing performance and provide guidance on appropriate choices for state-relevance weights.

All of our results are obtained in the setting of a (possibly multidimensional) linear-nonlinear (LN) cascade model for stimulus-driven neural activity. We start by giving exact rate of convergence results for the common spike-triggered average (STA) technique. Next, we analyze a spike-triggered covariance method, variants of which have been recently exploited successfully by Bialek, Simoncelli, and colleagues. These first two methods suffer from extraneous conditions on their convergence; therefore, we introduce an estimator for the LN model parameters which is designed to be consistent under general conditions. We provide an algorithm for the computation of this estimator and derive its rate of convergence. We close with a brief discussion of the efficiency of these estimators and an application to data recorded from the primary motor cortex of awake, behaving primates.

Convergence for iterative reinforcement learning algorithms like TD(O) depends on the sampling strategy for the transitions. However, in practical applications it is convenient to take transition data from arbitrary sources without losing convergence. In this paper we investigate the problem of repeated synchronous updates based on a fixed set of transitions. Our main theorem yields sufficient conditions of convergence for combinations of reinforcement learning algorithms and linear function approximation. This allows to analyse if a certain reinforcement learning algorithm and a certain function approximator are compatible.

Low rank approximation techniques are widespread in pattern recognition research -- they include Latent Semantic Analysis (LSA), Probabilistic LSA, Principal Components Analysus (PCA), the Generative Aspect Model, and many forms of bibliometric analysis. All make use of a low-dimensional manifold onto which data are projected. Such techniques are generally "unsupervised," which allows them to model data in the absence of labels or categories. With many practical problems, however, some prior knowledge is available in the form of context. In this paper, I describe a principled approach to incorporating such information, and demonstrate its application to PCA-based approximations of several data sets.

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 address the question of feature selection in the context of visual recognition. It is shown that, besides efficient from a computational standpoint, the infomax principle is nearly optimal in the minimum Bayes error sense. The concept of marginal diversity is introduced, leading to a generic principle for feature selection (the principle of maximum marginal diversity) of extreme computational simplicity. The relationships between infomax and the maximization of marginal diversity are identified, uncovering the existence of a family of classification procedures for which near optimal (in the Bayes error sense) feature selection does not require combinatorial search. Examination of this family in light of recent studies on the statistics of natural images suggests that visual recognition problems are a subset of it.

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.