Exact inference in large, richly connected noisy-OR networks is intractable, and most approximate inference algorithms tend to concentrate on a small number of most probable configurations of the hidden variables under the posterior. We presented an "inclusive" variational method for bipartite noisy-OR networks that favors including all probable configurations, at the cost of including some improbable configurations. The method fits a tree to the posterior distribution sequentially, i.e., one observation at a time. Results on an ensemble of QMR-DT type networks show that the method performs better than local probability propagation and a variational upper bound for ranking most probable diseases.

We present a bound on the generalisation error of linear classifiers in terms of a refined margin quantity on the training set. The result is obtained in a PAC-Bayesian framework and is based on geometrical arguments in the space of linear classifiers. The new bound constitutes an exponential improvement of the so far tightest margin bound by Shawe-Taylor et al. [8] and scales logarithmically in the inverse margin. Even in the case of less training examples than input dimensions sufficiently large margins lead to nontrivial bound values and - for maximum margins - to a vanishing complexity term. Furthermore, the classical margin is too coarse a measure for the essential quantity that controls the generalisation error: the volume ratio between the whole hypothesis space and the subset of consistent hypotheses.

Prior knowledge about video structure can be used both as a means to improve the peiformance of content analysis and to extract features that allow semantic classification. We introduce statistical models for two important components of this structure, shot duration and activity, and demonstrate the usefulness of these models by introducing a Bayesian formulation for the shot segmentation problem. The new formulations is shown to extend standard thresholding methods in an adaptive and intuitive way, leading to improved segmentation accuracy.

How should we decide among competing explanations of a cognitive process given limited observations? The problem of model selection is at the heart of progress in cognitive science. In this paper, Minimum Description Length (MDL) is introduced as a method for selecting among computational models of cognition. We also show that differential geometry provides an intuitive understanding of what drives model selection in MDL. Finally, adequacy of MDL is demonstrated in two areas of cognitive modeling.

In this paper, we derive a second order mean field theory for directed graphical probability models. By using an information theoretic argument it is shown how this can be done in the absense of a partition function. This method is a direct generalisation of the well-known TAP approximation for Boltzmann Machines. In a numerical example, it is shown that the method greatly improves the first order mean field approximation. For a restricted class of graphical models, so-called single overlap graphs, the second order method has comparable complexity to the first order method. For sigmoid belief networks, the method is shown to be particularly fast and effective.

We estimate a statistical model of typical activities from a large set of 3D periodic human motion data by segmenting these data automatically into "cycles". Then the mean and the principal components of the cycles are computed using a new algorithm that accounts for missing information and enforces smooth transitions between cycles. The learned temporal model provides a prior probability distribution over human motions that can be used in a Bayesian framework for tracking human subjects in complex monocular video sequences and recovering their 3D motion. 1 Introduction The modeling and tracking of human motion in video is important for problems as varied as animation, video database search, sports medicine, and human-computer interaction. Technically, the human body can be approximated by a collection of articulated limbs and its motion can be thought of as a collection of time-series describing the joint angles as they evolve over time. A key challenge in modeling these joint angles involves decomposing the time-series into suitable temporal primitives.

Jensen's inequality is a powerful mathematical tool and one of the workhorses in statistical learning. Its applications therein include the EM algorithm, Bayesian estimation and Bayesian inference. Jensen computes simple lower bounds on otherwise intractable quantities such as products of sums and latent log-likelihoods. This simplification then permits operations like integration and maximization. Quite often (i.e. in discriminative learning) upper bounds are needed as well. We derive and prove an efficient analytic inequality that provides such variational upper bounds. This inequality holds for latent variable mixtures of exponential family distributions and thus spans a wide range of contemporary statistical models. We also discuss applications of the upper bounds including maximum conditional likelihood, large margin discriminative models and conditional Bayesian inference. Convergence, efficiency and prediction results are shown.

Two well known classes of unsupervised procedures that can be cast in this manner are generative and recoding models. In a generative unsupervised framework, the environment generates training exampleswhich we will refer to as observations-by sampling from one distribution; the other distribution is embodied in the model. Examples of generative frameworks are mixtures of Gaussians (MoG) [2], factor analysis [4], and Boltzmann machines [8]. In the recoding unsupervised framework, the model transforms points from an obser- vation space to an output space, and the output distribution is compared either to a reference distribution or to a distribution derived from the output distribution. An example is independent component analysis (leA) [11], a method that discovers a representation of vector-valued observations in which the statistical dependence among the vector elements in the output space is minimized.

We introduce the mixture of Gaussian processes (MGP) model which is useful for applications in which the optimal bandwidth of a map is input dependent. The MGP is derived from the mixture of experts model and can also be used for modeling general conditional probability densities. We discuss how Gaussian processes -in particular in form of Gaussian process classification, the support vector machine and the MGP modelcan be used for quantifying the dependencies in graphical models. 1 Introduction Gaussian processes are typically used for regression where it is assumed that the underlying function is generated by one infinite-dimensional Gaussian distribution (i.e.

We present a simple sparse greedy technique to approximate the maximum a posteriori estimate of Gaussian Processes with much improved scaling behaviour in the sample size m.