The sum-product algorithm can be directly applied in Gaussian networks and in graphs for coding, but for many conditional probabilityfunctions - including the sigmoid function - direct application of the sum-product algorithm is not possible. We introduce "accumulator networks" that have low local complexity (but exponential global complexity) so the sum-product algorithm can be directly applied. In an accumulator network, the probability of a child given its parents is computed by accumulating the inputs from the parents in a Markov chain or more generally a tree. After giving expressions for inference and learning in accumulator networks, wegive results on the "bars problem" and on the problem of extracting translated, overlapping faces from an image. 1 Introduction Graphical probability models with hidden variables are capable of representing complex dependenciesbetween variables, filling in missing data and making Bayesoptimal decisionsusing probabilistic inferences (Hinton and Sejnowski 1986; Pearl 1988; Neal 1992). Large, richly-connected networks with many cycles can potentially beused to model complex sources of data, such as audio signals, images and video. However, when the number of cycles in the network is large (more precisely, when the cut set size is exponential), exact inference becomes intractable. Also, to learn a probability model with hidden variables, we need to fill in the missing data using probabilistic inference, so learning also becomes intractable. To cope with the intractability of exact inference, a variety of approximate inference methods have been invented, including Monte Carlo (Hinton and Sejnowski 1986; Neal 1992), Helmholz machines (Dayan et al. 1995; Hinton et al. 1995), and variational techniques (Jordan et al. 1998).

In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters toobtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particlefiltering and other nonlinear filtering methods very substantially.

Theneurons in these networks are the random variables, whereas the connections between them model the causal dependencies. Usually, some of the nodes have a direct relation with the random variables in the problem and are called'visibles'. The other nodes, known as'hiddens', are used to model more complex probability distributions. Learning in graphical models can be done as long as the likelihood that the visibles correspond to a pattern in the data set, can be computed. In general the time it takes, scales exponentially with the number of hidden neurons.

Many algorithms for approximate reinforcement learning are not known to converge. In fact, there are counterexamples showing that the adjustable weights in some algorithms may oscillate within a region rather than converging to a point. This paper shows that, for two popular algorithms, such oscillation is the worst that can happen: the weights cannot diverge, but instead must converge to a bounded region. The algorithms are SARSA(O) and V(O); the latter algorithm was used in the well-known TD-Gammon program. 1 Introduction Although there are convergent online algorithms (such as TD()') [1]) for learning the parameters of a linear approximation to the value function of a Markov process, no way is known to extend these convergence proofs to the task of online approximation ofeither the state-value (V*) or the action-value (Q*) function of a general Markov decision process. In fact, there are known counterexamples to many proposed algorithms.For example, fitted value iteration can diverge even for Markov processes [2]; Q-Iearning with linear function approximators can diverge, even when the states are updated according to a fixed update policy [3]; and SARSA(O) can oscillate between multiple policies with different value functions [4].

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Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoretical resultsfor the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms can be used in the inference step of variational Bayesian learning. Applying these results tothe Bayesian analysis of linear-Gaussian state-space models we obtain a learning procedure that exploits the Kalman smoothing propagation,while integrating over all model parameters. We demonstrate how this can be used to infer the hidden state dimensionality ofthe state-space model in a variety of synthetic problems and one real high-dimensional data set. 1 Introduction Bayesian approaches to machine learning have several desirable properties. Bayesian integration does not suffer overfitting (since nothing is fit to the data). Prior knowledge canbe incorporated naturally and all uncertainty is manipulated in a consistent manner. Moreover it is possible to learn model structures and readily compare between model classes. Unfortunately, for most models of interest a full Bayesian analysis is computationally intractable.

The principle of maximizing mutual information is applied to learning overcomplete and recurrent representations. The underlying model consists ofa network of input units driving a larger number of output units with recurrent interactions. In the limit of zero noise, the network is deterministic andthe mutual information can be related to the entropy of the output units.

Large margin linear classification methods have been successfully applied tomany applications. For a linearly separable problem, it is known that under appropriate assumptions, the expected misclassification error of the computed "optimal hyperplane" approaches zero at a rate proportional tothe inverse training sample size. This rate is usually characterized bythe margin and the maximum norm of the input data. In this paper, we argue that another quantity, namely the robustness of the input datadistribution, also plays an important role in characterizing the convergence behavior of expected misclassification error. Based on this concept of robustness, we show that for a large margin separable linear classification problem, the expected misclassification error may converge exponentially in the number of training sample size. 1 Introduction We consider the binary classification problem: to determine a label y E {-1, 1} associated withan input vector x. A useful method for solving this problem is by using linear discriminant functions .

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.

An online recursive algorithm for training support vector machines, one vector at a time, is presented. Adiabatic increments retain the Kuhn Tucker conditions on all previously seen training data, in a number of steps each computed analytically. The incremental procedure is reversible, anddecremental "unlearning" offers an efficient method to exactly evaluate leave-one-out generalization performance.