Missing data is common in real-world datasets and is a problem for many estimation techniques. We have developed a variational Bayesian method to perform Independent Component Analysis (ICA) on high-dimensional data containing missing entries. Missing data are handled naturally in the Bayesian framework by integrating the generative density model. Modeling the distributions of the independent sources with mixture of Gaussians allows sources to be estimated with different kurtosis and skewness. The variational Bayesian method automatically determines the dimensionality of the data and yields an accurate density model for the observed data without overfitting problems. This allows direct probability estimation of missing values in the high dimensional space and avoids dimension reduction preprocessing which is not feasible with missing data.

A key challenge for neural modeling is to explain how a continuous stream of multi-modal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real-time. We propose a new computational model that is based on principles of high dimensional dynamical systems in combination with statistical learning theory. It can be implemented on generic evolved or found recurrent circuitry.

This paper focuses on people's short-run behavior by examining dynamical versions of these three theories, and comparing their predictions to a real-world dataset.

We study a new, model-free form of approximate policy iteration which uses Sarsa updates with linear state-action value function approximation for policy evaluation, and a "policy improvement operator" to generate a new policy based on the learned state-action values. We prove that if the policy improvement operator produces -soft policies and is Lipschitz continuous in the action values, with a constant that is not too large, then the approximate policy iteration algorithm converges to a unique solution from any initial policy. To our knowledge, this is the first convergence result for any form of approximate policy iteration under similar computational-resource assumptions.

A framework is introduced for assessing the encoding accuracy and the discriminational ability of a population of neurons upon simultaneous presentation of multiple stimuli. Minimal square estimation errors are obtained from a Fisher information analysis in an abstract compound space comprising the features of all stimuli. Even for the simplest case of linear superposition of responses and Gaussian tuning, the symmetries in the compound space are very different from those in the case of a single stimulus. The analysis allows for a quantitative description of attentional effects and can be extended to include neural nonlinearities such as nonclassical receptive fields.

We report a system that classifies and can learn to classify patterns of visual motion online. The complete system is described by the dynamics of its physical network architectures. The combination of the following properties makes the system novel: Firstly, the front-end of the system consists of an aVLSI optical flow chip that collectively computes 2-D global visual motion in real-time [1]. Secondly, the complexity of the classification task is significantly reduced by mapping the continuous motion trajectories to sequences of'motion events'. And thirdly, all the network structures are simple and with the exception of the optical flow chip based on a Winner-Take-All (WTA) architecture. We demonstrate the application of the proposed generic system for a contactless man-machine interface that allows to write letters by visual motion. Regarding the low complexity of the system, its robustness and the already existing front-end, a complete aVLSI system-on-chip implementation is realistic, allowing various applications in mobile electronic devices.

The problem of extracting the relevant aspects of data, in face of multiple conflicting structures, is inherent to modeling of complex data. Extracting structure in one random variable that is relevant for another variable has been principally addressed recently via the information bottleneck method [15]. However, such auxiliary variables often contain more information than is actually required due to structures that are irrelevant for the task. In many other cases it is in fact easier to specify what is irrelevant than what is, for the task at hand. Identifying the relevant structures, however, can thus be considerably improved by also minimizing the information about another, irrelevant, variable. In this paper we give a general formulation of this problem and derive its formal, as well as algorithmic, solution. Its operation is demonstrated in a synthetic example and in two real world problems in the context of text categorization and face images. While the original information bottleneck problem is related to rate distortion theory, with the distortion measure replaced by the relevant information, extracting relevant features while removing irrelevant ones is related to rate distortion with side information.

We introduce a new learning algorithm for decision lists to allow features that are constructed from the data and to allow a tradeoff between accuracy and complexity. We bound its generalization error in terms of the number of errors and the size of the classifier it finds on the training data. We also compare its performance on some natural data sets with the set covering machine and the support vector machine.

Given a set of hidden variables with an a-priori Markov structure, we derive an online algorithm which approximately updates the posterior as pairwise measurements between the hidden variables become available. The update is performed using Assumed Density Filtering: to incorporate each pairwise measurement, we compute the optimal Markov structure which represents the true posterior and use it as a prior for incorporating the next measurement. We demonstrate the resulting algorithm by calculating globally consistent trajectories of a robot as it navigates along a 2D trajectory. To update a trajectory of length t, the update takes O(t). When all conditional distributions are linear-Gaussian, the algorithm can be thought of as a Kalman Filter which simplifies the state covariance matrix after incorporating each measurement.

We investigate a general semi-Markov Decision Process (SMDP) framework for modeling concurrent decision making, where agents learn optimal plans over concurrent temporally extended actions. We introduce three types of parallel termination schemes - all, any and continue - and theoretically and experimentally compare them.