We examine the problem of generating state-space compressions of POMDPs in a way that minimally impacts decision quality. We analyze the impact of compressions ondecision quality, observing that compressions that allow accurate policy evaluation (prediction of expected future reward) will not affect decision quality. Wederive a set of sufficient conditions that ensure accurate prediction in this respect, illustrate interesting mathematical properties these confer on lossless linear compressions,and use these to derive an iterative procedure for finding good linear lossy compressions. We also elaborate on how structured representations of a POMDP can be used to find such compressions.

In [1] we introduced a linear statistical model of joint color changes in images due to variation in lighting and certain non-geometric camera parameters.

A neurotrophic model for the co-development of topography and ocular dominance columns in the primary visual cortex has recently been proposed. Inthe present work, we test this model by driving it with the output of a pair of neuronal vision sensors stimulated by disparate moving patterns.We show that the temporal correlations in the spike trains generated by the two sensors elicit the development of refined topography andocular dominance columns, even in the presence of significant amounts of spontaneous activity and fixed-pattern noise in the sensors.

We report a system that classifies and can learn to classify patterns of visual motion online. The complete system is described by the dynamics ofits physical network architectures. The combination of the following propertiesmakes 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 motiontrajectories 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 theapplication of the proposed generic system for a contactless man-machine interface that allows to write letters by visual motion. Regarding thelow 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.

Gaussian process regression allows a simple analytical treatment of exact Bayesianinference and has been found to provide good performance, yet scales badly with the number of training data. In this paper we compare severalapproaches towards scaling Gaussian processes regression to large data sets: the subset of representers method, the reduced rank approximation, online Gaussian processes, and the Bayesian committee machine.Furthermore we provide theoretical insight into some of our experimental results. We found that subset of representers methods can give good and particularly fast predictions for data sets with high and medium noise levels. On complex low noise data sets, the Bayesian committee machine achieves significantly better accuracy, yet at a higher computational cost.

We focus on the problem of efficient learning of dependency trees. It is well-known that given the pairwise mutual information coefficients, a minimum-weight spanning tree algorithm solves this problem exactly and in polynomial time. However, for large data-sets it is the construction ofthe correlation matrix that dominates the running time. We have developed a new spanning-tree algorithm which is capable of exploiting partial knowledge about edge weights. The partial knowledge we maintain isa probabilistic confidence interval on the coefficients, which we derive by examining just a small sample of the data. The algorithm is able to flag the need to shrink an interval, which translates to inspection ofmore data for the particular attribute pair. Experimental results show running time that is near-constant in the number of records, without significantloss in accuracy of the generated trees. Interestingly, our spanning-tree algorithm is based solely on Tarjan's red-edge rule, which is generally considered a guaranteed recipe for bad performance.

We introduce a family of classifiers based on a physical analogy to an electrostatic system of charged conductors. The family, called Coulomb classifiers, includes the two best-known support-vector machines (SVMs), the ν-SVM and the C-SVM. In the electrostatics analogy,a training example corresponds to a charged conductor at a given location in space, the classification function corresponds to the electrostatic potential function, and the training objective function corresponds to the Coulomb energy. The electrostatic framework provides not only a novel interpretation of existing algorithms andtheir interrelationships, but it suggests a variety of new methods for SVMs including kernels that bridge the gap between polynomial and radial-basis functions, objective functions that do not require positive-definite kernels, regularization techniques that allow for the construction of an optimal classifier in Minkowski space. Based on the framework, we propose novel SVMs and perform simulationstudies to show that they are comparable or superior tostandard SVMs. The experiments include classification tasks on data which are represented in terms of their pairwise proximities, wherea Coulomb Classifier outperformed standard SVMs.

We investigate the generalization performance of some learning problems inHilbert function Spaces. We introduce a concept of scalesensitive effectivedata dimension, and show that it characterizes the convergence rateof the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to nonparametric kernel learning methods. We derive upperbounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.

Population-based Incremental Learning is shown require very sensitive scalingof its learning rate. The learning rate must scale with the system size in a problem-dependent way. This is shown in two problems: the needle-in-a haystack, in which the learning rate must vanish exponentially in the system size, and in a smooth function in which the learning rate must vanish like the square root of the system size. Two methods are proposed for removing this sensitivity. Alearning dynamics which obeys detailed balance is shown to give consistent performance over the entire range of learning rates. An analog of mutation is shown to require a learning rate which scales as the inverse system size, but is problem independent.

The direct neural control of external devices such as computer displays or prosthetic limbs requires the accurate decoding of neural activity representing continuousmovement. We develop a real-time control system using the spiking activity of approximately 40 neurons recorded with an electrode array implanted in the arm area of primary motor cortex. In contrast to previous work, we develop a control-theoretic approach that explicitly models the motion of the hand and the probabilistic relationship betweenthis motion and the mean firing rates of the cells in 70§ bins. We focus on a realistic cursor control task in which the subject mustmove a cursor to "hit" randomly placed targets on a computer monitor. Encoding and decoding of the neural data is achieved with a Kalman filter which has a number of advantages over previous linear filtering techniques. In particular, the Kalman filter reconstructions of hand trajectories in off-line experiments are more accurate than previously reportedresults and the model provides insights into the nature of the neural coding of movement.