N wideband sources recorded using N closely spaced receivers can feasibly be separated based only on second order statistics when using a physical model of the mixing process. In this case we show that the parameter estimation problem can be essentially reduced to considering directions of arrival and attenuations of each signal. The paper presents two demixing methods operating in the time and frequency domain and experimentally shows that it is always possible to demix signals arriving at different angles. Moreover, one can use spatial cues to solve the channel selection problem and a post-processing Wiener filter to ameliorate the artifacts caused by demixing.

We examine a psychophysical law that describes the influence of stimulus and context on perception. According to this law choice probability ratios factorize into components independently controlled bystimulus and context. It has been argued that this pattern of results is incompatible with feedback models of perception. In this paper we examine this claim using neural network models defined via stochastic differential equations. We show that the law is related to a condition named channel separability and has little to do with the existence of feedback connections. In essence, channels areseparable if they converge into the response units without direct lateral connections to other channels and if their sensors are not directly contaminated by external inputs to the other channels. Implicationsof the analysis for cognitive and computational neurosicence are discussed.

One of the open questions that remains is how to set the'tunable' parameters of an SVM algorithm: While methods forchoosing the width of the kernel function and the noise parameter C (which controls how closely the training data are fitted) have been proposed [4, 5] (see also, very recently, [6]), the effect of the overall shape of the kernel function remains imperfectly understood [1]. Error bars (class probabilities) for SVM predictions - important for safety-critical applications, for example - are also difficult to obtain. In this paper I suggest that a probabilistic interpretation of SVMs could be used to tackle these problems. It shows that the SVM kernel defines a prior over functions on the input space, avoiding the need to think in terms of high-dimensional feature spaces. It also allows one to define quantities such as the evidence (likelihood) for a set of hyperparameters (C, kernel amplitude Ko etc). I give a simple approximation to the evidence which can then be maximized to set such hyperparameters. The evidence is sensitive to the values of C and Ko individually, in contrast to properties (such as cross-validation error) of the deterministic solution, which only depends on the product CKo. It can thfrefore be used to assign an unambiguous value to C, from which error bars can be derived.

Recently, sample complexity bounds have been derived for problems involving linearfunctions such as neural networks and support vector machines. In this paper, we extend some theoretical results in this area by deriving dimensional independent covering number bounds for regularized linearfunctions under certain regularization conditions. We show that such bounds lead to a class of new methods for training linear classifiers withsimilar theoretical advantages of the support vector machine. Furthermore, we also present a theoretical analysis for these new methods fromthe asymptotic statistical point of view. This technique provides better description for large sample behaviors of these algorithms. 1 Introduction In this paper, we are interested in the generalization performance of linear classifiers obtained fromcertain algorithms.

Recent theoretical results suggest that the effectiveness of these algorithms is due to their tendency to produce large margin classifiers [1, 18]. Loosely speaking, if a combination of classifiers correctly classifies most of the training data with a large margin, then its error probability is small. In [14] we gave improved upper bounds on the misclassification probability of a combined classifier in terms of the average over the training data of a certain cost function of the margins. That paper also described DOOM, an algorithm for directly minimizingthe margin cost function by adjusting the weights associated with Boosting Algorithms as Gradient Descent 513 each base classifier (the base classifiers are suppiled to DOOM). DOOM exhibits performance improvements over AdaBoost, even when using the same base hypotheses, whichprovides additional empirical evidence that these margin cost functions are appropriate quantities to optimize. In this paper, we present a general class of algorithms (called AnyBoost) which are gradient descent algorithms for choosing linear combinations of elements of an inner product function space so as to minimize some cost functional. The normal operation of a weak learner is shown to be equivalent to maximizing a certain inner product. We prove convergence of AnyBoost under weak conditions. In Section 3, we show that this general class of algorithms includes as special cases nearly all existing voting methods.

We formulate the problem of retrieving images from visual databases as a problem of Bayesian inference. This leads to natural and effective solutions for two of the most challenging issues in the design of a retrieval system: providing support for region-based queries without requiring prior image segmentation, and accounting for user-feedback during a retrieval session. We present a new learning algorithm that relies on belief propagation to account for both positive and negative examples of the user's interests.

Model Predictive Control was developed in the late 70's and came into widespread use, particularly in the refining industry, in the 80's. The economic benefit of this approach to control has been documented [1,2] .

Previous biophysical modeling work showed that nonlinear interactions amongnearby synapses located on active dendritic trees can provide a large boost in the memory capacity of a cell (Mel, 1992a, 1992b).

The first two methods are related to mean field ideas known in Statistical Physics. The third approach is based on Bayesian online approach which was motivated by recent results in the Statistical Mechanics of Neural Networks. We present simulation results showing: 1. that the mean field Bayesian evidence may be used for hyperparameter tuning and 2. that the online approach may achieve a low training error fast. 1 Introduction Gaussian processes provide promising nonparametric Bayesian approaches to regression andclassification [2, 1].

Local "belief propagation" rules of the sort proposed by Pearl [15] are guaranteed to converge to the correct posterior probabilities in singly connected graphical models. Recently, a number of researchers have empirically demonstratedgood performance of "loopy belief propagation" using these same rules on graphs with loops. Perhaps the most dramatic instance is the near Shannon-limit performance of "Turbo codes", whose decoding algorithm is equivalent to loopy belief propagation. Except for the case of graphs with a single loop, there has been little theoretical understandingof the performance of loopy propagation. Here we analyze belief propagation in networks with arbitrary topologies when the nodes in the graph describe jointly Gaussian random variables.