Both mean-field analysis using the cavity method and simulations showthat it has the advantage of being robust against uncertainties in hyperparameter estimation. 1 Introduction In error-correcting codes [1] and image restoration [2], the choice of the so-called hyperparameters is an important factor in determining their performances.

Recent work has exploited boundedness of data in the unsupervised learning of new types of generative model. For nonnegative data it was recently shown that the maximum-entropy generative model is a Nonnegative BoltzmannDistribution not a Gaussian distribution, when the model is constrained to match the first and second order statistics of the data. Learning for practical sized problems is made difficult by the need to compute expectations under the model distribution. The computational costof Markov chain Monte Carlo methods and low fidelity of naive mean field techniques has led to increasing interest in advanced mean field theories and variational methods. Here I present a secondorder mean-fieldapproximation for the Nonnegative Boltzmann Machine model, obtained using a "high-temperature" expansion. The theory is tested on learning a bimodal 2-dimensional model, a high-dimensional translationally invariant distribution, and a generative model for handwritten digits.

A new incremental learning algorithm is described which approximates the maximal margin hyperplane w.r.t.

KenjiDoya ATR International; CREST, JST 2-2 Hikaridai Seika-cho Soraku-gun Kyoto 619-0288 JAPAN doya@isd.atr.co.jp Abstract This paper proposes a new reinforcement learning (RL) paradigm that explicitly takes into account input disturbance as well as modeling errors.The use of environmental models in RL is quite popular for both off-line learning by simulations and for online action planning. However, the difference between the model and the real environment can lead to unpredictable, often unwanted results. Based on the theory of H oocontrol, we consider a differential game in which a'disturbing' agent (disturber) tries to make the worst possible disturbance while a'control' agent (actor) tries to make the best control input. The problem is formulated as finding a minmax solutionof a value function that takes into account the norm of the output deviation and the norm of the disturbance. We derive online learning algorithms for estimating the value function and for calculating the worst disturbance and the best control in reference tothe value function.

Visual input, providedby a video camera on a miniature robot, is preprocessed by a set of Gabor filters on 31 nodes of a log-polar retinotopic graph.

Stimulus arrays are inevitably presented at different positions on the retina in visual tasks, even those that nominally require fixation.

Source separation, or computational auditory scene analysis, attempts to extract individual acoustic objects from input which contains a mixture of sounds from different sources, altered by the acoustic environment. Unmixing algorithms such as lCA and its extensions recover sources by reweighting multiple observation sequences,and thus cannot operate when only a single observation signal is available. I present a technique called refiltering which recovers sources by a nonstationary reweighting ("masking") of frequency sub-bands from a single recording, and argue for the application of statistical algorithms to learning this masking function. I present results of a simple factorial HMM system which learns on recordings of single speakers and can then separate mixtures using only one observation signal by computing the masking function and then refiltering.

FaceSync is an optimal linear algorithm that finds the degree of synchronization betweenthe audio and image recordings of a human speaker. Using canonical correlation, it finds the best direction to combine allthe audio and image data, projecting them onto a single axis. FaceSync uses Pearson's correlation to measure the degree of synchronization betweenthe audio and image data. We derive the optimal linear transform to combine the audio and visual information and describe an implementation that avoids the numerical problems caused by computing thecorrelation matrices.

In this communication we present a new algorithm for solving Support Vector Classifiers (SVC) with large training data sets. The new algorithm is based on an Iterative Re-Weighted Least Squares procedure which is used to optimize the SVc. Moreover, a novel sample selection strategy for the working set is presented, which randomly chooses the working set among the training samples that do not fulfill the stopping criteria. The validity of both proposals, the optimization procedure and sample selection strategy, is shown by means of computer experiments using well-known data sets.

We present a novel method for clustering using the support vector machine approach.Data points are mapped to a high dimensional feature space, where support vectors are used to define a sphere enclosing them. The boundary of the sphere forms in data space a set of closed contours containing the data. Data points enclosed by each contour are defined as a cluster. As the width parameter of the Gaussian kernel is decreased, these contours fit the data more tightly and splitting of contours occurs. The algorithm works by separating clusters according to valleys in the underlying probabilitydistribution, and thus clusters can take on arbitrary geometrical shapes.