Two avenues will be explored: the first is to maximize the ()-average divergence between the class densities and the second is to minimize the union Bhattacharyya bound in the range of (). While both approaches yield similar performance in practice, they outperform standard LDA features and show a 10% relative improvement in the word error rate over state-of-the-art cepstral features on a large vocabulary telephony speech recognition task. 1 Introduction Modern speech recognition systems use cepstral features characterizing the short-term spectrum of the speech signal for classifying frames into phonetic classes. These features are augmented with dynamic information from the adjacent frames to capture transient spectral events in the signal.

It should be stressed that in our model information is coded in the non-stationary rates that underlie the input spike trains. As these rates are not observable, any learning must depends on the observable input spikes that realize those underlying rates.

We introduce a new, nonparametric and principled, distance based clustering method. This method combines a pairwise based approach with a vector-quantization method which provide a meaningful interpretation to the resulting clusters. The idea is based on turning the distance matrix into a Markov process and then examine the decay of mutual-information during the relaxation of this process. The clusters emerge as quasi-stable structures during this relaxation, and then are extracted using the information bottleneck method.

This basic question in the theory of knowledge seems to be beyond the scope of experimental investigation. An accessible version of this question is whether different observers of the same sense data have the same neural representation of these data: how much of the neural code is universal, and how much is individual? Differences in the neural codes of different individuals may arise from various sources: First, different individuals may use different'vocabularies' of coding symbols. Second, they may use the same symbols to encode different stimulus features. Third, they may have different latencies, so they'say' the same things at slightly different times.

In this paper we will discuss a variational mean-field theory and its application to BNs, sigmoidal BNs in particular. We present a variational derivation of the mean-field theory, proposed by Plefka[2].

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

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.

This basic question in the theory of knowledge seems to be beyond the scope of experimental investigation. An accessible version of this question is whether different observers of the same sense data have the same neural representation of these data: how much of the neural code is universal, and how much is individual? Differences in the neural codes of different individuals may arise from various sources: First, different individuals may use different'vocabularies' of coding symbols. Second, they may use the same symbols to encode different stimulus features.

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).

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.