Hidden Markov models (HMMs) for automatic speech recognition rely on high dimensional feature vectors to summarize the shorttime propertiesof speech. Correlations between features can arise when the speech signal is non-stationary or corrupted by noise. We investigate how to model these correlations using factor analysis, a statistical method for dimensionality reduction. Factor analysis uses a small number of parameters to model the covariance structure ofhigh dimensional data. These parameters are estimated by an Expectation-Maximization (EM) algorithm that can be embedded inthe training procedures for HMMs.

Monotonicity is a constraint which arises in many application domains. Wepresent a machine learning model, the monotonic network, for which monotonicity can be enforced exactly, i.e., by virtue offunctional form. A straightforward method for implementing and training a monotonic network is described. Monotonic networks are proven to be universal approximators of continuous, differentiable monotonicfunctions. We apply monotonic networks to a real-world task in corporate bond rating prediction and compare them to other approaches. 1 Introduction Several recent papers in machine learning have emphasized the importance of priors anddomain-specific knowledge. In their well-known presentation of the biasvariance tradeoff(Geman and Bienenstock, 1992)' Geman and Bienenstock conclude by arguing that the crucial issue in learning is the determination of the "right biases" whichconstrain the model in the appropriate way given the task at hand.

Prioritized sweeping is a model-based reinforcement learning method that attempts to focus an agent's limited computational resources to achieve a good estimate of the value of environment states. To choose effectively whereto spend a costly planning step, classic prioritized sweeping uses a simple heuristic to focus computation on the states that are likely to have the largest errors. In this paper, we introduce generalized prioritized sweeping, a principled method for generating such estimates in a representation-specific manner. This allows us to extend prioritized sweeping beyond an explicit, state-based representation to deal with compact representationsthat are necessary for dealing with large state spaces. We apply this method for generalized model approximators (such as Bayesian networks), and describe preliminary experiments that compare our approach with classical prioritized sweeping.

This idea has been extended compute the relative Hessian by (Pham, 1996).

The problem of time series prediction is studied within the uniform convergence frameworkof Vapnik and Chervonenkis. The dependence inherent in the temporal structure is incorporated into the analysis, thereby generalizing the available theory for memoryless processes. Finite sample boundsare calculated in terms of covering numbers of the approximating class,and the tradeoff between approximation and estimation is discussed. A complexity regularization approach is outlined, based on Vapnik's method of Structural Risk Minimization, and shown to be applicable inthe context of mixing stochastic processes.

Given a melody, the system invents afour-part chorale harmonization and a variation of any chorale voice, after being trained on music pieces of composers like J. S. Bach and J .

The inverse of the Fisher information matrix is used in the natural gradientdescent algorithm to train single-layer and multi-layer perceptrons. We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron. Based on this scheme, we have designed an algorithm to compute the natural gradient. When the input dimension n is much larger than the number of hidden neurons, the complexity of this algorithm isof order O(n). It is confirmed by simulations that the natural gradient descent learning rule is not only efficient but also robust. 1 INTRODUCTION The inverse of the Fisher information matrix is required to find the Cramer-Rae lower bound to analyze the performance of an unbiased estimator. It is also needed in the natural gradient learning framework (Amari, 1997) to design statistically efficient algorithms for estimating parameters in general and for training neural networks in particular. In this paper, we assume a stochastic model for multilayer perceptrons.Considering a Riemannian parameter space in which the Fisher information matrix is a metric tensor, we apply the natural gradient learning rule to train single-layer and multi-layer perceptrons. The main difficulty encountered is to compute the inverse of the Fisher information matrix of large dimensions when the input dimension is high. By exploring the structure of the Fisher information matrix and its inverse, we design a fast algorithm with lower complexity to implement the natural gradient learning algorithm.

Gabor filters are used as preprocessing stages for different tasks in machine vision and image processing. Their use has been partially motivated by findings that two dimensional Gabor filters can be used to model receptive fields of orientation selective neurons in the visual cortex (Daugman, 1980) and three dimensional spatiotemporal Gabor filters can be used to model biological image motion analysis (Adelson, 1985). A Gabor filter has a complex valued impulse response which is a complex exponential modulated by a Gaussian function.

Next, C1 is used to form the indicator matrix, N. A correspondence analysis is performed on N to derive the scaled space, A

We derive a first-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D differential entropy is derived. The approximation of entropy is both more exact and more robust againstoutliers than the classical approximation based on the polynomial density expansions, without being computationally more expensive. The approximation has applications, for example, in independent component analysis and projection pursuit. 1 Introduction The basic information-theoretic quantity for continuous one-dimensional random variables is differential entropy. The differential entropy H of a scalar random variable X with density f(x) is defined as H(X) - / f(x) log f(x)dx.