We present a new method for obtaining local error bars for nonlinear regression, i.e., estimates of the confidence in predicted values that depend on the input. We approach this problem by applying a maximumlikelihood framework to an assumed distribution of errors. We demonstrate our method first on computer-generated data with locally varying, normally distributed target noise. We then apply it to laser data from the Santa Fe Time Series Competition where the underlying system noise is known quantization error and the error bars give local estimates of model misspecification. In both cases, the method also provides a weightedregression effect that improves generalization performance.

Instead of "ground truth" one may only have the subjective opinion(s) of one or more experts. For example, medical data or image data may be collected off-line and some time later a set of experts analyze the data and produce a set of class labels. The central problem is that of trying to infer the "ground truth" given the noisy subjective estimates of the experts. When one wishes to apply a supervised learning algorithm to the data, the problem is primarily twofold: (i) how to evaluate the relative performance of experts and algorithms, and (ii) how to train a pattern recognition system in the absence of absolute ground truth. In this paper we focus on problem (i), namely the performance evaluation issue, and in particular we discuss the application of a particular modelling technique to the problem of counting volcanoes on the surface of Venus.

Many real world learning problems are best characterized by an interaction of multiple independent causes or factors. Discovering such causal structure from the data is the focus of this paper. Based on Zemel and Hinton's cooperative vector quantizer (CVQ) architecture, an unsupervised learning algorithm is derived from the Expectation-Maximization (EM) framework. Due to the combinatorial nature of the data generation process, the exact E-step is computationally intractable. Two alternative methods for computing the E-step are proposed: Gibbs sampling and mean-field approximation, and some promising empirical results are presented.

In this paper, we derive classifiers which are winner-take-all (WTA) approximations to a Bayes classifier with Gaussian mixtures for class conditional densities. The derived classifiers include clustering based algorithms like LVQ and k-Means. We propose a constrained rank Gaussian mixtures model and derive a WTA algorithm for it. Our experiments with two speech classification tasks indicate that the constrained rank model and the WTA approximations improve the performance over the unconstrained models. 1 Introduction A classifier assigns vectors from Rn (n dimensional feature space) to one of K classes, partitioning the feature space into a set of K disjoint regions. A Bayesian classifier builds the partition based on a model of the class conditional probability densities of the inputs (the partition is optimal for the given model).

We develop a principled strategy to sample a function optimally for function approximation tasks within a Bayesian framework. Using ideas from optimal experiment design, we introduce an objective function (incorporating both bias and variance) to measure the degree of approximation, and the potential utility of the data points towards optimizing this objective. We show how the general strategy can be used to derive precise algorithms to select data for two cases: learning unit step functions and polynomial functions. In particular, we investigate whether such active algorithms can learn the target with fewer examples. We obtain theoretical and empirical results to suggest that this is the case. 1 INTRODUCTION AND MOTIVATION Learning from examples is a common supervised learning paradigm that hypothesizes a target concept given a stream of training examples that describes the concept. In function approximation, example-based learning can be formulated as synthesizing an approximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source.

If data collection is costly, there is much to be gained by actively selecting particularly informative data points in a sequential way. In a Bayesian decision-theoretic framework we develop a query selection criterion which explicitly takes into account the intended use of the model predictions. By Markov Chain Monte Carlo methods the necessary quantities can be approximated to a desired precision. As the number of data points grows, the model complexity is modified by a Bayesian model selection strategy. The properties of two versions of the criterion ate demonstrated in numerical experiments.

Increasing attention has been paid to reinforcement learning algorithms in recent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of non-Markov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a Monte-Carlo policy evaluation combined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerably better than any deterministic policy. Although the space of stochastic policies is continuous-even for a discrete action space-our algorithm is computationally tractable.

We present a deterministic annealing variant of the EM algorithm for maximum likelihood parameter estimation problems. In our approach, the EM process is reformulated as the problem of minimizing the thermodynamic free energy by using the principle of maximum entropy and statistical mechanics analogy. Unlike simulated annealing approaches, this minimization is deterministically performed. Moreover, the derived algorithm, unlike the conventional EM algorithm, can obtain better estimates free of the initial parameter values.

We introduce a recurrent architecture having a modular structure and we formulate a training procedure based on the EM algorithm. The resulting model has similarities to hidden Markov models, but supports recurrent networks processing style and allows to exploit the supervised learning paradigm while using maximum likelihood estimation. 1 INTRODUCTION Learning problems involving sequentially structured data cannot be effectively dealt with static models such as feedforward networks. Recurrent networks allow to model complex dynamical systems and can store and retrieve contextual information in a flexible way. Up until the present time, research efforts of supervised learning for recurrent networks have almost exclusively focused on error minimization by gradient descent methods. Although effective for learning short term memories, practical difficulties have been reported in training recurrent neural networks to perform tasks in which the temporal contingencies present in the input/output sequences span long intervals (Bengio et al., 1994; Mozer, 1992).

This paper presents ongoing work on a speaker independent visual speech recognition system. The work presented here builds on previous research efforts in this area and explores the potential use of simple hidden Markov models for limited vocabulary, speaker independent visual speech recognition. The task at hand is recognition of the first four English digits, a task with possible applications in car-phone dialing. The images were modeled as mixtures of independent Gaussian distributions, and the temporal dependencies were captured with standard left-to-right hidden Markov models. The results indicate that simple hidden Markov models may be used to successfully recognize relatively unprocessed image sequences.