We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hi-erarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM’s). Learning is treated as a max-imum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parame-ters of the architecture. We also develop an on-line learning algorithm in which the pa-rameters are updated incrementally. Com-parative simulation results are presented in the robot dynamics domain. 1

This paper presents a general theoretical framework for ensemble methods of constructing significantly improved regression estimates. Given a population of regression estimators, we construct a hybrid estimator which is as good or better in the MSE sense than any estimator in the population. We argue that the ensemble method presented has several properties: 1) It efficiently uses all the networks of a population - none of the networks need be discarded. 2) It efficiently uses all the available data for training without over-fitting. 3) It inherently performs regularization by smoothing in functional space which helps to avoid over-fitting. 4) It utilizes local minima to construct improved estimates whereas other neural network algorithms are hindered by local minima. 5) It is ideally suited for parallel computation. 6) It leads to a very useful and natural measure of the number of distinct estimators in a population. 7) The optimal parameters of the ensemble estimator are given in clo...

this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the ill-defined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.

Humans demonstrate a remarkable ability to generate accurate and appropriate motor behavior under many different and often uncertain environmental conditions. In this paper, we propose a modular approach to such motor learning and control. We review the behavioral evidence and benefits of modularity, and propose a new architecture based on multiple pairs of inverse (controller) and forward (predictor) models. Within each pair, the inverse and forward models are tightly coupled both during their acquisition, through motor learning, and use, during which the forward models determine the contribution of each inverse model's output to the final motor command. This architecture can simultaneously learn the multiple inverse models necessary for control as well as how to select the inverse models appropriate for a given environment. Finally, we describe specific predictions of the model, which can be tested experimentally. # 1998 Elsevier Science Ltd. All rights reserved. Keywords: Motor con...

Real-world learning tasks may involve high-dimensional data sets with arbitrary patterns of missing data. In this paper we present a framework based on maximum likelihood density estimation for learning from such data sets. We use mixture models for the density estimates and make two distinct appeals to the ExpectationMaximization (EM) principle (Dempster et al., 1977) in deriving a learning algorithm---EM is used both for the estimation of mixture components and for coping with missing data. The resulting algorithm is applicable to a wide range of supervised as well as unsupervised learning problems. Results from a classification benchmark---the iris data set---are presented. 1 Introduction Adaptive systems generally operate in environments that are fraught with imperfections; nonetheless they must cope with these imperfections and learn to extract as much relevant information as needed for their particular goals. One form of imperfection is incompleteness in sensing information. Inc...

An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble. Bagging (Breiman, 1996c) and Boosting (Freund & Schapire, 1996; Schapire, 1990) are two relatively new but popular methods for producing ensembles. In this paper we evaluate these methods on 23 data sets using both neural networks and decision trees as our classification algorithm. Our results clearly indicate a number of conclusions. First, while Bagging is almost always more accurate than a single classifier, it is sometimes much less accurate than Boosting. On the other hand, Boosting can create ensembles that are less accurate than a single classifier – especially when using neural networks. Analysis indicates that the performance of the Boosting methods is dependent on the characteristics of the data set being examined. In fact, further results show that Boosting ensembles may overfit noisy data sets, thus decreasing its performance. Finally, consistent with previous studies, our work suggests that most of the gain in an ensemble’s performance comes in the first few classifiers combined; however, relatively large gains can be seen up to 25 classifiers when Boosting decision trees. 1.

Using an ensemble of classifiers, instead of a single classifier, can lead to improved generalization. The gains obtained by combining however, are often affected more by the selection of what is presented to the combiner, than by the actual combining method that is chosen. In this paper we focus on data selection and classifier training methods, in order to "prepare" classifiers for combining. We review a combining framework for classification problems that quantifies the need for reducing the correlation among individual classifiers. Then, we discuss several methods that make the classifiers in an ensemble more complementary. Experimental results are provided to illustrate the benefits and pitfalls of reducing the correlation among classifiers, especially when the training data is in limited supply. 2 1 Introduction A classifier's ability to meaningfully respond to novel patterns, or generalize, is perhaps its most important property (Levin et al., 1990; Wolpert, 1990). In...

... This article illustrates the potential learning capabilities of purely local learning and offers an interesting and powerful approach to learning with receptive fields.

We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models -- hidden Markov models and linear dynamical systems -- and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forward-backward recursions for hidden Markov models and the Kalman lter recursions for linear dynamical systems. We tested the algorithm both on artificial data sets and on a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching state-space models.

The classical way of attempting to solve the face (or object) recognition problem is by using large and representative datasets. In many applications though, only one sample per class is available to the system. In this contribution, we describe a probabilistic approach that is able to compensate for imprecisely localized, partially occluded and expression variant faces even when only one single training sample per class is available to the system. To solve the localization problem, we find the subspace (within the feature space, e.g. eigenspace) that represents this error for each of the training images. To resolve the occlusion problem, each face is divided into k local regions which are analyzed in isolation. In contrast with other approaches, where a simple voting space is used, we present a probabilistic method that analyzes how "good" a local match is. To make the recognition system less sensitive to the differences between the facial expression displayed on the training and the testing images, we weight the results obtained on each local area on the bases of how much of this local area is affected by the expression displayed on the current test image.