We describe Maximum-Likelihood Continuity Mapping (MALCOM), an alternative to hidden Markov models (HMMs) for processing sequence data such as speech. While HMMs have a discrete "hidden" space constrained by a fixed finite-automaton architecture, MALCOM has a continuous hidden space-a continuity map-that is constrained only by a smoothness requirement on paths through the space. MALCOM fits into the same probabilistic framework for speech recognition as HMMs, but it represents a more realistic model of the speech production process. To evaluate the extent to which MALCOM captures speech production information, we generated continuous speech continuity maps for three speakers and used the paths through them to predict measured speech articulator data. The median correlation between the MALCOM paths obtained from only the speech acoustics and articulator measurements was 0.77 on an independent test set not used to train MALCOM or the predictor.

Determining the relationship between the activity of a single nerve cell to that of an entire population is a fundamental question that bears on the basic neural computation paradigms. In this paper we apply an information theoretic approach to quantify the level of cooperative activity among cells in a behavioral context. It is possible to discriminate between synergetic activity of the cells vs. redundant activity, depending on the difference between the information they provide when measured jointly and the information they provide independently. We define a synergy value that is positive in the first case and negative in the second and show that the synergy value can be measured by detecting the behavioral mode of the animal from simultaneously recorded activity of the cells. We observe that among cortical cells positive synergy can be found, while cells from the basal ganglia, active during the same task, do not exhibit similar synergetic activity.

A directed generative model for binary data using a small number of hidden continuous units is investigated. The relationships between the correlations of the underlying continuous Gaussian variables and the binary output variables are utilized to learn the appropriate weights of the network. The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten digit images. Introduction Principal Components Analysis (PCA) is a widely used statistical technique for representing data with a large number of variables [1]. It is based upon the assumption that although the data is embedded in a high dimensional vector space, most of the variability in the data is captured by a much lower climensional manifold.

A directed generative model for binary data using a small number of hidden continuous units is investigated. The relationships between the correlations of the underlying continuous Gaussian variables and the binary output variables are utilized to learn the appropriate weights of the network. The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten digit images. Introduction Principal Components Analysis (PCA) is a widely used statistical technique for representing data with a large number of variables [1]. It is based upon the assumption that although the data is embedded in a high dimensional vector space, most of the variability in the data is captured by a much lower climensional manifold. In particular for PCA, this manifold is described by a linear hyperplane whose characteristic directions are given by the eigenvectors of the correlation matrix with the largest eigenvalues. The success of PCA and closely related techniques such as Factor Analysis (FA) and PCA mixtures clearly indicate that much real world data exhibit the low dimensional manifold structure assumed by these models [2, 3]. However, the linear manifold structure of PCA is not appropriate for data with binary valued variables.

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classification models with Gaussian processes. In contrast to previous approaches, no knowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given.

A dynamic tree model specifies a prior over a large number of trees, each one of which is a tree-structured belief net (TSBN). Our aim is to retain the advantages of tree-structured belief networks, namely the hierarchical structure of the model and (in part) the efficient inference algorithms, while avoiding the "blocky" artifacts that derive from a single, fixed TSBN structure. One use for DTs is as prior models over labellings for image segmentation problems. Section 2 of the paper gives the theory of DTs, and experiments are described in section 3. 2 Theory There are two essential components that make up a dynamic tree network (i) the tree architecture and (ii) the nodes and conditional probability tables (CPTs) in the given tree. We consider the architecture question first.

We describe a real-time computer vision and machine learning system for modeling and recognizing human behaviors in two different scenarios: (1) complex, twohanded action recognition in the martial art of Tai Chi and (2) detection and recognition of individual human behaviors and multiple-person interactions in a visual surveillance task. In the latter case, the system is particularly concerned with detecting when interactions between people occur, and classifying them. Graphical models, such as Hidden Markov Models (HMMs) [6] and Coupled Hidden Markov Models (CHMMs) [3, 2], seem appropriate for modeling and, classifying human behaviors because they offer dynamic time warping, a well-understood training algorithm, and a clear Bayesian semantics for both individual (HMMs) and interacting or coupled (CHMMs) generative processes. A major problem with this data-driven statistical approach, especially when modeling rare or anomalous behaviors, is the limited number of training examples. A major emphasis of our work, therefore, is on efficient Bayesian integration of both prior knowledge with evidence from data. We will show that for situations involving multiple independent (or partially independent) agents the Coupled HMM approach generates much better results than traditional HMM methods. In addition, we have developed a synthetic agent or Alife modeling environment for building and training flexible a priori models of various behaviors using software agents. Simulation with these software agents yields synthetic data that can be used to train prior models. These prior models can then be used recursively in a Bayesian framework to fit real behavioral data.

Arguably one of the most important types of information processing is the capacity for probabilistic reasoning. The properties of undirectedproDabilistic models represented as symmetric networks have been studied extensively using methods from statistical mechanics (Hertz et aI, 1991). Detailed analyses of these models are possible by exploiting averaging phenomena that occur in the thermodynamic limit of large networks. In this paper, we analyze the limit of large, multilayer networks for probabilistic models represented as directed acyclic graphs. These models are known as Bayesian networks (Pearl, 1988; Neal, 1992), and they have different probabilistic semantics than symmetric neural networks (such as Hopfield models or Boltzmann machines). We show that the intractability of exact inference in multilayer Bayesian networks Inference in Multilayer Networks via Large Deviation Bounds 261 does not preclude their effective use. Our work builds on earlier studies of variational methods (Jordan et aI, 1997).

The model parameters are learned in an unsupervised manner by maximizing the likelihood that these data are generated by the model. A multilayer belief network is a realization of such a model. Many belief networks have been proposed that are composed of binary units. The hidden units in such networks represent latent variables that explain different features of the data, and whose relation to the ·Current address: Gatsby Computational Neuroscience Unit, University College London, 17 Queen Square, London WC1N 3AR, U.K. 362 H. Attias data is highly nonlinear. However, for tasks such as object and speech recognition which produce real-valued data, the models provided by binary networks are often inadequate.

One of the simplest methods is to use linear transformations of the observed data.