We propose a novel clustering method that is an extension of ideas inherent toscale-space clustering and support-vector clustering. Like the latter, itassociates every data point with a vector in Hilbert space, and like the former it puts emphasis on their total sum, that is equal to the scalespace probabilityfunction. The novelty of our approach is the study of an operator in Hilbert space, represented by the Schrödinger equation of which the probability function is a solution. This Schrödinger equation contains a potential function that can be derived analytically from the probability function.

Hinton Gatsby Unit, UCL London, UK WCIN 3AR hinton@gatsby.ucl.ac.uk Abstract Logistic units in the first hidden layer of a feedforward neural network computethe relative probability of a data point under two Gaussians. This leads us to consider substituting other density models. We present an architecture for performing discriminative learning of Hidden Markov Models using a network of many small HMM's. Experiments on speech data show it to be superior to the standard method of discriminatively training HMM's. 1 Introduction A standard way of performing classification using a generative model is to divide the training cases into their respective classes and then train a set of class conditional models. This unsupervised approach to classification is appealing for two reasons.

We propose a novel method for the analysis of sequential data that exhibits an inherent mode switching. In particular, the data might be a non-stationary time series from a dynamical system that switches between multiple operating modes. Unlike other approaches, ourmethod processes the data incrementally and without any training of internal parameters. We use an HMM with a dynamically changingnumber of states and an online variant of the Viterbi algorithm that performs an unsupervised segmentation and classification of the data on-the-fly, i.e. the method is able to process incomingdata in real-time. The main idea of the approach is to track and segment changes of the probability density of the data in a sliding window on the incoming data stream.

The choice of an SVM kernel corresponds to the choice of a representation ofthe data in a feature space and, to improve performance, it should therefore incorporate prior knowledge such as known transformation invariances. We propose a technique which extends earlier work and aims at incorporating invariances in nonlinear kernels.We show on a digit recognition task that the proposed approach is superior to the Virtual Support Vector method, which previously had been the method of choice. 1 Introduction In some classification tasks, an a priori knowledge is known about the invariances related to the task. For instance, in image classification, we know that the label of a given image should not change after a small translation or rotation.

The partition function for a Boltzmann machine can be bounded from above and below. We can use this to bound the means and the correlations. For networks with small weights, the values of these statistics can be restricted to nontrivial regions (i.e. a subset of [-1, 1]). Experimental results show that reasonable bounding occurs for weight sizes where mean field expansions generally give good results. 1 Introduction Over the last decade, bounding techniques have become a popular tool to deal with graphical models that are too complex for exact computation. A nice property of bounds is that they give at least some information you can rely on.

Originally introduced them together in a synergistic manner has resulted by Clausewitz in his classical work On in faster progress for each of them. War (1976), the center of gravity is now understood Moreover, it offers a new perspective on how to as representing "those characteristics, capabilities, combine research in AI with research in a specialized or localities from which a military domain and with the development force derives its freedom of action, physical and deployment of prototype systems in education strength, or will to fight" (Joint Chiefs of Staff and practice.

Send applications and inquiries to May Cheh; National Library of Medicine, 8600 Rockville Pike, Mail Stop 54, Bethesda, MD 20894-6075; Email: cheh@nlm.nih.gov

Much work in AI deals with the selection of proper actions in a given (known or unknown) environment. However, the way to select a proper action when facing other agents is quite unclear. Most work in AI adopts classical game-theoretic equilibrium analysis to predict agent behavior in such settings. This approach however does not provide us with any guarantee for the agent. In this paper we introduce competitive safety analysis. This approach bridges the gap between the desired normative AI approach, where a strategy should be selected in order to guarantee a desired payoff, and equilibrium analysis. We show that a safety level strategy is able to guarantee the value obtained in a Nash equilibrium, in several classical computer science settings. Then, we discuss the concept of competitive safety strategies, and illustrate its use in a decentralized load balancing setting, typical to network problems. In particular, we show that when we have many agents, it is possible to guarantee an expected payoff which is a factor of 8/9 of the payoff obtained in a Nash equilibrium. Our discussion of competitive safety analysis for decentralized load balancing is further developed to deal with many communication links and arbitrary speeds. Finally, we discuss the extension of the above concepts to Bayesian games, and illustrate their use in a basic auctions setup.

We develop, analyze, and evaluate a novel, supervised, specific-to-general learner for a simple temporal logic and use the resulting algorithm to learn visual event definitions from video sequences. First, we introduce a simple, propositional, temporal, event-description language called AMA that is sufficiently expressive to represent many events yet sufficiently restrictive to support learning. We then give algorithms, along with lower and upper complexity bounds, for the subsumption and generalization problems for AMA formulas. We present a positive-examples--only specific-to-general learning method based on these algorithms. We also present a polynomial-time--computable ``syntactic'' subsumption test that implies semantic subsumption without being equivalent to it. A generalization algorithm based on syntactic subsumption can be used in place of semantic generalization to improve the asymptotic complexity of the resulting learning algorithm. Finally, we apply this algorithm to the task of learning relational event definitions from video and show that it yields definitions that are competitive with hand-coded ones.

This paper presents a new classifier combination technique based on the Dempster-Shafer theory of evidence. The Dempster-Shafer theory of evidence is a powerful method for combining measures of evidence from different classifiers. However, since each of the available methods that estimates the evidence of classifiers has its own limitations, we propose here a new implementation which adapts to training data so that the overall mean square error is minimized. The proposed technique is shown to outperform most available classifier combination methods when tested on three different classification problems.