We present a new approximate learning algorithm for Boltzmann Machines, using a systematic expansion of the Gibbs free energy to second order in the weights. The linear response correction to the correlations is given by the Hessian of the Gibbs free energy. The computational complexity of the algorithm is cubic in the number of neurons. We compare the performance of the exact BM learning algorithm with first order (Weiss) mean field theory and second order (TAP) mean field theory. The learning task consists of a fully connected Ising spin glass model on 10 neurons. We conclude that 1) the method works well for paramagnetic problems 2) the TAP correction gives a significant improvement over the Weiss mean field theory, both for paramagnetic and spin glass problems and 3) that the inclusion of diagonal weights improves the Weiss approximation for paramagnetic problems, but not for spin glass problems.

A simple linear averaging of the outputs of several networks as e.g. in bagging [3], seems to follow naturally from a bias/variance decomposition of the sum-squared error. The sum-squared error of the average model is a quadratic function of the weighting factors assigned to the networks in the ensemble [7], suggesting a quadratic programming algorithm for finding the "optimal" weighting factors. If we interpret the output of a network as a probability statement, the sum-squared error corresponds to minus the loglikelihood or the Kullback-Leibler divergence, and linear averaging of the outputs tologarithmic averaging of the probability statements: the logarithmic opinion pool. The crux of this paper is that this whole story about model averaging, bias/variancedecompositions, and quadratic programming to find the optimal weighting factors, is not specific for the sumsquared error,but applies to the combination of probability statements of any kind in a logarithmic opinion pool, as long as the Kullback-Leibler divergence plays the role of the error measure. As examples we treat model averaging for classification models under a cross-entropy error measure and models for estimating variances.

Conditioning experiments probe the ways that animals make predictions aboutrewards and punishments and use those predictions to control their behavior. One standard model of conditioning paradigms which involve many conditioned stimuli suggests that individual predictions should be added together. Various key results show that this model fails in some circumstances, and motivate analternative model, in which there is attentional selection between different available stimuli. The new model is a form of mixture of experts, has a close relationship with some other existing psychologicalsuggestions, and is statistically well-founded.

The National Aeronautics and Space Administration Jet Propulsion Laboratory (Pasadena, Calif.) has developed The chip, which has The National Aeronautics and Chester, N.Y.) to improve its ability to been licensed by automaker Ford Space Administration (NASA) Goddard match reported wage information. Motor (Dearborn, Mich.), is designed Space Flight Center (Greenbelt, The solution will help the agency to augment current vehicle on-board Md.) has developed the The Philippines (Quezon City, The process for outside scientists wanting RoyScot Trust, the asset finance arm Philippines) has adopted an intelligent to use NASA's space telescopes. of the Royal Bank of Scotland (Edinburgh, agent-based software system to The system is designed to capture and Scotland), has implemented an manage mission-critical tax processes maintain key scientific knowledge expert system-based solution to automate across The Philippines. The intelligent while it reduces common errors made the credit-underwriting process. The firm has set up a credit control management of the bureau's entire Johnson Controls (Milwaukee, Wis.), system, The turnkey expert installs and maintains. By integrating component has deployed a speech-recognition- frequent air travelers through U.S. math data with work-cell visualization based application for its frequent flier Immigration inspection in less than software, engineers can simulate customers.

This article introduces a generic framework for constraint-directed search. The research literature in constraint-directed scheduling is placed within the framework both to provide insight into, and examples of, the framework and to allow a new perspective on the scheduling literature. We show how a number of algorithms from the constraint-directed scheduling research can be conceptualized within the framework. This conceptualization allows us to identify and compare variations of components of our framework and provides new perspective on open research issues. We discuss the prospects for an overall comparison of scheduling strategies and show that firm conclusions vis-a-vis such a comparison are not supported by the literature. Our principal conclusion is the need for an empirical model of both the characteristics of scheduling problems and the solution techniques themselves. Our framework is offered as a tool for the development of such an understanding of constraint-directed scheduling and, more generally, constraint-directed search.

The "Naive Physics Manifesto" of Pat Hayes (1978) proposes a large-scale project to develop a formal theory encompassing the entire knowledge of physics of naive reasoners, expressed in a declarative symbolic form. The theory is organized in clusters of closely interconnected concepts and axioms. More recent work on the representation of commonsense physical knowledge has followed a somewhat different methodology. The goal has been to develop a competence theory powerful enough to justify commonsense physical inferences, and the research is organized in microworlds, each microworld covering a small range of physical phenomena. In this article, I compare the advantages and disadvantages of the two approaches.

Artificial Intelligence (AAAI) Email: zhong@ai.csse.

It is a northern European city of 100,000, almost on the border between the Republic of Ireland and Northern Ireland. The local press (The Derry Journal north Derry coast, with beautiful meetings enjoyed themselves and & Belfast Telegraph) and radio (BBC beaches at Benone and Castlenock expressed their congratulations on Northern Ireland) ran a number of and then through Coleraine to the the program and organization. Also, articles leading up to and during the seaside resorts of Portstewart and for the first time, AICS attracted a conference. All plenary invited speaker Portrush. A few kilometers further large number of delegates and papers talks and the panel session went out along the north Antrim coast, we from abroad, including many from on streaming video and audio, stored arrive at the Giants' Causeway and the United Kingdom, Europe, and Sauce!); Gweedore, home of the Clannad and live with the possibility of phonein for Pattern Recognition (IAPR), the They did lie in the areas of evidential reasoning, AICS-97, the Annual Conference of a supreme job.

Fourth, causality is still an important issue; some formal models of causality have surprisingly close connections to standard nonmonotonic techniques. Fifth, the nonmonotonic logics being used most widely are the classical ones: default logic, circumscription, and by Isaac Levi; (3) Nonmonotonic Reasoning autoepistemic logic. Maybe the most remarkable trend he Seventh International Workshop was held in Trento, Italy, Tolerance by John McCarthy; (4) that became apparent during the on 30 May to 1 June 1998 in conjunction Learning to Make Nonmonotonic workshop was the new excitement with the Sixth International Inferences by Dan Roth; and (5) From among the participants. The depression Conference on the Principles of Features and Fluents to Thinking that plagued a number of people Knowledge Representation and Reasoning When Flying--Reasoning about in the field seems to be over. The workshop was Actions in an Intelligent UAV by Erik common feeling was that the theory sponsored by the American Association Sandewall.

The Second International Symposium on Intelligent Data Analysis (IDA97) was held at Birkbeck College, University of London, on 4 to 6 August 1997. The main theme of IDA97 was to reason about how to analyze data,perhaps as human analysts do, by exploiting many methods from diverse disciplines. This article outlines several key issues and challenges, discusses how they were addressed at the conference, and presents opportunities for further work in the field.