The technique of principal component analysis (PCA) has recently been expressed as the maximum likelihood solution for a generative latent variable model. In this paper we use this probabilistic reformulation as the basis for a Bayesian treatment of PCA. Our key result is that effective dimensionalityof the latent space (equivalent to the number of retained principal components) can be determined automatically as part of the Bayesian inference procedure. An important application of this framework is to mixtures of probabilistic PCA models, in which each component can determine its own effective complexity. 1 Introduction Principal component analysis (PCA) is a widely used technique for data analysis. Recently Tipping and Bishop (1997b) showed that a specific form of generative latent variable model has the property that its maximum likelihood solution extracts the principal subspace of the observed data set.

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classification modelswith Gaussian processes. In contrast to previous approaches, noknowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given. They have been recently introduced into the Neural Computation community (Neal 1996, Williams & Rasmussen 1996, Mackay 1997). If we assume fields with zero prior mean, the statistics of h is entirely defined by the second order correlations C(s, S') E[h(s)h(S')], where E denotes expectations 310 MOpper and 0. Winther with respect to the prior. Interesting examples are C(s, s') (1) C(s, s') (2) The choice (1) can be motivated as a limit of a two-layered neural network with infinitely many hidden units with factorizable input-hidden weight priors (Williams 1997).

I consider the problem of learning concepts from small numbers of positive examples,a feat which humans perform routinely but which computers arerarely capable of. Bridging machine learning and cognitive science perspectives, I present both theoretical analysis and an empirical study with human subjects for the simple task oflearning concepts corresponding toaxis-aligned rectangles in a multidimensional feature space. Existing learning models, when applied to this task, cannot explain how subjects generalize from only a few examples of the concept. I propose a principled Bayesian model based on the assumption that the examples are a random sample from the concept to be learned. The model gives precise fits to human behavior on this simple task and provides qualitati ve insights into more complex, realistic cases of concept learning.

The Association for the Advancement of Artificial Intelligence (AAAI) held its 1998 Fall Symposium Series on 23 to 25 October at the Omni Rosen Hotel in Orlando, Florida. This article contains summaries of seven of the symposia that were conducted: (1) Cognitive Robotics; (2) Distributed, Continual Planning; (3) Emotional and Intelligent: The Tangled Knot of Cognition; (4) Integrated Planning for Autonomous Agent Architectures; (5) Planning with Partially Observable Markov Decision Processes; (6) Reasoning with Visual and Diagrammatic Representations; and (7) Robotics and Biology: Developing Connections.

AI has embraced medical applications from its inception, and some of the earliest work in successful application of AI technology occurred in medical contexts. Medicine in the twenty-first century will be very different than medicine in the late twentieth century. Fortunately, the technical challenges to AI that emerge are similar, and the prospects for success are high.

A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduces major current methods for exact computation, briefly surveys approximation methods, and closes with a brief discussion of open issues.

The last few years have seen a surge in interest in the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. The articles cover the topics of inference in Bayesian networks, decision-theoretic planning, and qualitative decision theory. Here, I provide a brief introduction to Bayesian networks and then cover applications of Bayesian problem-solving techniques, knowledge-based model construction and structured representations, and the learning of graphic probability models.

The recent advances in computer speed and algorithms for probabilistic inference have led to a resurgence of work on planning under uncertainty. The aim is to design AI planners for environments where there might be incomplete or faulty information, where actions might not always have the same results, and where there might be trade-offs between the different possible outcomes of a plan. Addressing uncertainty in AI, planning algorithms will greatly increase the range of potential applications, but there is plenty of work to be done before we see practical decision-theoretic planning systems. This article outlines some of the challenges that need to be overcome and surveys some of the recent work in the area.

The recent advances in computer speed and algorithms for probabilistic inference have led to a resurgence of work on planning under uncertainty. The aim is to design AI planners for environments where there might be incomplete or faulty information, where actions might not always have the same results, and where there might be trade-offs between the different possible outcomes of a plan. Addressing uncertainty in AI, planning algorithms will greatly increase the range of potential applications, but there is plenty of work to be done before we see practical decision-theoretic planning systems. This article outlines some of the challenges that need to be overcome and surveys some of the recent work in the area.

A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduces major current methods for exact computation, briefly surveys approximation methods, and closes with a brief discussion of open issues.