Classifiers often achieve higher test set accuracy than generative Classifiers (e.g., [6, 4, 14]).

Discrete Fourier transforms and other related Fourier methods have been practically implementable due to the fast Fourier transform (FFT). However there are many situations where doing fast Fourier transforms without complete data would be desirable. In this paper itis recognised that formulating the FFT algorithm as a belief network allows suitable priors to be set for the Fourier coefficients. Furthermore efficient generalised belief propagation methods between clustersof four nodes enable the Fourier coefficients to be inferred and the missing data to be estimated in near to O(n log n) time, where n is the total of the given and missing data points. This method is compared with a number of common approaches such as setting missing data to zero or to interpolation. It is tested on generated data and for a Fourier analysis of a damaged audio signal.

Recent multi-agent extensions of Q-Learning require knowledge of other agents' payoffs and Q-functions, and assume game-theoretic play at all times by all other agents. This paper proposes a fundamentally different approach, dubbed "Hyper-Q" Learning, in which values of mixed strategies rather than base actions are learned, and in which other agents' strategies are estimated from observed actions via Bayesian inference. Hyper-Qmay be effective against many different types of adaptive agents, even if they are persistently dynamic. Against certain broad categories of adaptation, it is argued that Hyper-Q may converge to exact optimaltime-varying policies. In tests using Rock-Paper-Scissors, Hyper-Q learns to significantly exploit an Infinitesimal Gradient Ascent (IGA) player, as well as a Policy Hill Climber (PHC) player. Preliminary analysis of Hyper-Q against itself is also presented.

Existing source location and recovery algorithms used in magnetoencephalographic imaginggenerally assume that the source activity at different brain locations is independent or that the correlation structure is known.

The purpose of this paper is to investigate infinity-sample properties of risk minimization based multi-category classification methods. These methods can be considered as natural extensions to binary large margin classification. We establish conditions that guarantee the infinity-sample consistency of classifiers obtained in the risk minimization framework. Examples are provided for two specific forms of the general formulation, which extend a number of known methods. Using these examples, we show that some risk minimization formulations can also be used to obtain conditionalprobability estimates for the underlying problem. Such conditional probability information will be useful for statistical inferencing tasksbeyond classification.

When we learn a new motor skill, we have to contend with both the variability inherentin our sensors and the task. The sensory uncertainty can be reduced by using information about the distribution of previously experienced tasks.Here we impose a distribution on a novel sensorimotor task and manipulate the variability of the sensory feedback. We show that subjects internally represent both the distribution of the task as well as their sensory uncertainty. Moreover, they combine these two sources of information in a way that is qualitatively predicted by optimal Bayesian processing. We further analyze if the subjects can represent multimodal distributions such as mixtures of Gaussians. The results show that the CNS employs probabilistic models during sensorimotor learning even when the priors are multimodal.

Rao-Blackwellization is an approximation technique for probabilistic inference thatflexibly combines exact inference with sampling. It is useful in models where conditioning on some of the variables leaves a simpler inferenceproblem that can be solved tractably. This paper presents Sample Propagation, an efficient implementation of Rao-Blackwellized approximate inference for a large class of models. Sample Propagation tightly integrates sampling with message passing in a junction tree, and is named for its simple, appealing structure: it walks the clusters of a junction tree, sampling some of the current cluster's variables and then passing a message to one of its neighbors. We discuss the application of Sample Propagation to conditional Gaussian inference problems such as switching linear dynamical systems.

Loopy belief propagation (BP) has been successfully used in a number ofdifficult graphical models to find the most probable configuration ofthe hidden variables. In applications ranging from protein folding to image analysis one would like to find not just the best configuration but rather the top M. While this problem has been solved using the junction tree formalism, in many real world problems theclique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configurations whenexact inference is impossible. We start by developing a new exact inference algorithm for calculating thebest configurations that uses only max-marginals. For approximate inference,we replace the max-marginals with the beliefs calculated using max-product BP and generalized BP. We show empirically thatthe algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.

The bootstrap has become a popular method for exploring model (structure) uncertainty. Our experiments with artificial and realworld datademonstrate that the graphs learned from bootstrap samples can be severely biased towards too complex graphical models. Accountingfor this bias is hence essential, e.g., when exploring model uncertainty. We find that this bias is intimately tied to (well-known) spurious dependences induced by the bootstrap. The leading-order bias-correction equals one half of Akaike's penalty for model complexity. We demonstrate the effect of this simple bias-correction in our experiments. We also relate this bias to the bias of the plugin estimator for entropy, as well as to the difference betweenthe expected test and training errors of a graphical model, which asymptotically equals Akaike's penalty (rather than one half).

A general linear response method for deriving improved estimates of correlations in the variational Bayes framework is presented.