Recent research has demonstrated that useful POMDP solutions do not require consideration of the entire belief space. We extend this idea with the notion of temporal abstraction. We present and explore a new reinforcement learning algorithm over grid-points in belief space, which uses macro-actions and Monte Carlo updates of the Q-values. We apply the algorithm to a large scale robot navigation task and demonstrate that with temporal abstraction we can consider an even smaller part of the belief space, we can learn POMDP policies faster, and we can do information gathering more efficiently.

Recent developments in grid-based and point-based approximation algorithms for POMDPs have greatly improved the tractability of POMDP planning. These approaches operate on sets of belief points by individually learning a value function for each point. In reality, belief points exist in a highly-structured metric simplex, but current POMDP algorithms do not exploit this property. This paper presents a new metric-tree algorithm which can be used in the context of POMDP planning to sort belief points spatially, and then perform fast value function updates over groups of points. We present results showing that this approach can reduce computation in point-based POMDP algorithms for a wide range of problems.

We consider learning to classify cognitive states of human subjects, based on their brain activity observed via functional Magnetic Resonance Imaging (fMRI). This problem is important because such classifiers constitute "virtual sensors" of hidden cognitive states, which may be useful in cognitive science research and clinical applications. In recent work, Mitchell, et al. [6,7,9] have demonstrated the feasibility of training such classifiers for individual human subjects (e.g., to distinguish whether the subject is reading an ambiguous or unambiguous sentence, or whether they are reading a noun or a verb). Here we extend that line of research, exploring how to train classifiers that can be applied across multiple human subjects, including subjects who were not involved in training the classifier. We describe the design of several machine learning approaches to training multiple-subject classifiers, and report experimental results demonstrating the success of these methods in learning cross-subject classifiers for two different fMRI data sets.

We examine the use of hidden Markov and hidden semi-Markov models for automatically segmenting an electrocardiogram waveform into its constituent waveform features. An undecimated wavelet transform is used to generate an overcomplete representation of the signal that is more appropriate for subsequent modelling. We show that the state durations implicit in a standard hidden Markov model are ill-suited to those of real ECG features, and we investigate the use of hidden semi-Markov models for improved state duration modelling.

Although discriminatively trained classifiers are usually more accurate when labeled training data is abundant, previous work has shown that when training data is limited, generative classifiers can outperform them. This paper describes a hybrid model in which a high-dimensional subset of the parameters are trained to maximize generative likelihood, and another, small, subset of parameters are discriminatively trained to maximize conditional likelihood. We give a sample complexity bound showing that in order to fit the discriminative parameters well, the number of training examples required depends only on the logarithm of the number of feature occurrences and feature set size. Experimental results show that hybrid models can provide lower test error and can produce better accuracy/coverage curves than either their purely generative or purely discriminative counterparts. We also discuss several advantages of hybrid models, and advocate further work in this area.

In pattern classification tasks, errors are introduced because of differences between the true model and the one obtained via model estimation. Using likelihood-ratio based classification, it is possible to correct for this discrepancy by finding class-pair specific terms to adjust the likelihood ratio directly, and that can make class-pair preference relationships intransitive. In this work, we introduce new methodology that makes necessary corrections to the likelihood ratio, specifically those that are necessary to achieve perfect classification (but not perfect likelihood-ratio correction which can be overkill). The new corrections, while weaker than previously reported such adjustments, are analytically challenging since they involve discontinuous functions, therefore requiring several approximations. We test a number of these new schemes on an isolatedword speech recognition task as well as on the UCI machine learning data sets. Results show that by using the bias terms calculated in this new way, classification accuracy can substantially improve over both the baseline and over our previous results.

The bootstrap has become a popular method for exploring model (structure) uncertainty. Our experiments with artificial and realworld data demonstrate that the graphs learned from bootstrap samples can be severely biased towards too complex graphical models. Accounting for 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 between the expected test and training errors of a graphical model, which asymptotically equals Akaike's penalty (rather than one half).

We present a novel method for approximate inference in Bayesian models and regularized risk functionals. It is based on the propagation of mean and variance derived from the Laplace approximation of conditional probabilities in factorizing distributions, much akin to Minka's Expectation Propagation. In the jointly normal case, it coincides with the latter and belief propagation, whereas in the general case, it provides an optimization strategy containing Support Vector chunking, the Bayes Committee Machine, and Gaussian Process chunking as special cases.

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 it is 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 clusters of 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.

Rao-Blackwellization is an approximation technique for probabilistic inference that flexibly combines exact inference with sampling. It is useful in models where conditioning on some of the variables leaves a simpler inference problem 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.