We develop a framework based on Bayesian model averaging to explain how animals cope with uncertainty about contingencies in classical conditioning experiments. Traditional accounts of conditioning fit parameters within a fixed generative model of reinforcer delivery; uncertainty over the model structure is not considered. We apply the theory to explain the puzzling relationship between second-order conditioning and conditioned inhibition, two similar conditioning regimes that nonetheless result in strongly divergent behavioral outcomes. According to the theory, second-order conditioning results when limited experience leads animals to prefer a simpler world model that produces spurious correlations; conditioned inhibition results when a more complex model is justified by additional experience.

We describe a Markov chain method for sampling from the distribution of the hidden state sequence in a nonlinear dynamical system, given a sequence of observations. This method updates all states in the sequence simultaneously using an embedded Hidden Markov Model (HMM). An update begins with the creation of "pools" of candidate states at each time. We then define an embedded HMM whose states are indexes within these pools. Using a forward-backward dynamic programming algorithm, we can efficiently choose a state sequence with the appropriate probabilities from the exponentially large number of state sequences that pass through states in these pools. We illustrate the method in a simple one-dimensional example, and in an example showing how an embedded HMM can be used to in effect discretize the state space without any discretization error. We also compare the embedded HMM to a particle smoother on a more substantial problem of inferring human motion from 2D traces of markers.

We describe a nonparametric Bayesian approach to generalizing from few labeled examples, guided by a larger set of unlabeled objects and the assumption of a latent tree-structure to the domain. The tree (or a distribution over trees) may be inferred using the unlabeled data. A prior over concepts generated by a mutation process on the inferred tree(s) allows efficient computation of the optimal Bayesian classification function from the labeled examples. We test our approach on eight real-world datasets.

In applying Hidden Markov Models to the analysis of massive data streams, it is often necessary to use an artificially reduced set of states; this is due in large part to the fact that the basic HMM estimation algorithms have a quadratic dependence on the size of the state set. We present algorithms that reduce this computational bottleneck to linear or near-linear time, when the states can be embedded in an underlying grid of parameters. This type of state representation arises in many domains; in particular, we show an application to traffic analysis at a high-volume Web site.

We present a connectionist architecture that can learn a model of the relations between perceptions and actions and use this model for behavior planning. State representations are learned with a growing selforganizing layer which is directly coupled to a perception and a motor layer. Knowledge about possible state transitions is encoded in the lateral connectivity. Motor signals modulate this lateral connectivity and a dynamic field on the layer organizes a planning process. All mechanisms are local and adaptation is based on Hebbian ideas. The model is continuous in the action, perception, and time domain.

Optimal solutions to Markov Decision Problems (MDPs) are very sensitive with respect to the state transition probabilities. In many practical problems, the estimation of those probabilities is far from accurate. Hence, estimation errors are limiting factors in applying MDPs to realworld problems. We propose an algorithm for solving finite-state and finite-action MDPs, where the solution is guaranteed to be robust with respect to estimation errors on the state transition probabilities. Our algorithm involves a statistically accurate yet numerically efficient representation of uncertainty, via Kullback-Leibler divergence bounds. The worst-case complexity of the robust algorithm is the same as the original Bellman recursion. Hence, robustness can be added at practically no extra computing cost.

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.

Predictive state representations (PSRs) use predictions of a set of tests to represent the state of controlled dynamical systems. One reason why this representation is exciting as an alternative to partially observable Markov decision processes (POMDPs) is that PSR models of dynamical systems may be much more compact than POMDP models. Empirical work on PSRs to date has focused on linear PSRs, which have not allowed for compression relative to POMDPs. We introduce a new notion of tests which allows us to define a new type of PSR that is nonlinear in general and allows for exponential compression in some deterministic dynamical systems. These new tests, called e-tests, are related to the tests used by Rivest and Schapire [1] in their work with the diversity representation, but our PSR avoids some of the pitfalls of their representation--in particular, its potential to be exponentially larger than the equivalent POMDP.

Loopy belief propagation (BP) has been successfully used in a number of difficult graphical models to find the most probable configuration of the 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 the clique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configurations when exact inference is impossible. We start by developing a new exact inference algorithm for calculating the best 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 that the algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.

We describe a new approximation algorithm for solving partially observable MDPs. Our bounded policy iteration approach searches through the space of bounded-size, stochastic finite state controllers, combining several advantages of gradient ascent (efficiency, search through restricted controller space) and policy iteration (less vulnerability to local optima).