How does the brain combine prior knowledge with sensory evidence when making decisions under uncertainty? Two competing descriptive models have been proposed based on experimental data. The first posits an additive offset to a decision variable, implying a static effect of the prior. However, this model is inconsistent with recent data from a motion discrimination task involving temporal integration of uncertain sensory evidence. To explain this data, a second model has been proposed which assumes a time-varying influence of the prior.

We consider the problem of learning control policies via trajectory preference queries to an expert. In particular, the learning agent can present an expert with short runs of a pair of policies originating from the same state and the expert then indicates the preferred trajectory. The agent's goal is to elicit a latent target policy from the expert with as few queries as possible. To tackle this problem we propose a novel Bayesian model of the querying process and introduce two methods that exploit this model to actively select expert queries. Experimental results on four benchmark problems indicate that our model can effectively learn policies from trajectory preference queries and that active query selection can be substantially more efficient than random selection.

Bayesian model-based reinforcement learning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, finding the resulting Bayes-optimal policies is notoriously taxing, since the search space becomes enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach outperformed prior Bayesian model-based RL algorithms by a significant margin on several well-known benchmark problems -- because it avoids expensive applications of Bayes rule within the search tree by lazily sampling models from the current beliefs. We illustrate the advantages of our approach by showing it working in an infinite state space domain which is qualitatively out of reach of almost all previous work in Bayesian exploration.

Focusing on short term trend prediction in a financial context, we consider the problem of selective prediction whereby the predictor can abstain from prediction in order to improve performance. We examine two types of selective mechanisms for HMM predictors. The first is a rejection in the spirit of Chow's well-known ambiguity principle. The second is a specialized mechanism for HMMs that identifies low quality HMM states and abstain from prediction in those states. We call this model selective HMM (sHMM).

We propose a novel class of Bayesian nonparametric models for sequential data called fragmentation-coagulation processes (FCPs). An FCP is exchangeable, projective, stationary and reversible, and its equilibrium distributions are given by the Chinese restaurant process. As opposed to hidden Markov models, FCPs allow for flexible modelling of the number of clusters, and they avoid label switching non-identifiability problems. We develop an efficient Gibbs sampler for FCPs which uses uniformization and the forward-backward algorithm. Our development of FCPs is motivated by applications in population genetics, and we demonstrate the utility of FCPs on problems of genotype imputation with phased and unphased SNP data.

This paper introduces timeline trees, which are partial models of partially observable environments. Timeline trees are given some specific predictions to make and learn a decision tree over history. The main idea of timeline trees is to use temporally abstract features to identify and split on features of key events, spread arbitrarily far apart in the past (whereas previous decision-tree-based methods have been limited to a finite suffix of history). Experiments demonstrate that timeline trees can learn to make high quality predictions in complex, partially observable environments with high-dimensional observations (e.g. an arcade game). Papers published at the Neural Information Processing Systems Conference.

The partition function plays a key role in probabilistic modeling including conditional random fields, graphical models, and maximum likelihood estimation. To optimize partition functions, this article introduces a quadratic variational upper bound. This inequality facilitates majorization methods: optimization of complicated functions through the iterative solution of simpler sub-problems. Such bounds remain efficient to compute even when the partition function involves a graphical model (with small tree-width) or in latent likelihood settings. For large-scale problems, low-rank versions of the bound are provided and outperform LBFGS as well as first-order methods.

We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We use this to show that the maximal Kullback-Leibler divergence to the RBM model with n visible and m hidden units is bounded from above by (n-1)-log(m 1). In this way we can specify the number of hidden units that guarantees a sufficiently rich model containing different classes of distributions and respecting a given error tolerance. Papers published at the Neural Information Processing Systems Conference.

We present a truncation-free online variational inference algorithm for Bayesian nonparametric models. Unlike traditional (online) variational inference algorithms that require truncations for the model or the variational distribution, our method adapts model complexity on the fly. Our experiments for Dirichlet process mixture models and hierarchical Dirichlet process topic models on two large-scale data sets show better performance than previous online variational inference algorithms. Papers published at the Neural Information Processing Systems Conference.

In this paper, we derive a novel algorithm to cluster hidden Markov models (HMMs) according to their probability distributions. We propose a variational hierarchical EM algorithm that i) clusters a given collection of HMMs into groups of HMMs that are similar, in terms of the distributions they represent, and ii) characterizes each group by a cluster center'', i.e., a novel HMM that is representative for the group. We illustrate the benefits of the proposed algorithm on hierarchical clustering of motion capture sequences as well as on automatic music tagging. Papers published at the Neural Information Processing Systems Conference.