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 Bayesoptimal 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.

A model connecting visual tracking and saliency has recently been proposed. This model is based on the saliency hypothesis for tracking which postulates that tracking is achieved by the top-down tuning, based on target features, of discriminant center-surround saliency mechanisms over time. In this work, we identify three main predictions that must hold if the hypothesis were true: 1) tracking reliability should be larger for salient than for non-salient targets, 2) tracking reliability should have a dependence on the defining variables of saliency, namely feature contrast and distractor heterogeneity, and must replicate the dependence of saliency on these variables, and 3) saliency and tracking can be implemented with common low level neural mechanisms. We confirm that the first two predictions hold by reporting results from a set of human behavior studies on the connection between saliency and tracking. We also show that the third prediction holds by constructing a common neurophysiologically plausible architecture that can computationally solve both saliency and tracking. This architecture is fully compliant with the standard physiological models of V1 and MT, and with what is known about attentional control in area LIP, while explaining the results of the human behavior experiments.

Statistical decision theory axiomatically assumes that the relative desirability of different options that humans perceive is well described by assigning them optionspecific scalar utility functions. However, this assumption is refuted by observed human behavior, including studies wherein preferences have been shown to change systematically simply through variation in the set of choice options presented. In this paper, we show that interpreting desirability as a relative comparison between available options at any particular decision instance results in a rational theory of value-inference that explains heretofore intractable violations of rational choice behavior in human subjects. Complementarily, we also characterize the conditions under which a rational agent selecting optimal options indicated by dynamic value inference in our framework will behave identically to one whose preferences are encoded using a static ordinal utility function.

We develop convergent minimization algorithms for Bethe variational approximations which explicitly constrain marginal estimates to families of valid distributions. While existing message passing algorithms define fixed point iterations corresponding to stationary points of the Bethe free energy, their greedy dynamics do not distinguish between local minima and maxima, and can fail to converge. For continuous estimation problems, this instability is linked to the creation of invalid marginal estimates, such as Gaussians with negative variance. Conversely, our approach leverages multiplier methods with well-understood convergence properties, and uses bound projection methods to ensure that marginal approximations are valid at all iterations. We derive general algorithms for discrete and Gaussian pairwise Markov random fields, showing improvements over standard loopy belief propagation. We also apply our method to a hybrid model with both discrete and continuous variables, showing improvements over expectation propagation.

This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions rather than to the usual sparse signals. The compressive measurements correspond to expected values of nonlinear functions of the probabilistically distributed variables. When these expected values are estimated by sampling, the quality of the compressed representation is limited only by the quality of sampling. Since the compression preserves the geometric structure of the space of sparse probability distributions, probabilistic computation can be performed in the compressed domain. Interestingly, functions satisfying the requirements of compressive sensing can be implemented as simple perceptrons. If we use perceptrons as a simple model of feedforward computation by neurons, these results show that the mean activity of a relatively small number of neurons can accurately represent a highdimensional joint distribution implicitly, even without accounting for any noise correlations. This comprises a novel hypothesis for how neurons could encode probabilities in the brain.

The variational Bayesian (VB) approach is one of the best tractable approximations to the Bayesian estimation, and it was demonstrated to perform well in many applications. However, its good performance was not fully understood theoretically. For example, VB sometimes produces a sparse solution, which is regarded as a practical advantage of VB, but such sparsity is hardly observed in the rigorous Bayesian estimation. In this paper, we focus on probabilistic PCA and give more theoretical insight into the empirical success of VB. More specifically, for the situation where the noise variance is unknown, we derive a sufficient condition for perfect recovery of the true PCA dimensionality in the large-scale limit when the size of an observed matrix goes to infinity. In our analysis, we obtain bounds for a noise variance estimator and simple closed-form solutions for other parameters, which themselves are actually very useful for better implementation of VB-PCA.

We present a novel method for learning densities with bounded support which enables us to incorporate'hard' topological constraints. In particular, we show how emerging techniques from computational algebraic topology and the notion of persistent homology can be combined with kernel-based methods from machine learning for the purpose of density estimation. The proposed formalism facilitates learning of models with bounded support in a principled way, and - by incorporating persistent homology techniques in our approach - we are able to encode algebraic-topological constraints which are not addressed in current state of the art probabilistic models. We study the behaviour of our method on two synthetic examples for various sample sizes and exemplify the benefits of the proposed approach on a real-world dataset by learning a motion model for a race car. We show how to learn a model which respects the underlying topological structure of the racetrack, constraining the trajectories of the car.

Mixture distributions are often used to model complex data. In this paper, we develop a new method that jointly estimates mixture models over multiple data sets by exploiting the statistical dependencies between them. Specifically, we introduce a set of latent Dirichlet processes as sources of component models (atoms), and for each data set, we construct a nonparametric mixture model by combining sub-sampled versions of the latent DPs. Each mixture model may acquire atoms from different latent DPs, while each atom may be shared by multiple mixtures. This multi-to-multi association distinguishes the proposed method from previous ones that require the model structure to be a tree or a chain, allowing more flexible designs. We also derive a sampling algorithm that jointly infers the model parameters and present experiments on both document analysis and image modeling.

We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.

We present a multi-task learning approach to jointly estimate the means of multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the single-task averages. We derive the optimal amount of regularization, and show that it can be effectively estimated. Simulations and real data experiments demonstrate that MTA outperforms both maximum likelihood and James-Stein estimators, and that our approach to estimating the amount of regularization rivals cross-validation in performance but is more computationally efficient.