Figure/ground assignment, in which the visual image is divided into nearer (figural) andfarther (ground) surfaces, is an essential step in visual processing, but its underlying computational mechanisms are poorly understood. Figural assignment (often referred to as border ownership) can vary along a contour, suggesting a spatially distributed process whereby local and global cues are combined to yield local estimates of border ownership. In this paper we model figure/ground estimation ina Bayesian belief network, attempting to capture the propagation of border ownership across the image as local cues (contour curvature and T-junctions) interact withmore global cues to yield a figure/ground assignment. Our network includes as a nonlocal factor skeletal (medial axis) structure, under the hypothesis that medial structure "draws" border ownership so that borders are owned by the skeletal hypothesis that best explains them. We also briefly present a psychophysical experimentin which we measured local border ownership along a contour at various distances from an inducing cue (a T-junction).

We consider reinforcement learning in partially observable domains where the agent can query an expert for demonstrations. Our nonparametric Bayesian approach combines model knowledge, inferred from expert information and independent exploration, with policy knowledge inferred from expert trajectories. We introduce priors that bias the agent towards models with both simple representations and simple policies, resulting in improved policy and model learning.

This paper introduces the first set of PAC-Bayesian bounds for the batch reinforcement learning problem in finite state spaces. These bounds hold regardless of the correctness of the prior distribution. We demonstrate how such bounds can be used for model-selection in control problems where prior information is available either on the dynamics of the environment, or on the value of actions. Our empirical results confirm that PAC-Bayesian model-selection is able to leverage prior distributions when they are informative and, unlike standard Bayesian RL approaches, ignores them when they are misleading.

A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Though these methods work well for low-dimensional problems, they are not suitable in high dimensional settings. In this paper, we present StARS: a new stability-based method for choosing the regularization parameter in high dimensional inference for undirected graphs. The method has a clear interpretation: we use the least amount of regularization that simultaneously makes a graph sparse and replicable under random sampling. This interpretation requires essentially no conditions. Under mild conditions, we show that StARS is partially sparsistent in terms of graph estimation: i.e. with high probability, all the true edges will be included in the selected model even when the graph size asymptotically increases with the sample size. Empirically, the performance of StARS is compared with the state-of-the-art model selection procedures, including $K$-CV, AIC, and BIC, on both synthetic data and a real microarray dataset. StARS outperforms all competing procedures.

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the asymptotic consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjuction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordinary Bayesian information criterion when p and the number of non-zero parameters q both scale with n.

Optimal coding provides a guiding principle for understanding the representation of sensory variables in neural populations. Here we consider the influence of a prior probability distribution over sensory variables on the optimal allocation of cells and spikes in a neural population. We model the spikes of each cell as samples from an independent Poisson process with rate governed by an associated tuning curve. For this response model, we approximate the Fisher information in terms of the density and amplitude of the tuning curves, under the assumption that tuning width varies inversely with cell density. We consider a family of objective functions based on the expected value, over the sensory prior, of a functional of the Fisher information. This family includes lower bounds on mutual information and perceptual discriminability as special cases. In all cases, we find a closed form expression for the optimum, in which the density and gain of the cells in the population are power law functions of the stimulus prior. This also implies a power law relationship between the prior and perceptual discriminability. We show preliminary evidence that the theory successfully predicts the relationship between empirically measured stimulus priors, physiologically measured neural response properties (cell density, tuning widths, and firing rates), and psychophysically measured discrimination thresholds.

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn the structure of the graph by estimating a sparse inverse covariance matrix from sample data, by solving a convex maximum likelihood problem with an $\ell_1$-regularization term. In this paper, we propose a first-order method based on an alternating linearization technique that exploits the problem's special structure; in particular, the subproblems solved in each iteration have closed-form solutions. Moreover, our algorithm obtains an $\epsilon$-optimal solution in $O(1/\epsilon)$ iterations. Numerical experiments on both synthetic and real data from gene association networks show that a practical version of this algorithm outperforms other competitive algorithms.

Identifying the features of objects becomes a challenge when those features can change in their appearance. We introduce the Transformed Indian Buffet Process (tIBP), and use it to define a nonparametric Bayesian model that infers features that can transform across instantiations. We show that this model can identify features that are location invariant by modeling a previous experiment on human feature learning. However, allowing features to transform adds new kinds of ambiguity: Are two parts of an object the same feature with different transformations or two unique features? What transformations can features undergo? We present two new experiments in which we explore how people resolve these questions, showing that the tIBP model demonstrates a similar sensitivity to context to that shown by human learners when determining the invariant aspects of features.

We present a novel method for constructing dependent Dirichlet processes. The approach exploits the intrinsic relationship between Dirichlet and Poisson processes inorder to create a Markov chain of Dirichlet processes suitable for use as a prior over evolving mixture models. The method allows for the creation, removal, andlocation variation of component models over time while maintaining the property that the random measures are marginally DP distributed. Additionally, wederive a Gibbs sampling algorithm for model inference and test it on both synthetic and real data. Empirical results demonstrate that the approach is effective inestimating dynamically varying mixture models.

Bayesian approaches to utility elicitation typically adopt (myopic) expected value of information (EVOI)as a natural criterion for selecting queries. However, EVOI-optimization is usually computationally prohibitive. In this paper, we examine EVOI optimization using choice queries, queries in which a user is ask to select her most preferred product from a set. We show that, under very general assumptions, the optimal choice query w.r.t. EVOI coincides with the optimal recommendation set, that is, a set maximizing the expected utility ofthe user selection. Since recommendation set optimization is a simpler, submodular problem, this can greatly reduce the complexity of both exact and approximate (greedy) computation of optimal choice queries. We also examine the case where user responses to choice queries are error-prone (using both constant and mixed multinomial logit noise models) and provide worst-case guarantees. Finally we present a local search technique for query optimization that works extremely well with large outcome spaces.