With the increased availability of data for complex domains, it is desirable to learn Bayesian network structures that are sufficiently expressive for generalization while also allowing for tractable inference. While the method of thin junction trees can, in principle, be used for this purpose, its fully greedy nature makes it prone to overfitting, particularly when data is scarce. In this work we present a novel method for learning Bayesian networks of bounded treewidth that employs global structure modifications and that is polynomial in the size of the graph and the treewidth bound. At the heart of our method is a triangulated graph that we dynamically update in a way that facilitates the addition of chain structures that increase the bound on the model's treewidth by at most one. We demonstrate the effectiveness of our ``treewidth-friendly'' method on several real-life datasets. Importantly, we also show that by using global operators, we are able to achieve better generalization even when learning Bayesian networks of unbounded treewidth.

We propose a new model for natural image statistics. Instead of minimizing dependency between components of natural images, we maximize a simple form of dependency in the form of tree-dependency. By learning filters and tree structures which are best suited for natural images we observe that the resulting filters are edge filters, similar to the famous ICA on natural images results. Calculating the likelihood of the model requires estimating the squared output of pairs of filters connected in the tree. We observe that after learning, these pairs of filters are predominantly of similar orientations but different phases, so their joint energy resembles models of complex cells.

Cell assemblies exhibiting episodes of recurrent coherent activity have been observed in several brain regions including the striatum[1] and hippocampus CA3[2]. Here we address the question of how coherent dynamically switching assemblies appear in large networks of biologically realistic spiking neurons interacting deterministically.We show by numerical simulations of large asymmetric inhibitory networks with fixed external excitatory drive that if the network has intermediate to sparse connectivity, the individual cells are in the vicinity of a bifurcation betweena quiescent and firing state and the network inhibition varies slowly on the spiking timescale, then cells form assemblies whose members show strong positive correlation, while members of different assemblies show strong negative correlation. We show that cells and assemblies switch between firing and quiescent states with time durations consistent with a power-law. Our results are in good qualitative agreement with the experimental studies. The deterministic dynamical behaviouris related to winner-less competition[3], shown in small closed loop inhibitory networks with heteroclinic cycles connecting saddle-points.

We extend Dyna planning architecture for policy evaluation and control in two significant aspects. First, we introduce a multi-step Dyna planning that projects the simulated state/feature many steps into the future. Our multi-step Dyna is based on a multi-step model, which we call the {\em $\lambda$-model}. The $\lambda$-model interpolates between the one-step model and an infinite-step model, and can be learned efficiently online. Second, we use for Dyna control a dynamic multi-step model that is able to predict the results of a sequence of greedy actions and track the optimal policy in the long run. Experimental results show that Dyna using the multi-step model evaluates a policy faster than using single-step models; Dyna control algorithms using the dynamic tracking model are much faster than model-free algorithms; further, multi-step Dyna control algorithms enable the policy and value function to converge much faster to their optima than single-step Dyna algorithms.

Policy gradient Reinforcement Learning (RL) algorithms have received substantial attention,seeking stochastic policies that maximize the average (or discounted cumulative) reward. In addition, extensions based on the concept of the Natural Gradient (NG) show promising learning efficiency because these regard metrics for the task. Though there are two candidate metrics, Kakade's Fisher Information Matrix (FIM) for the policy (action) distribution and Morimura's FIM for the stateaction jointdistribution, but all RL algorithms with NG have followed Kakade's approach. In this paper, we describe a generalized Natural Gradient (gNG) that linearly interpolates the two FIMs and propose an efficient implementation for the gNG learning based on a theory of the estimating function, the generalized Natural Actor-Critic(gNAC) algorithm. The gNAC algorithm involves a near optimal auxiliary function to reduce the variance of the gNG estimates. Interestingly, the gNAC can be regarded as a natural extension of the current state-of-the-art NAC algorithm [1], as long as the interpolating parameter is appropriately selected. Numerical experimentsshowed that the proposed gNAC algorithm can estimate gNG efficiently and outperformed the NAC algorithm.

We propose a new approach to the analysis of Loopy Belief Propagation (LBP) by establishing a formula that connects the Hessian of the Bethe free energy with the edge zeta function. The formula has a number of theoretical implications on LBP. It is applied to give a sufficient condition that the Hessian of the Bethe free energy is positive definite, which shows non-convexity for graphs with multiple cycles. The formula clarifies the relation between the local stability of a fixed point of LBP and local minima of the Bethe free energy. We also propose a new approach to the uniqueness of LBP fixed point, and show various conditions of uniqueness.

When individuals independently recollect events or retrieve facts from memory, how can we aggregate these retrieved memories to reconstruct the actual set of events or facts? In this research, we report the performance of individuals in a series of general knowledge tasks, where the goal is to reconstruct from memory the order of historic events, or the order of items along some physical dimension. We introduce two Bayesian models for aggregating order information based on a Thurstonian approach and Mallows model. Both models assume that each individuals reconstruction is based on either a random permutation of the unobserved ground truth, or by a pure guessing strategy. We apply MCMC to make inferences about the underlying truth and the strategies employed by individuals. The models demonstrate a wisdom of crowds" effect, where the aggregated orderings are closer to the true ordering than the orderings of the best individual."

Motivated from real world problems, like object categorization, we study a particular mixed-norm regularization for Multiple Kernel Learning (MKL). It is assumed that the given set of kernels are grouped into distinct components where each component is crucial for the learning task at hand. The formulation hence employs $l_\infty$ regularization for promoting combinations at the component level and $l_1$ regularization for promoting sparsity among kernels in each component. While previous attempts have formulated this as a non-convex problem, the formulation given here is an instance of non-smooth convex optimization problem which admits an efficient Mirror-Descent (MD) based procedure. The MD procedure optimizes over product of simplexes, which is not a well-studied case in literature. Results on real-world datasets show that the new MKL formulation is well-suited for object categorization tasks and that the MD based algorithm outperforms state-of-the-art MKL solvers like \texttt{simpleMKL} in terms of computational effort.

We are often interested in casting classification and clustering problems in a regression framework, because it is feasible to achieve some statistical properties in this framework by imposing some penalty criteria. In this paper we illustrate optimal scoring, which was originally proposed for performing Fisher linear discriminant analysis by regression, in the application of unsupervised learning. In particular, we devise a novel clustering algorithm that we call optimal discriminant clustering (ODC). We associate our algorithm with the existing unsupervised learning algorithms such as spectral clustering, discriminative clustering and sparse principal component analysis. Thus, our work shows that optimal scoring provides a new approach to the implementation of unsupervised learning. This approach facilitates the development of new unsupervised learning algorithms.

We consider the problem of bounding from above the log-partition function corresponding to second-order Ising models for binary distributions. We introduce a new bound, the cardinality bound, which can be computed via convex optimization. The corresponding error on the logpartition functionis bounded above by twice the distance, in model parameter space, to a class of "standard" Ising models, for which variable interdependence is described via a simple mean field term. In the context of maximum-likelihood, using the new bound instead of the exact log-partition function, while constraining the distance to the class of standard Ising models, leads not only to a good approximation to the log-partition function, but also to a model that is parsimonious, and easily interpretable.We compare our bound with the log-determinant bound introduced by Wainwright and Jordan (2006), and show that when the l