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.

A non-parametric Bayesian model is proposed for processing multiple images. The analysis employs image features and, when present, the words associated with accompanying annotations. The model clusters the images into classes, and each image is segmented into a set of objects, also allowing the opportunity to assign a word to each object (localized labeling). Each object is assumed to be represented as a heterogeneous mix of components, with this realized via mixture models linking image features to object types. The number of image classes, number of object types, and the characteristics of the object-feature mixture models are inferred non-parametrically.

We present a nonparametric Bayesian method for texture learning and synthesis. A texture image is represented by a 2D-Hidden Markov Model (2D-HMM) where the hidden states correspond to the cluster labeling of textons and the transition matrix encodes their spatial layout (the compatibility between adjacent textons). The HDP makes use of Dirichlet process prior which favors regular textures by penalizing the model complexity. This framework (HDP-2D-HMM) learns the texton vocabulary and their spatial layout jointly and automatically. The HDP-2D-HMM results in a compact representation of textures which allows fast texture synthesis with comparable rendering quality over the state-of-the-art image-based rendering methods.

Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements.

The Partially Observable Markov Decision Process (POMDP) framework has proven useful in planning domains that require balancing actions that increase an agents knowledge and actions that increase an agents reward. Unfortunately, most POMDPs are complex structures with a large number of parameters. In many realworld problems, both the structure and the parameters are difficult to specify from domain knowledge alone. Recent work in Bayesian reinforcement learning has made headway in learning POMDP models; however, this work has largely focused on learning the parameters of the POMDP model. We define an infinite POMDP (iPOMDP) model that does not require knowledge of the size of the state space; instead, it assumes that the number of visited states will grow as the agent explores its world and explicitly models only visited states.

Markov random fields (MRFs), or undirected graphical models, provide a powerful framework for modeling complex dependencies among random variables. Maximum likelihood learning in MRFs is hard due to the presence of the global normalizing constant. In this paper we consider a class of stochastic approximation algorithms of Robbins-Monro type that uses Markov chain Monte Carlo to do approximate maximum likelihood learning. We show that using MCMC operators based on tempered transitions enables the stochastic approximation algorithm to better explore highly multimodal distributions, which considerably improves parameter estimates in large densely-connected MRFs. Our results on MNIST and NORB datasets demonstrate that we can successfully learn good generative models of high-dimensional, richly structured data and perform well on digit and object recognition tasks.

Continuous-time Markov chains are used to model systems in which transitions between states as well as the time the system spends in each state are random. Many computational problems related to such chains have been solved, including determining state distributions as a function of time, parameter estimation, and control. However, the problem of inferring most likely trajectories, where a trajectory is a sequence of states as well as the amount of time spent in each state, appears unsolved. We study three versions of this problem: (i) an initial value problem, in which an initial state is given and we seek the most likely trajectory until a given final time, (ii) a boundary value problem, in which initial and final states and times are given, and we seek the most likely trajectory connecting them, and (iii) trajectory inference under partial observability, analogous to finding maximum likelihood trajectories for hidden Markov models. We show that maximum likelihood trajectories are not always well-defined, and describe a polynomial time test for well-definedness.

In recent years, deep learning approaches have gained significant interest as a way of building hierarchical representations from unlabeled data. However, to our knowledge, these deep learning approaches have not been extensively studied for auditory data. In this paper, we apply convolutional deep belief networks to audio data and empirically evaluate them on various audio classification tasks. For the case of speech data, we show that the learned features correspond to phones/phonemes. In addition, our feature representations trained from unlabeled audio data show very good performance for multiple audio classification tasks. We hope that this paper will inspire more research on deep learning approaches applied to a wide range of audio recognition tasks.

In this paper we explore the problem of biasing unsupervised models to favor sparsity. We extend the posterior regularization framework [8] to encourage the model to achieve posterior sparsity on the unlabeled training data. We apply this new method to learn first-order HMMs for unsupervised part-of-speech (POS) tagging, and show that HMMs learned this way consistently and significantly out-performs both EM-trained HMMs, and HMMs with a sparsity-inducing Dirichlet prior trained by variational EM. We evaluate these HMMs on three languages -- English, Bulgarian and Portuguese -- under four conditions. We find that our method always improves performance with respect to both baselines, while variational Bayes actually degrades performance in most cases.

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in nonparametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations.