Data sets involving multiple groups with shared characteristics frequently arise in practice. In this paper we extend hierarchical Dirichlet processes to model such data. Each group is assumed to be generated from a template mixture model with group level variability in both the mixing proportions and the component parameters. Variabilities in mixing proportions across groups are handled using hierarchical Dirichlet processes, also allowing for automatic determination of the number of components. In addition, each group is allowed to have its own component parameters coming from a prior described by a template mixture model. This group-level variability in the component parameters is handled using a random effects model. We present a Markov Chain Monte Carlo (MCMC) sampling algorithm to estimate model parameters and demonstrate the method by applying it to the problem of modeling spatial brain activation patterns across multiple images collected via functional magnetic resonance imaging (fMRI).

Everyday inductive reasoning draws on many kinds of knowledge, including knowledge about relationships between properties and knowledge about relationships between objects. Previous accounts of inductive reasoning generally focus on just one kind of knowledge: models of causal reasoning often focus on relationships between properties, and models of similarity-based reasoning often focus on similarity relationships between objects. We present a Bayesian model of inductive reasoning that incorporates both kinds of knowledge, and show that it accounts well for human inferences about the properties of biological species.

This paper introduces adaptor grammars, a class of probabilistic models of language that generalize probabilistic context-free grammars (PCFGs). Adaptor grammars augment the probabilistic rules of PCFGs with "adaptors" that can induce dependencies among successive uses. With a particular choice of adaptor, based on the Pitman-Yor process, nonparametric Bayesian models of language using Dirichlet processes and hierarchical Dirichlet processes can be written as simple grammars. We present a general-purpose inference algorithm for adaptor grammars, making it easy to define and use such models, and illustrate how several existing nonparametric Bayesian models can be expressed within this framework.

Human listeners have the extraordinary ability to hear and recognize speech even when more than one person is talking. Their machine counterparts have historically been unable to compete with this ability, until now. We present a modelbased system that performs on par with humans in the task of separating speech of two talkers from a single-channel recording.

The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

By adopting Gaussian process priors a fully Bayesian solution to the problem of integrating possibly heterogeneous data sets within a classification setting is presented. Approximate inference schemes employing Variational & Expectation Propagation based methods are developed and rigorously assessed. We demonstrate our approach to integrating multiple data sets on a large scale protein fold prediction problem where we infer the optimal combinations of covariance functions and achieve state-of-the-art performance without resorting to any ad hoc parameter tuning and classifier combination.

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate this gradient. Since Monte Carlo methods tend to have high variance, a large number of samples is required, resulting in slow convergence. In this paper, we propose a Bayesian framework that models the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient as well as a measure of the uncertainty in the gradient estimates are provided at little extra cost.

We present a generalization of dynamic Bayesian networks to concisely describe complex probability distributions such as in problems with multiple interacting variable-length streams of random variables. Our framework incorporates recent graphical model constructs to account for existence uncertainty, value-specific independence, aggregation relationships, and local and global constraints, while still retaining a Bayesian network interpretation and efficient inference and learning techniques. We introduce one such general technique, which is an extension of Value Elimination, a backtracking search inference algorithm. Multi-dynamic Bayesian networks are motivated by our work on Statistical Machine Translation (MT). We present results on MT word alignment in support of our claim that MDBNs are a promising framework for the rapid prototyping of new MT systems.

This paper proposes a new approach to model-based clustering under prior knowledge. The proposed formulation can be interpreted from two different angles: as penalized logistic regression, where the class labels are only indirectly observed (via the probability density of each class); as finite mixture learning under a grouping prior. To estimate the parameters of the proposed model, we derive a (generalized) EM algorithm with a closed-form E-step, in contrast with other recent approaches to semi-supervised probabilistic clustering which require Gibbs sampling or suboptimal shortcuts. We show that our approach is ideally suited for image segmentation: it avoids the combinatorial nature Markov random field priors, and opens the door to more sophisticated spatial priors (e.g., wavelet-based) in a simple and computationally efficient way. Finally, we extend our formulation to work in unsupervised, semi-supervised, or discriminative modes.

Correlation between instances is often modelled via a kernel function using input attributes of the instances. Relational knowledge can further reveal additional pairwise correlations between variables of interest. In this paper, we develop a class of models which incorporates both reciprocal relational information and input attributes using Gaussian process techniques. This approach provides a novel nonparametric Bayesian framework with a data-dependent covariance function for supervised learning tasks. We also apply this framework to semi-supervised learning. Experimental results on several real world data sets verify the usefulness of this algorithm.