A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlyingrelations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

This paper describes a new acoustic model based on variational Gaussian process dynamical system (VGPDS) for phoneme classification. The proposed model overcomes the limitations of the classical HMM in modeling the real speech data, by adopting a nonlinear and nonparametric model. In our model, the GP prior on the dynamics function enables representing the complex dynamic structure of speech, while the GP prior on the emission function successfully models the global dependency over the observations. Additionally, we introduce variance constraint to the original VGPDS for mitigating sparse approximation error of the kernel matrix. The effectiveness of the proposed model is demonstrated with extensive experimental results including parameter estimation, classification performance on the synthetic and benchmark datasets.

For modeling data matrices, this paper introduces Probabilistic Co-Subspace Addition (PCSA) model by simultaneously capturing the dependent structures among both rows and columns. Briefly, PCSA assumes that each entry of a matrix is generated by the additive combination of the linear mappings of two features, which distribute in the row-wise and column-wise latent subspaces. Consequently, it captures the dependencies among entries intricately, and is able to model the non-Gaussian and heteroscedastic density. Variational inference is proposed on PCSA for approximate Bayesian learning, where the updating for posteriors is formulated into the problem of solving Sylvester equations. Furthermore, PCSA is extended to tackling and filling missing values, to adapting its sparseness, and to modelling tensor data. In comparison with several state-of-art approaches, experiments demonstrate the effectiveness and efficiency of Bayesian (sparse) PCSA on modeling matrix (tensor) data and filling missing values.

The Restricted Boltzmann Machine (RBM) is a popular density model that is also good for extracting features. A main source of tractability in RBM models is the model's assumption that given an input, hidden units activate independently from one another. Sparsity and competition in the hidden representation is believed to be beneficial, and while an RBM with competition among its hidden units would acquire some of the attractive properties of sparse coding, such constraints are not added due to the widespread belief that the resulting model would become intractable. In this work, we show how a dynamic programming algorithm developed in 1981 can be used to implement exact sparsity in the RBM's hidden units. We then expand on this and show how to pass derivatives through a layer of exact sparsity, which makes it possible to fine-tune a deep belief network (DBN) consisting of RBMs with sparse hidden layers. We show that sparsity in the RBM's hidden layer improves the performance of both the pre-trained representations and of the fine-tuned model.

Links between probabilistic and non-probabilistic learning algorithms can arise by performing small-variance asymptotics, i.e., letting the variance of particular distributions in a graphical model go to zero. For instance, in the context of clustering, such an approach yields precise connections between the k-means and EM algorithms. In this paper, we explore small-variance asymptotics for exponential family Dirichlet process (DP) and hierarchical Dirichlet process (HDP) mixture models. Utilizing connections between exponential family distributions and Bregman divergences, we derive novel clustering algorithms from the asymptotic limit of the DP and HDP mixtures that feature the scalability of existing hard clustering methods as well as the flexibility of Bayesian nonparametric models. We focus on special cases of our analysis for discrete-data problems, including topic modeling, and we demonstrate the utility of our results by applying variants of our algorithms to problems arising in vision and document analysis.

Accurate and detailed models of the progression of neurodegenerative diseases such as Alzheimer's (AD) are crucially important for reliable early diagnosis and the determination and deployment of effective treatments. In this paper, we introduce the ALPACA (Alzheimer's disease Probabilistic Cascades) model, a generative model linking latent Alzheimer's progression dynamics to observable biomarker data. In contrast with previous works which model disease progression as a fixed ordering of events, we explicitly model the variability over such orderings among patients which is more realistic, particularly for highly detailed disease progression models. We describe efficient learning algorithms for ALPACA and discuss promising experimental results on a real cohort of Alzheimer's patients from the Alzheimer's Disease Neuroimaging Initiative.

In this paper, we consider Bayesian reinforcement learning (BRL) where actions incur costs in addition to rewards, and thus exploration has to be constrained in terms of the expected total cost while learning to maximize the expected long-term total reward. In order to formalize cost-sensitive exploration, we use the constrained Markov decision process (CMDP) as the model of the environment, in which we can naturally encode exploration requirements using the cost function. We extend BEETLE, a model-based BRL method, for learning in the environment with cost constraints. We demonstrate the cost-sensitive exploration behaviour in a number of simulated problems.

We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the distribution over extrema. To this end, we devise a non-parametric conjugate prior where the natural parameter corresponds to a given kernel function and the sufficient statistic is composed of the observed function values. The resulting posterior distribution directly captures the uncertainty over the maximum of the unknown function.

Factor analysis models effectively summarise the covariance structure of high dimensional data,but the solutions are typically hard to interpret. This motivates attempting to find a disjoint partition, i.e. a simple clustering, of observed variables into highly correlated subsets. We introduce a Bayesian nonparametric approach to this problem, and demonstrate advantages over heuristic methods proposed to date. Our Dirichlet process variable clustering (DPVC) model can discover blockdiagonal covariancestructures in data. We evaluate our method on both synthetic and gene expression analysis problems.

We introduce a new prior for use in Nonparametric Bayesian Hierarchical Clustering. The prior is constructed by marginalizing out the time information of Kingman’s coalescent, providing a prior over tree structures which we call the Time-Marginalized Coalescent (TMC). This allows for models which factorize the tree structure and times, providing two benefits: more flexible priors may be constructed and more efficient Gibbs type inference can be used. We demonstrate this on an example model for density estimation and show the TMC achieves competitive experimental results.