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The development of parsimonious models for reliable inference and prediction of responses in high-dimensional regression settings is often challenging due to relatively small sample sizes and the presence of complex interaction patterns…
Mixtures of Gaussian process experts is a class of models that can simultaneously address two of the key limitations inherent in standard Gaussian processes: scalability and predictive performance. In particular, models that use Dirichlet…
We develop a Bayesian framework for tackling the supervised clustering problem, the generic problem encountered in tasks such as reference matching, coreference resolution, identity uncertainty and record linkage. Our clustering model is…
The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian…
Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet…
In recent years, we have seen a handful of work on inference algorithms over non-stationary data streams. Given their flexibility, Bayesian non-parametric models are a good candidate for these scenarios. However, reliable streaming…
Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize…
Ongoing advances in microbiome profiling have allowed unprecedented insights into the molecular activities of microbial communities. This has fueled a strong scientific interest in understanding the critical role the microbiome plays in…
In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying…
We propose an empirical Bayes estimator based on Dirichlet process mixture model for estimating the sparse normalized mean difference, which could be directly applied to the high dimensional linear classification. In theory, we build a…
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…
We propose a geometric framework to assess global sensitivity in Bayesian nonparametric models for density estimation. We study sensitivity of nonparametric Bayesian models for density estimation, based on Dirichlet-type priors, to…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…