Related papers: Scalable Nonparametric Sampling from Multimodal Po…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…
This paper proposes Bayesian mosaic, a parallelizable composite posterior, for scalable Bayesian inference on a broad class of multivariate discrete data models. Sampling is embarrassingly parallel since Bayesian mosaic is a multiplication…
High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
We develop a scalable multi-step Monte Carlo algorithm for inference under a large class of nonparametric Bayesian models for clustering and classification. Each step is "embarrassingly parallel" and can be implemented using the same Markov…
We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…
Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…
We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such…
In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian…
In recent years, the shortcomings of Bayesian posteriors as inferential devices have received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
In this paper we consider the problem of dynamic clustering, where cluster memberships may change over time and clusters may split and merge over time, thus creating new clusters and destroying existing ones. We propose a Bayesian…
Let $X_1,\ldots,X_n$ be a random sample from an unknown probability distribution $P$ on the sample space ${\cal X}$, and let $\theta=\theta(P)$ be a parameter of interest. The present paper proposes a nonparametric `Bayesian bootstrap'…