Related papers: Scalable Bayesian transport maps for high-dimensio…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…

We introduce fully scalable Gaussian processes, an implementation scheme that tackles the problem of treating a high number of training instances together with high dimensional input data. Our key idea is a representation trick over the…

Robots rely on motion planning to navigate safely and efficiently while performing various tasks. In this paper, we investigate motion planning through Bayesian inference, where motion plans are inferred based on planning objectives and…

Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…

One among several advantages of measure transport methods is that they allow for a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results…

In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower dimensional…

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…

Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative…

Distribution regression, where the goal is to predict a scalar response from a distribution-valued predictor, arises naturally in settings where observations are grouped and outcomes depend on group-level characteristics rather than on…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

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 propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…

It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…

A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the…

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale…

We study distribution-on-distribution regression problems in which a response distribution depends on multiple distributional predictors. Such settings arise naturally in applications where the outcome distribution is driven by several…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…