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Obtaining accurate estimates of machine learning model uncertainties on newly predicted data is essential for understanding the accuracy of the model and whether its predictions can be trusted. A common approach to such uncertainty…

Methods utilizing instrumental variables have been a fundamental statistical approach to estimation in the presence of unmeasured confounding, usually occurring in non-randomized observational data common to fields such as economics and…

We investigate the frequentist properties of Bayesian procedures for estimation based on the horseshoe prior in the sparse multivariate normal means model. Previous theoretical results assumed that the sparsity level, that is, the number of…

We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard…

In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…

Bayesian neural networks perform variational inference over the weights however calculation of the posterior distribution remains a challenge. Our work builds on variational inference techniques for bayesian neural networks using the…

Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…

In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…

Bayesian neural networks (BNNs) combine the expressive power of deep learning with the advantages of Bayesian formalism. In recent years, the analysis of wide, deep BNNs has provided theoretical insight into their priors and posteriors.…

Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations…

The Highly-Adaptive-LASSO Targeted Minimum Loss Estimator (HAL-TMLE) is an efficient plug-in estimator of a pathwise differentiable parameter in a statistical model that at minimal (and possibly only) assumes that the sectional variation…

Instrumental variable regression is a foundational tool for causal analysis across the social and biomedical sciences. Recent advances use kernel methods to estimate nonparametric causal relationships, with general data types, while…

The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance…

Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first…

There remain theoretical gaps in deep neural network estimators for the nonparametric Cox proportional hazards model. In particular, it is unclear how gradient-based optimization error propagates to population risk under partial likelihood,…

A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…

Quantile regression is a powerful data analysis tool that accommodates heterogeneous covariate-response relationships. We find that by coupling the asymmetric Laplace working likelihood with appropriate shrinkage priors, we can deliver…

Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

We propose a coupled bootstrap (CB) method for the test error of an arbitrary algorithm that estimates the mean in a Poisson sequence, often called the Poisson means problem. The idea behind our method is to generate two carefully-designed…