Related papers: Generalized Fiducial Inference for Ultrahigh Dimen…

This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the…

This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…

We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $\theta$ that utilizes the uncertain prior information that a distinct scalar parameter…

A great deal of interest has recently focused on conducting inference on the parameters in a high-dimensional linear model. In this paper, we consider a simple and very na\"{i}ve two-step procedure for this task, in which we (i) fit a lasso…

Variable selection for regression models plays a key role in the analysis of biomedical data. However, inference after selection is not covered by classical statistical frequentist theory which assumes a fixed set of covariates in the…

Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…

We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…

Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many…

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…

In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi (1969). This solves a long-standing open problem…

Prediction credibility measures, in the form of confidence intervals or probability distributions, are fundamental in statistics and machine learning to characterize model robustness, detect out-of-distribution samples (outliers), and…

We study asymptotically normal estimation and confidence regions for low-dimensional parameters in high-dimensional sparse models. Our approach is based on the $\ell_1$-penalized M-estimator which is used for construction of a bias…

Motivated by big data and the vast parameter spaces in modern machine learning models, optimisation approaches to Bayesian inference have seen a surge in popularity in recent years. In this paper, we address the connection between the…

A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…

In this paper, we develop an {\em epsilon admissible subsets} (EAS) model selection approach for performing group variable selection in the high-dimensional multivariate regression setting. This EAS strategy is designed to estimate a…

A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…

Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial…

Proper quantification and propagation of uncertainties in computational simulations are of critical importance. This issue is especially challenging for CFD applications. A particular obstacle for uncertainty quantifications in CFD problems…

Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these…

Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {\em uncertainty}. Quantifying…