Related papers: Approximating high-dimensional infinite-order $U$-…

Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…

In this paper, we aim to develop stochastic hard thresholding algorithms for the important problem of AUC maximization in imbalanced classification. The main challenge is the pairwise loss involved in AUC maximization. We overcome this…

We study asymptotic anytime-valid confidence sequences for degree-two U-statistics under continuous monitoring. In the nondegenerate case, Hoeffding's projection reduces the problem to a time-uniform central limit theory for the partial…

This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…

This paper demonstrates a methodology for examining the accuracy of uncertain inference systems (UIS), after their parameters have been optimized, and does so for several common UIS's. This methodology may be used to test the accuracy when…

We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional P\'olya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions…

Using and extending fractional order statistic theory, we characterize the $O(n^{-1})$ coverage probability error of the previously proposed confidence intervals for population quantiles using $L$-statistics as endpoints in Hutson (1999).…

We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…

Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…

Extreme U-statistics arise when the kernel of a U-statistic has a high degree but depends only on its arguments through a small number of top order statistics. As the kernel degree of the U-statistic grows to infinity with the sample size,…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…

Learning high-dimensional distributions is a significant challenge in machine learning and statistics. Classical research has mostly concentrated on asymptotic analysis of such data under suitable assumptions. While existing works…

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…

The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…

Inverse optimization (IO) is used to estimate unknown parameters of an optimization model from observed decisions. In the data-driven context, the estimated parameters are inherently uncertain, yet quantifying this uncertainty has received…

We study the fundamental problems of Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination. Our main contribution is the design of the first sample near-optimal and almost linear-time…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters,…