Related papers: High-Performance Variance-Covariance Matrix Constr…
This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a…
Many learning tasks represent responses as multivariate probability measures, requiring repeated computation of weighted barycenters in Wasserstein space. In multivariate settings, transport barycenters are often computationally demanding…
This paper proposes a family of weighted batch means variance estimators, which are computationally efficient and can be conveniently applied in practice. The focus is on Markov chain Monte Carlo simulations and estimation of the asymptotic…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
Using Bayesian methods for extreme value analysis offers an alternative to frequentist ones, with several advantages such as easily dealing with parametric uncertainty or studying irregular models. However, computations can be challenging…
Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…
The paper provides a parametrization of Vector Autoregression (VAR) that enables one to look at the parameters associated with unit root dynamics and those associated with stable dynamics separately. The task is achieved via a novel…
A randomized version of the recently developed barycenter method for derivative--free optimization has desirable properties of a gradient search. We developed a complex version to avoid evaluations at high--gradient points. The method,…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…
The behavior of a GP regression depends on the choice of covariance function. Stationary covariance functions are preferred in machine learning applications. However, (non-periodic) stationary covariance functions are always mean reverting…
Matrices of the form $\bf{A} + (\bf{V}_1 + \bf{W}_1)\bf{G}(\bf{V}_2 + \bf{W}_2)^*$ are considered where $\bf{A}$ is a $singular$ $\ell \times \ell$ matrix and $\bf{G}$ is a nonsingular $k \times k$ matrix, $k \le \ell$. Let the columns of…
In two influential contributions, Rosenbaum (2005, 2020) advocated for using the distances between component-wise ranks, instead of the original data values, to measure covariate similarity when constructing matching estimators of average…
Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
Modern datasets are often in the form of matrices or arrays,potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as…
Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. The most popular inference algorithms for SBL exhibit prohibitively large computational costs for…