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We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex traits, and some variants are shown to be associated with multiple complex traits. Genetic covariance between two traits is defined…
Under covariate shift, training (source) data and testing (target) data differ in input space distribution, but share the same conditional label distribution. This poses a challenging machine learning task. Robust Bias-Aware (RBA)…
This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
We address the problem of how to achieve optimal inference in distributed quantile regression without stringent scaling conditions. This is challenging due to the non-smooth nature of the quantile regression (QR) loss function, which…
Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. The theory of debiased estimators can be…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to…
This paper develops distribution theory and bootstrap-based inference methods for a broad class of convex pairwise difference estimators. These estimators minimize a kernel-weighted convex-in-parameter function over observation pairs with…
A major challenge in cluster analysis is that the number of data clusters is mostly unknown and it must be estimated prior to clustering the observed data. In real-world applications, the observed data is often subject to heavy tailed noise…
We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…
Semiparametric estimators admitting a von Mises expansion often reduce inference to the influence-function variance. This reduction is justified when the second-order remainder is negligible in variance, a condition that is stronger than…
We consider quantile estimation in a semi-supervised setting, characterized by two available data sets: (i) a small or moderate sized labeled data set containing observations for a response and a set of possibly high dimensional covariates,…
Bayesian graphical modeling provides an appealing way to obtain uncertainty estimates when inferring network structures, and much recent progress has been made for Gaussian models. These models have been used extensively in applications to…
This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
We study partially linear models in settings where observations are arranged in independent groups but may exhibit within-group dependence. Existing approaches estimate linear model parameters through weighted least squares, with optimal…
We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from…
We study a multi-factor block model for variable clustering and connect it to regularized subspace clustering through a distributionally robust version of nodewise regression. To solve the latter problem, we derive a convex relaxation,…