相关论文: Tractable Evaluation of Stein's Unbiased Risk Esti…

We derive the asymptotic risk function of regularized empirical risk minimization (ERM) estimators tuned by $n$-fold cross-validation (CV). The out-of-sample prediction loss of such estimators converges in distribution to the squared-error…

The estimation of signal dimension under heavy-tailed latent factor models is studied. As a primary contribution, robust extensions of an earlier estimator based on Gaussian Stein's unbiased risk estimation are proposed. These novel…

Stein's unbiased risk estimator (SURE) has been shown to be an effective metric for determining optimal parameters for many applications. The topic of this article is focused on the use of SURE for determining parameters for blind…

Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the…

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach…

To address the challenges of reliable statistical inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via…

We identify and correct an error in the paper "Excess Optimism: How Biased is the Apparent Error of an Estimator Tuned by SURE?" This correction allows new guarantees on the excess degrees of freedom--the bias in the error estimate of…

In contrast to the standard learning paradigm where all classes can be observed in training data, learning with augmented classes (LAC) tackles the problem where augmented classes unobserved in the training data may emerge in the test…

In constrained stochastic optimization, one naturally expects that imposing a stricter feasible set does not increase the statistical risk of an estimator defined by projection onto that set. In this paper, we show that this intuition can…

We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly,…

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an at- tractive method for…

We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined…

To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…

Unbiased risk estimation, \`a la Stein, is studied for infinitely divisible laws with finite second moment.

Consider $n$ independent and identically distributed $p$-dimensional Gaussian random vectors with covariance matrix $\Sigma.$ The problem of estimating $\Sigma$ when $p$ is much larger than $n$ has received a lot of attention in recent…

Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects…

Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…

In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…

Many modern datasets, such as those in ecology and geology, are composed of samples with spatial structure and dependence. With such data violating the usual independent and identically distributed (IID) assumption in machine learning and…

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…