Related papers: High-Dimensional Precision Matrix Quadratic Forms:…

In this paper, we consider matrix completion with absolute deviation loss and obtain an estimator of the median matrix. Despite several appealing properties of median, the non-smooth absolute deviation loss leads to computational challenge…

Effective operators have been used extensively to understand small deviations from the Standard Model in the search for new physics. So far there has been no general method to fit for small parameters when higher order corrections in these…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…

This paper proposes a new method for finding the highest predictive density set or region, within the heteroscedastic regression framework. This framework enjoys the property that any highest predictive density set is a translation of some…

We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series $p$ is large in relation to the length of time series $n$. Our first step performs an…

We propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative loglikelihood plus an $L_1$ penalty on a…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…

In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…

We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…

We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…

We provide a unified approach to a method of estimation of the regression parameter in balanced linear models with a structured covariance matrix that combines a high breakdown point and bounded influence with high asymptotic efficiency at…

Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging…

The family of rank estimators, including Han's maximum rank correlation (Han, 1987) as a notable example, has been widely exploited in studying regression problems. For these estimators, although the linear index is introduced for…

This paper presents a novel quadratic projection based feature extraction framework, where a set of quadratic matrices is learned to distinguish each class from all other classes. We formulate quadratic matrix learning (QML) as a standard…