Related papers: High-dimensional Tensor Response Regression using …

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…

We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard $L_0$ constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard…

High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…

We provide an improved analysis of standard differentially private gradient descent for linear regression under the squared error loss. Under modest assumptions on the input, we characterize the distribution of the iterate at each time…

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…

Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated…

This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density…

Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations…

This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…

This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…

Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…

Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty, offering strong out-of-sample performance and principled regularization. In this paper, we propose a DRO-based method for linear…