Related papers: Hypothesis Testing for High-Dimensional Matrix-Val…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…
Random geometric graphs (RGGs) offer a powerful tool for analyzing the geometric and dependence structures in real-world networks. For example, it has been observed that RGGs are a good model for protein-protein interaction networks. In…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
This paper considers testing the covariance matrices structure based on Wald's score test in large dimensional setting. The hypothesis $H_0: \Sigma =\Sigma_0 $ for a given matrix $\Sigma_0$, which covers the identity hypothesis test and…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
Tests based on sample mean vectors and sample spatial signs have been studied in the recent literature for high dimensional data with the dimension larger than the sample size. For suitable sequences of alternatives, we show that the powers…
This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…
The package High-dimensional Metrics (\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate…
We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula…
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…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…
We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than…
This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable.…
Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics and image processing the matrices are dense, but low-rank…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
In this paper, we consider testing the correlation coefficient matrix between two subsets of high-dimensional variables. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of…