Related papers: Hypothesis Testing for High-Dimensional Matrix-Val…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to…
Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a P-value, we construct a…
We propose a method for constructing p-values for general hypotheses in a high-dimensional linear model. The hypotheses can be local for testing a single regression parameter or they may be more global involving several up to all…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…
Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in…
In this paper, we consider the problem of testing equality of the covariance matrices of L complex Gaussian multivariate time series of dimension $M$ . We study the special case where each of the L covariance matrices is modeled as a rank K…
Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…
The item response theory obtains the estimates and their confidence intervals for parameters of abilities of examinees and difficulties of problems by using the observed item response matrix consisting of 0/1 value elements. Many papers…
Sparse representation-based classification (SRC), proposed by Wright et al., seeks the sparsest decomposition of a test sample over the dictionary of training samples, with classification to the most-contributing class. Because it assumes…
We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the…
We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…
The Randomized Singular Value Decomposition (RSVD) is a widely used algorithm for efficiently computing low-rank approximations of large matrices, without the need to construct a full-blown SVD. Of interest, of course, is the approximation…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual subsampling (RIRS)…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
With the emergence of dynamic multiplex networks, corresponding to graphs where multiple types of edges evolve over time, a key inferential task is to determine whether the layers associated with different edge types differ in their…