Related papers: Spiked Models in Wishart Ensemble

Motivated by dimension reduction in regression analysis and signal detection, we investigate the order determination for large dimension matrices including spiked models of which the numbers of covariates are proportional to the sample…

We consider matrices formed by a random $N\times N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $\theta$, and focus on the largest eigenvalue, $x$, and the…

Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\eta$. Motivated by problems in signal processing and…

We introduce a class of separable sample covariance matrices of the form $\widetilde{\mathcal{Q}}_1:=\widetilde A^{1/2} X \widetilde B X^* \widetilde A^{1/2}.$ Here $\widetilde{A}$ and $\widetilde{B}$ are positive definite matrices whose…

We study the computational task of detecting and estimating correlated signals in a pair of spiked matrices $$ X=\tfrac{\lambda}{\sqrt{n}} xu^{\top}+W, \quad Y=\tfrac{\mu}{\sqrt{n}} yv^{\top}+Z $$ where the spikes $x,y$ have correlation…

We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix…

In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues $\widehat{\lambda}_i$ and the generalized…

We study the asymptotic behavior of the spectrum of a random matrix where a non-linearity is applied entry-wise to a Wigner matrix perturbed by a rank-one spike with independent and identically distributed entries. In this setting, we show…

The proliferation of science and technology has led to the prevalence of voluminous data sets that are distributed across multiple machines. It is an established fact that conventional statistical methodologies may be unfeasible in the…

We use tools from random matrix theory to study the multi-spiked tensor model, i.e., a rank-$r$ deformation of a symmetric random Gaussian tensor. In particular, thanks to the nature of local optimization methods used to find the maximum…

In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…

We prove the equivalent of the Baik, Ben Arous, P\'ech\'e (2004) phenomenon for a novel, doubly sparse model where both the Wigner noise matrix and signal vector(s) are sparse. Specifically, we consider a deformed sub-Gaussian sparse Wigner…

The spiked Wigner ensemble is a prototypical model for high-dimensional inference. We study the spectral properties of an inhomogeneous rank-one spiked Wigner model in which the variance of each entry of the noise matrix is itself a random…

We studied universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues and the number of each of these eigenvalue goes to infinity in the asymptotic limit. In this case, the limiting eigenvalue distribution can be…

This is the second part of a study of the limiting distributions of the top eigenvalues of a Hermitian matrix model with spiked external source under a general external potential. The case when the external source is of rank one was…

In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block…

We characterize the limiting smallest eigenvalue distributions (or hard edge laws) for sample covariance type matrices drawn from a spiked population. In the case of a single spike, the results are valid in the context of the general beta…

We discuss the inhomogeneous spiked Wigner model, a theoretical framework recently introduced to study structured noise in various learning scenarios, through the prism of random matrix theory, with a specific focus on its spectral…

In this paper we study random matrix models where the matrices in question contain infinitely many spikes. Recent work has characterized the possible outliers in the spectrum of large deformed unitarily invariant models when the number of…

We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when…