Related papers: Theoretical Performance Analysis of Eigenvalue-bas…
We consider the problem of estimating the principal components of a population correlation matrix from a limited number of measurement data. Using a combination of random matrix and information-theoretic tools, we show that all the…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…
In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…
In this paper, we propose an algorithm for estimating the parameters of a time-homogeneous hidden Markov model from aggregate observations. This problem arises when only the population level counts of the number of individuals at each time…
For a passive direction of arrival (DoA) measurement system using massive multiple input multiple output (MIMO), it is mandatory to infer whether the emitter exists or not before performing DOA estimation operation. Inspired by the…
This paper describes computationally efficient approaches and associated theoretical performance guarantees for the detection of known targets and anomalies from few projection measurements of the underlying signals. The proposed approaches…
In this paper, we address the problem of target detection in the presence of coherent (or fully correlated) signals, which can be due to multipath propagation effects or electronic attacks by smart jammers. To this end, we formulate the…
Estimating the number of signals embedded in noise is a fundamental problem in signal processing. As a classic estimator based on random matrix theory (RMT), the RMT estimator estimates the number of signals via sequentially testing the…
Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of…
Signal detection in colored noise with an unknown covariance matrix has a myriad of applications in diverse scientific/engineering fields. The test statistic is the largest generalized eigenvalue (l.g.e.) of the whitened sample covariance…
This paper describes a model for power distribution network, which is hten utilized for eigenvalue behavior distribution analysis. We utilized the compensation theory to model the event that occurs in the network and derived the relation…
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…
Spectral methods have myriad applications in high-dimensional statistics and data science, and while previous works have primarily focused on $\ell_2$ or $\ell_{2,\infty}$ eigenvector and singular vector perturbation theory, in many…
Characterizing the asymptotic distributions of eigenvectors for large random matrices poses important challenges yet can provide useful insights into a range of statistical applications. To this end, in this paper we introduce a general…
We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of…