Related papers: A Lanczos-Based Algorithmic Approach for Spike Det…
We show that the standard Lanczos algorithm can be efficiently implemented statistically and self consistently improved, using the stochastic reconfigurat ion method, which has been recently introduced to stabilize the Monte Carlo sign…
This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…
In this paper, we consider directly estimating the eigenvalues of precision matrix, without inverting the corresponding estimator for the eigenvalues of covariance matrix. We focus on a general asymptotic regime, i.e., the large dimensional…
In this paper, we study the convergent limits and rates of the eigenvalues and eigenvectors for spiked sample covariance matrices whose spectrum can have multiple bulk components. Our model is an extension of Johnstone's spiked covariance…
Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious…
We propose a spectral method by using the Jacobi functions for computing eigenvalue gaps and their distribution statistics of the fractional Schr\"{o}dinger operator (FSO). In the problem, in order to get reliable gaps distribution…
Accurate detection of signal components is a frequently-encountered challenge in statistical applications with low signal-to-noise ratio. This problem is particularly challenging in settings with heteroscedastic noise. In certain…
In high-dimensional principal component analysis, important inferential targets include both leading spikes and the associated principal eigenspaces. Such problems arise naturally in high-dimensional factor models, where leading principal…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
Recent work found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for…
Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution…
Quadratic forms of Hermitian matrix resolvents involve the solutions of shifted linear systems. Efficient iterative solutions use the shift-invariance property of Krylov subspaces The Hermitian Lanczos method reduces a given vector and…
Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatialtemporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is…
A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random…
In this paper, we consider a data matrix $X\in\mathbb{C}^{N\times M}$ where all the columns are i.i.d. samples being $N$ dimensional complex Gaussian of mean zero and covariance $\Sigma\in\mathbb{C}^{N\times N}$. Here the population matrix…
We study spectral properties of unbounded Jacobi matrices with periodically modulated or blended entries. Our approach is based on uniform asymptotic analysis of generalized eigenvectors. We determine when the studied operators are…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSSs) of a large-dimensional sample covariance matrix when the population covariance matrices are involved with diverging spikes. This constitutes a…
We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…