相关论文: A note on switching eigenvalues under small pertur…
The variance of an arbitrary pointer observable is considered for the general case that a complex weak value is measured using a complex valued pointer state. For the typical cases where the pointer observable is either its position or…
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of…
In this article, the joint fluctuations of the extreme eigenvalues and eigenvectors of a large dimensional sample covariance matrix are analyzed when the associated population covariance matrix is a finite-rank perturbation of the identity…
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is…
While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…
We derive an exact general formalism that expresses the eigenvector and the eigenvalue dynamics as a set of coupled equations of motion in terms of the matrix elements dynamics. Combined with an appropriate model Hamiltonian, these…
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine…
The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds are available and the pseudospectrum can be computed to gain…
We consider sample covariance matrices $S_N=\frac{1}{p}\Sigma_N^{1/2}X_NX_N^* \Sigma_N^{1/2}$ where $X_N$ is a $N \times p$ real or complex matrix with i.i.d. entries with finite $12^{\rm th}$ moment and $\Sigma_N$ is a $N \times N$…
In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…
In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…
In environmental sciences, it is often of interest to assess whether the dependence between extreme measurements has changed during the observation period. The aim of this work is to propose a statistical test that is particularly sensitive…
In this work we present a framework for studying the eigenvalues of a family of matrices with a particular displacement structure. The family admits a specific decomposition as the product of an upper and a lower triangular matrices having…
We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need…
The problem of estimating parameters of switched affine systems with noisy input-output observations is considered. The switched affine models is transformed into a switched linear one by removing its intersection subspace, which is…
This paper considers a sequence of random variables generated according to a common distribution. The distribution might undergo periods of transient changes at an unknown set of time instants, referred to as change-points. The objective is…
External effects such as shocks and temperature variations affect the calibration of visual-inertial sensor systems and thus they cannot fully rely on factory calibrations. Re-calibrations performed on short user-collected datasets might…
We study principal components analyses in multivariate random and mixed effects linear models, assuming a spherical-plus-spikes structure for the covariance matrix of each random effect. We characterize the behavior of outlier sample…
The problem of sequential change diagnosis is considered, where observations are obtained on-line, an abrupt change occurs in their distribution, and the goal is to quickly detect the change and accurately identify the post-change…
Eigenvector perturbation analysis plays a vital role in various data science applications. A large body of prior works, however, focused on establishing $\ell_{2}$ eigenvector perturbation bounds, which are often highly inadequate in…