Related papers: Signal-plus-noise matrix models: eigenvector devia…
We perform a non-asymptotic analysis on the singular vector distribution under Gaussian noise. In particular, we provide sufficient conditions on a matrix for its first few singular vectors to have near normal distribution. Our result can…
We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or,…
Recent advances in transport properties measurements of disordered materials and lattice simulations, using superconducting qubits, have rekindled interest in Anderson localization, motivating our study of highly disordered quantum…
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 propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…
We study ill-conditioned positive definite matrices that are disturbed by the sum of $m$ rank-one matrices of a specific form. We provide estimates for the eigenvalues and eigenvectors. When the condition number of the initial matrix tends…
Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise.…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always…
We propose a theory of unimodal maps perturbed by an heteroscedastic Markov chain noise and experiencing another heteroscedastic noise due to uncertain observation. We address and treat the filtering problem showing that by collecting more…
We investigate the noise sensitivity of the top eigenvector of a sparse random symmetric matrix. Let $v$ be the top eigenvector of an $N\times N$ sparse random symmetric matrix with an average of $d$ non-zero centered entries per row. We…
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule…
This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all…
Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…
Direct loss minimization is a popular approach for learning predictors over structured label spaces. This approach is computationally appealing as it replaces integration with optimization and allows to propagate gradients in a deep net…
We perturb a real matrix $A$ of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions,…
Inhomogeneous random matrices with non-trivial variance profiles determined by symmetric stochastic matrices and with independent sub-Gaussian entries up to Hermitian symmetry, encompass a wide range of important models, including sparse…
We study feature selection in high-dimensional regression under two distinct sources of instability: sampling variability and measurement error in the design matrix. Stability Selection addresses the former through sub-sampling and…
Explainable AI methods facilitate the understanding of model behaviour, yet, small, imperceptible perturbations to inputs can vastly distort explanations. As these explanations are typically evaluated holistically, before model deployment,…