相关论文: Fundamental limits of detection in the spiked Wign…

We study Bayesian inference in the spiked covariance model, where a small number of spiked eigenvalues dominate the spectrum. Our goal is to infer the spiked eigenvalues, their corresponding eigenvectors, and the number of spikes, providing…

We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…

This work concerns elementwise-transformations of spiked matrices: $Y_n = n^{-1/2} f( \sqrt{n} X_n + Z_n)$. Here, $f$ is a function applied elementwise, $X_n$ is a low-rank signal matrix, and $Z_n$ is white noise. We find that principal…

Consider a Hermitian matrix model under an external potential with spiked external source. When the external source is of rank one, we compute the limiting distribution of the largest eigenvalue for general, regular, analytic potential for…

Across many disciplines from neuroscience and genomics to machine learning, atmospheric science and finance, the problems of denoising large data matrices to recover signals obscured by noise, and of estimating the structure of these…

We study estimation of the covariance matrix under relative condition number loss $\kappa(\Sigma^{-1/2} \hat{\Sigma} \Sigma^{-1/2})$, where $\kappa(\Delta)$ is the condition number of matrix $\Delta$, and $\hat{\Sigma}$ and $\Sigma$ are the…

In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…

In its original form the peak model for rank one supersingular perturbations of class $\mathfrak{H}_{-4}$ or higher of a nonnegative self-adjoint operator requires that the Gram matrix of the model should be diagonal. Here we remove the…

We investigate the Langevin dynamics for Wigner matrices with a spherical spike, in the regime where the signal-to-noise ratio $\theta$ is large, but order one. For large, order-$1$, signal-to-noise, the (worst-case) mixing time undergoes a…

This note considers the problem of approximating the locations of dominant spikes for a probability measure from noisy spectrum measurements under the condition of residue signal, significant noise level, and no minimum spectrum separation.…

The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model with added Mattis interaction. The exact solution of the…

This is the first part of a paper that studies the phase transition in the asymptotic limit of the rank 1 real Wishart spiked model. In this paper, we consider $N$-dimensional real Wishart matrices $S$ in the class…

In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main…

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrice under the assumption that the off-diagonal matrix entries have uniformly bounded fifth moment and the diagonal entries have…

Modern datasets are trending towards ever higher dimension. In response, recent theoretical studies of covariance estimation often assume the proportional-growth asymptotic framework, where the sample size $n$ and dimension $p$ are…

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific…

We study the Schwinger mechanism in the presence of an additional uniformly oriented, weak super Gaussian of integer order $4N+2$. Using the worldline approach, we determine the relevant critical points to compute the leading order…

In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…

Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile.…

Modeling spike firing assumes that spiking statistics are Poisson, but real data violates this assumption. To capture non-Poissonian features, in order to fix the inevitable inherent irregularity, researchers rescale the time axis with…