Related papers: Sampling Spiked Wishart Eigenvalues
In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…
This paper deals with the problem of extracting the activity of individual neurons from multi-electrode recordings. Important aspects of this work are: 1) the sorting is done in two stages - a statistical model of the spikes from different…
In this paper, we propose new sampling approaches for the Shrinkage Inverse-Wishart (SIW) distribution, a generalized family of the Inverse-Wishart distribution originally proposed by Berger et al. (2020, Annals of Statistics). It offers a…
This paper develops on-line inference for the multivariate local level model, with the focus being placed on covariance estimation of the innovations. We assess the application of the inverse Wishart prior distribution in this context and…
This paper focuses on the non-asymptotic concentration of the heteroskedastic Wishart-type matrices. Suppose $Z$ is a $p_1$-by-$p_2$ random matrix and $Z_{ij} \sim N(0,\sigma_{ij}^2)$ independently, we prove the expected spectral norm of…
Brain-inspired spiking neural networks (SNNs) have recently drawn more and more attention due to their event-driven and energy-efficient characteristics. The integration of storage and computation paradigm on neuromorphic hardwares makes…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
In \cite{Diaz} beta type I and II doubly singular distributions were introduced and their densities and the joint densities of nonzero eigenvalues were derived. In such matrix variate distributions $p$, the dimension of two singular Wishart…
The problem of infering the top component of a noisy sample covariance matrix with prior information about the distribution of its entries is considered, in the framework of the spiked covariance model. Using the replica method of…
We solve the largest sample eigenvalue distribution problem in the rank 1 spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge.…
In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…
The aim of this note is to provide a pedagogical survey of the recent works by the authors ( arXiv:1409.7548 and arXiv:1507.06013) concerning the local behavior of the eigenvalues of large complex correlated Wishart matrices at the edges…
Investigating the spectral properties of the neural covariates that underlie spiking activity is an important problem in systems neuroscience, as it allows to study the role of brain rhythms in cognitive functions. While the spectral…
We present an improved analysis of mini-batched stochastic dual coordinate ascent for regularized empirical loss minimization (i.e. SVM and SVM-type objectives). Our analysis allows for flexible sampling schemes, including where data is…
We consider rectangular random matrices of size $p\times n$ belonging to the real Wishart-Laguerre ensemble also known as the chiral Gaussian orthogonal ensemble. This ensemble appears in many applications like QCD, mesoscopic physics, and…
In this paper we consider some hypothesis tests within a family of Wishart distributions, where both the sample space and the parameter space are symmetric cones. For such testing problems, we first derive the joint density of the ordered…
We studied universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues and the number of each of these eigenvalue goes to infinity in the asymptotic limit. In this case, the limiting eigenvalue distribution can be…
Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the…
We explore the limiting empirical eigenvalue distributions arising from matrices of the form \[A_{n+1} = \begin{bmatrix} A_n & I\\ I & A_n \end{bmatrix} , \]where $A_0$ is the adjacency matrix of a $k$-regular graph. We find that for…
The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…