Related papers: On Random Matrices Arising in Deep Neural Networks…
This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices. We show that the result can be derived directly as a consequence of two common…
Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…
A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
In this paper we consider Wigner random matrices -- symmetric n by n random matrices whose entries are independent identically distributed real random variables. We prove that the probability distribution of one or several eigenvalues close…
Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat…
Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
Based on the random matrix model, we can build statistical models using massive datasets across the power grid, and employ hypothesis testing for anomaly detection. First, the aim of this paper is to make the first attempt to apply the…
For two large matrices ${\mathbf X}$ and ${\mathbf Y}$ with Gaussian i.i.d.\ entries and dimensions $T\times N_X$ and $T\times N_Y$, respectively, we derive the probability distribution of the singular values of $\mathbf{X}^T \mathbf{Y}$ in…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to…
Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approach and the concept of polynomial ensembles. Very recently, it…