Related papers: Application of Random Matrix Theory in High-Dimens…

Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov regularization), regularized discriminant…

As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of…

In this article, we discuss the remarkable connection between two very different fields, number theory and nuclear physics. We describe the essential aspects of these fields, the quantities studied, and how insights in one have been…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…

Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…

Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT…

Invisible units mainly refer to small-scale units that are not monitored by, and thus are not visible to utilities. Integration of these invisible units into power systems does significantly affect the way in which a distribution grid is…

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…

Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…

Random correlation matrices are studied for both theoretical interestingness and importance for applications. The author of [6] is interested in their interpretation as covariance matrices of purely random signals, the authors of [16]…

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…

Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…

Power systems are developing very fast nowadays, both in size and in complexity; this situation is a challenge for Early Event Detection (EED). This paper proposes a data- driven unsupervised learning method to handle this challenge.…

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…

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been…

Introduction: Machine learning (ML) has been extremely successful in identifying key features from high-dimensional datasets and executing complicated tasks with human expert levels of accuracy or greater. Methods: We summarize and…

Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor…