Related papers: Eigenvalue and Eigenvector Statistics in Time Seri…

While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

Regression models are essential for a wide range of real-world applications. However, in practice, target values are not always precisely known; instead, they may be represented as intervals of acceptable values. This challenge has led to…

Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore…

We consider a setting where multiple entities inter-act with each other over time and the time-varying statuses of the entities are represented as multiple correlated time series. For example, speed sensors are deployed in different…

Time-series data is being increasingly collected and stud- ied in several areas such as neuroscience, climate science, transportation, and social media. Discovery of complex patterns of relationships between individual time-series, using…

Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite…

High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…

It is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might have been. One might also wish to estimate the significance of a…

Multivariate spatial phenomena are ubiquitous, spanning domains such as climate, pandemics, air quality, and social economy. Cross-correlation between different quantities of interest at different locations is asymmetric in general. This…

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…

Time series analysis has gained significant attention due to its critical applications in diverse fields such as healthcare, finance, and sensor networks. The complexity and non-stationarity of time series make it challenging to capture the…

Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes…

Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…

Time series and signals are attracting more attention across statistics, machine learning and pattern recognition as it appears widely in the industry especially in sensor and IoT related research and applications, but few advances has been…

We consider the problem of estimating the principal components of a population correlation matrix from a limited number of measurement data. Using a combination of random matrix and information-theoretic tools, we show that all the…

Eigenvalue-based detectors are considered as an important method of spectrum sensing since they do not require the information about the primary user (PU) signal. In this paper we propose a method to improve the performance of the…

Estimating the covariance structure of multivariate time series is a fundamental problem with a wide-range of real-world applications -- from financial modeling to fMRI analysis. Despite significant recent advances, current state-of-the-art…

Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…