Related papers: Eigenvalue and Eigenvector Statistics in Time Seri…
Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…
We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension $d$ to scale with the series length $T$. We treat the transition matrix of…
A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly.…
We propose a novel framework in high-dimensional factor models to simultaneously analyse multiple tensor time series, each with potentially different tensor orders and dimensionality. The connection between different tensor time series is…
Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…
We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the "population spectrum"), given access to samples drawn from the…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
In this paper we develop a complete analytical framework based on Random Matrix Theory for the performance evaluation of Eigenvalue-based Detection. While, up to now, analysis was limited to false-alarm probability, we have obtained an…
Currently, machine learning is widely used across various domains, including time series data analysis. However, some machine learning models function as black boxes, making interpretability a critical concern. One approach to address this…
When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high…
Recent advances in data collection technology, accompanied by the ever-rising volume and velocity of streaming data, underscore the vital need for time series analytics. In this regard, time-series anomaly detection has been an important…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
Correlations among spikes, both on the same neuron and across neurons, are ubiquitous in the brain. For example cross-correlograms can have large peaks, at least in the periphery, and smaller -- but still non-negligible -- ones in cortex,…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
The inverse relationship between energy and time is as familiar as Planck's constant. From the point of view of a system with many states, perhaps a better representation of the system is a vector of characteristic times (one per state) for…
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…