Efficient Covariance Estimation from Temporal Data

TL;DR

This paper introduces T-CorEx, a scalable and efficient method for covariance estimation in multivariate time series that performs well in high-dimensional, undersampled, and complex real-world datasets, with minimal assumptions.

Contribution

The paper presents T-CorEx, a novel covariance estimation method with linear complexity, capable of handling large datasets and capturing dynamic correlations in high-dimensional time series.

Findings

T-CorEx achieves state-of-the-art results in undersampled regimes.

It effectively detects changes and transient correlations.

It scales to high-dimensional data like fMRI.

Abstract

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 methods are still severely limited in terms of scalability, and do not work well in high-dimensional undersampled regimes. In this work we propose a novel method called Temporal Correlation Explanation, or T-CorEx, that (a) has linear time and memory complexity with respect to the number of variables, and can scale to very large temporal datasets that are not tractable with existing methods; (b) gives state-of-the-art results in highly undersampled regimes on both synthetic and real-world datasets; and (c) makes minimal assumptions about the character of the dynamics of the system. T-CorEx optimizes an information-theoretic objective function to learn a latent factor graphical model for each time period and applies two regularization techniques to induce temporal consistency of estimates. We perform extensive evaluation of T-Corex using both synthetic and real-world data and demonstrate that it can be used for detecting sudden changes in the underlying covariance matrix, capturing transient correlations and analyzing extremely high-dimensional complex multivariate time series such as high-resolution fMRI data.