Adaptive covariance estimation of non-stationary processes and its application to infer dynamic connectivity from fMRI

Zening Fu, Shing Chow Chan, Xin Di, Bharat Biswal, Zhiguo Zhang

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Time-varying covariance is an important metric to measure the statistical dependence between non-stationary biological processes. Time-varying covariance is conventionally estimated from short-time data segments within a window having a certain bandwidth, but it is difficult to choose an appropriate bandwidth to estimate covariance with different degrees of non-stationarity. This paper introduces a local polynomial regression (LPR) method to estimate time-varying covariance and performs an asymptotic analysis of the LPR covariance estimator to show that both the estimation bias and variance are functions of the bandwidth and there exists an optimal bandwidth to minimize the mean square error (MSE) locally. A data-driven variable bandwidth selection method, namely the intersection of confidence intervals (ICI), is adopted in LPR for adaptively determining the local optimal bandwidth that minimizes the MSE. Experimental results on simulated signals show that the LPR-ICI method can achieve robust and reliable performance in estimating time-varying covariance with different degrees of variations and under different noise scenarios, making it a powerful tool to study the dynamic relationship between non-stationary biomedical signals. Further, we apply the LPR-ICI method to estimate time-varying covariance of functional magnetic resonance imaging (fMRI) signals in a visual task for the inference of dynamic functional brain connectivity. The results show that the LPR-ICI method can effectively capture the transient connectivity patterns from fMRI.

Original languageEnglish (US)
Article number6800130
Pages (from-to)228-239
Number of pages12
JournalIEEE Transactions on Biomedical Circuits and Systems
Volume8
Issue number2
DOIs
StatePublished - Apr 2014

All Science Journal Classification (ASJC) codes

  • Biomedical Engineering
  • Electrical and Electronic Engineering

Keywords

  • Dynamic functional connectivity
  • functional magnetic resonance imaging (fMRI)
  • local polynomial regression
  • locally stationary processes
  • time-varying covariance

Fingerprint Dive into the research topics of 'Adaptive covariance estimation of non-stationary processes and its application to infer dynamic connectivity from fMRI'. Together they form a unique fingerprint.

Cite this