# Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models

## TL;DR

This paper introduces a regime-switching factor model for high-dimensional fMRI data that captures both smooth and abrupt changes in brain connectivity, enabling more accurate detection of dynamic states and effective connectivity patterns.

## Contribution

It proposes a novel three-step estimation method combining PCA, switching VAR models, and subspace estimates to analyze dynamic brain connectivity with high-dimensional data.

## Key findings

- Outperforms K-means clustering in regime detection accuracy
- Identifies distinct brain states with unique connectivity patterns
- Reveals modular organization in resting-state networks

## Abstract

Recent studies on analyzing dynamic brain connectivity rely on sliding-window analysis or time-varying coefficient models which are unable to capture both smooth and abrupt changes simultaneously. Emerging evidence suggests state-related changes in brain connectivity where dependence structure alternates between a finite number of latent states or regimes. Another challenge is inference of full-brain networks with large number of nodes. We employ a Markov-switching dynamic factor model in which the state-driven time-varying connectivity regimes of high-dimensional fMRI data are characterized by lower-dimensional common latent factors, following a regime-switching process. It enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We consider the switching VAR to quantity the dynamic effective connectivity. We propose a three-step estimation procedure: (1) extracting the factors using principal component analysis (PCA) and (2) identifying dynamic connectivity states using the factor-based switching vector autoregressive (VAR) models in a state-space formulation using Kalman filter and expectation-maximization (EM) algorithm, and (3) constructing the high-dimensional connectivity metrics for each state based on subspace estimates. Simulation results show that our proposed estimator outperforms the K-means clustering of time-windowed coefficients, providing more accurate estimation of regime dynamics and connectivity metrics in high-dimensional settings. Applications to analyzing resting-state fMRI data identify dynamic changes in brain states during rest, and reveal distinct directed connectivity patterns and modular organization in resting-state networks across different states.