Coupled Hidden Markov Models for Estimating Multivariate Transfer Entropy in Neural Mass Models: A Simulation Study

TL;DR: In this article , latent structure influence models (LSIMs) are adapted to develop a novel multivariate transfer entropy estimator that measures effective connectivity in multivariate time series, which can be inferred in linear and nonlinear ways.

Abstract: Studying complex dynamical systems such as the brain requires identifying causal relationships from brain signals like EEG. In such systems, causal inference is challenging since datasets are often high-dimensional, nonlinear, noisy, and often with small sample sizes. Using multivariate transfer entropy (MTE), causal relationships can be inferred in linear and nonlinear ways. In the current study, latent structure influence models (LSIMs) are adapted to develop a novel MTE estimator that measures effective connectivity in multivariate time series. LSIMs are a specific type of coupled hidden Markov model (CHMM) in which hidden Markov chain interactions are expressed as influence models. Simulated datasets from neural mass models (NMMs) are used to compare the proposed estimator with the existing k-nearest neighbors (kNN) method at different conditions, including data length, signal-to-noise ratio, and network size. Using ground-truth structure networks, we define a binary classification problem for recovering directed edges from NMM simulation datasets in each specific condition. Based on the AUCPR criterion, the proposed MTE estimator for NMMs is more effective than the standard kNN method. The proposed LSIM-based method outperforms the existing kNN method by about 3.7% in AUCPR values for SNRs in the range of 0 dB to 5 dB.