Modeling state-transition dynamics in brain signals by memoryless Gaussian mixtures

Recent studies have proposed that one can summarize brain activity into dynamics among a relatively small number of hidden states and that such an approach is a promising tool for revealing brain function. Hidden Markov models (HMMs) are a prevalent approach to inferring such neural dynamics among discrete brain states. However, the validity of modeling neural time series data with HMMs has not been established. Here, to address this situation and examine the performance of the HMM, we compare the model with the Gaussian mixture model (GMM), which is a statistically simpler model than the HMM with no assumption of Markovianity, by applying both models to synthetic and empirical resting-state functional magnetic resonance imaging (fMRI) data. We find that the GMM allows us to interpret the sequence of the estimated hidden states as a time series obeying some patterns and is often better than HMMs in terms of the accuracy and consistency of estimating the time course of the hidden state. These results suggest that GMMs can be a model of first choice for investigating hidden-state dynamics in data even if the time series is apparently not memoryless.