Switching state-space modeling of neural signal dynamics
Authors: He Mingjian , Das Proloy , Hotan Gladia , Purdon Patrick L. 
Published: November 2022

Linear parametric state-space models are a ubiquitous tool for analyzing neural time series data, providing a way to characterize the underlying brain dynamics with much greater statistical efficiency than non-parametric data analysis approaches. However, neural time series data are frequently time-varying, exhibiting rapid changes in dynamics, with transient activity that is often the key feature of interest in the data. Stationary methods can be adapted to time-varying scenarios by employing fixed-duration windows under an assumption of quasi-stationarity. But time-varying dynamics can be explicitly modeled by switching state-space models, i.e., by using a pool of state-space models with different dynamics selected by a probabilistic switching process. Unfortunately, exact solutions for state inference and parameter learning with switching state-space models are intractable. Here we revisit a switching state-space model inference approach first proposed by Ghahramani and Hinton. We provide explicit derivations for solving the inference problem iteratively after applying variational approximation on the joint posterior of the hidden states and the switching process. We introduce a novel initialization procedure using an efficient leave-one-out strategy to compare among candidate models, which significantly improves performance compared to the existing method that relies on deterministic annealing. We then utilize this state-inference solution within a generalized expectation-maximization algorithm to estimate model parameters of the switching process and the linear state-space models with dynamics potentially shared among candidate models. We perform extensive simulations under different settings to benchmark performance against existing switching inference methods and further validate the robustness of our switching inference solution outside the generative switching model class. Finally, we demonstrate the utility of our method for sleep spindle detection in real recordings, showing how switching state-space models can be used to detect and extract transient spindles from human sleep electroencephalograms in an unsupervised manner.

Author summary

An inherent aspect of brain activity is that it changes over time, but existing methods for analyzing neuroscience data typically assume that the underlying activity is strictly stationary, i.e., the properties of that activity do not change over time. One way of handling time-varying data is to break the data into smaller segments that one assumes to be quasi-stationary, but this approach only works if signals vary gradually, and tends to perform poorly when changes are rapid or the target activity is transient in nature. A class of models called linear switching state-space models can explicitly represent time-varying activity, but they pose another set of challenges: exact solutions for such models are intractable, and existing approximate solutions can be highly inaccurate. In this work we present a solution for linear switching state-space models that is able to recover the underlying hidden states and model parameters for time-varying dynamics in a way that is robust to model mis-specification and that outperforms previously proposed methods. We demonstrate the utility of our method by applying it to the problem of sleep spindle detection and show that switching state-space models can automatically detect transient spindle activity from human sleep electroencephalograms.