Switching state-space modeling of neural signal dynamics

Abstract

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 non-stationary, 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 properties selected by a probabilistic switching process. Unfortunately, unlike linear state-space models, exact solutions for state inference and parameter learning with switching state-space models are intractable. Here we derive a solution to the inference problem for a general probabilistic switching state-space framework based on a variational approximation on the joint posterior distribution of the underlying states and the switching process. We then use this state-inference solution within a generalized expectation-maximization (EM) algorithm to learn the model parameters of the linear state-space models and the switching process. We perform extensive simulations in different settings to benchmark the performance of our method against existing switching inference methods. We also demonstrate the robustness of our switching inference to characterize dynamics outside the generative switching model class. In addition, we introduce a novel initialization strategy for the expectation step of the generalized EM algorithm using a leave-one-out strategy to compare among candidate models, which significantly improves performance compared to existing switching methods that employ deterministic annealing. Finally, we demonstrate the utility of our method for the problem of sleep spindle detection, showing how switching state-space models can be used to detect and extract transient spindles from human sleep electroencephalograms in an unsupervised manner.

Detection of High-Frequency Oscillations from Intracranial EEG Data with Switching State Space Model

“…Oscillatory patterns are pervasive in neural signals, necessitating their modeling with a high degree of accuracy and precision to detect any brief oscillatory events. In this context, we utilize a novel state-space model specifically tailored for the task of capturing oscillations [8][12]: The model can be interpreted as a phasor that rotates around the origin in the complex plane with a frequency ω ( m ) (in radians). The constant a represents the damping factor, which dictates the rate at which the oscillations diminish over time.…”

“…Recently, a new SSSM inference paradigm was introduced by He et al [8], which leverages state inference solutions within the generalized expectation-maximization algorithm to estimate model parameters for the switching process, which it is particularly suitable for neural signal analysis. Inspired by He et al [8], we propose to leverage SSSM for identifying HFOs. The advantage of using SSSM is its capability of identifying HFOs instantaneously without relying on feature extraction within an epoched iEEG window.…”

“…We applied the novel method proposed by He et al [8] to the problem of detecting HFOs in the iEEG data.…”

“…• We applied the novel method proposed by He et al [8] to the problem of detecting HFOs in the iEEG data. • We evaluate our model using the Zurich iEEG HFO Dataset [11], demonstrating its ability to achieve more accurate results compared to the original event annotations.…”

An unbiased method to partition diverse neuronal responses into functional ensembles reveals interpretable population dynamics during innate social behavior

“…Other modern approaches have fewer free parameters and are feature-based 10 , lack interpretability because of their reliance on opaque artificial neural networks 11,12 , do not provide a direct link to the dynamics of a given ensemble 13 , or are not based on state-space models of neural activity 14 . State-space models can uncover the underlying neural dynamics with high efficiency and flexibility 15 . Thus, there is a need for approaches that, starting with large amounts of time-varying neural activity, can not only cluster individual neurons into ensembles able to decode naturalistic behavior 16,17 , but can also give interpretable insights into the nature of computations in these ensembles.…”