Dynamic estimation of auditory temporal response functions via state-space models with Gaussian mixture process noise

Estimating the latent dynamics underlying biological processes is a central problem in computational biology. State-space models with Gaussian statistics are widely used for estimation of such latent dynamics and have been successfully utilized in the analysis of biological data. Gaussian statistics, however, fail to capture several key features of the dynamics of biological processes (e.g., brain dynamics) such as abrupt state changes and exogenous processes that affect the states in a structured fashion. Although Gaussian mixture process noise models have been considered as an alternative to capture such effects, data-driven inference of their parameters is not well-established in the literature. The objective of this paper is to develop efficient algorithms for inferring the parameters of a general class of Gaussian mixture process noise models from noisy and limited observations, and to utilize them in extracting the neural dynamics that underlie auditory processing from magnetoencephalography (MEG) data in a cocktail party setting. We develop an algorithm based on Expectation-Maximization to estimate the process noise parameters from state-space observations. We apply our algorithm to simulated and experimentally-recorded MEG data from auditory experiments in the cocktail party paradigm to estimate the underlying dynamic Temporal Response Functions (TRFs). Our simulation results show that the richer representation of the process noise as a Gaussian mixture significantly improves state estimation and capturing the heterogeneity of the TRF dynamics. Application to MEG data reveals improvements over existing TRF estimation techniques, and provides a reliable alternative to current approaches for probing neural dynamics in a cocktail party scenario, as well as attention decoding in emerging applications such as smart hearing aids. Our proposed methodology provides a framework for efficient inference of Gaussian mixture process noise models, with application to a wide range of biological data with underlying heterogeneous and latent dynamics.Author summary: While Gaussian statistics are widely-used in analyzing biological data, they are not able to fully capture the observed heterogeneity and abrupt changes in the dynamics that govern the underlying biological processes. A notable example of such a process is the ability of the human brain to focus attention on one speaker among many in a cocktail party and switch attention to any other at will. We propose a signal processing methodology to extract the dynamics of such switching processes from noisy biological data in a robust and computationally efficient manner, and apply them to experimentally-recoded magnetoencephalography data from the human brain under cocktail party settings. Our results provide new insight on the heterogeneous neural dynamics that govern auditory attention switching. While our proposed methodology can be readily used as a reliable alternative to existing approaches in studying auditory processing in the human brain, it is suitable to be applied to a wide range of biological data with underlying heterogeneous dynamics.