Multitaper Analysis of Semi-Stationary Spectra From Multivariate Neuronal Spiking Observations

Anuththara Rupasinghe, Behtash Babadi

Abstract: Extracting the spectral representations of neural processes that underlie spiking activity is key to understanding how brain rhythms mediate cognitive functions. While spectral estimation of continuous time-series is well studied, inferring the spectral representation of latent non-stationary processes based on spiking observations is challenging due to the underlying nonlinearities that limit the spectrotemporal resolution of existing methods. In this paper, we address this issue by developing a multitaper spectral estimation methodology that can be directly applied to multivariate spiking observations in order to extract the semi-stationary spectral density of the latent non-stationary processes that govern spiking activity. We establish theoretical bounds on the bias-variance trade-off of our proposed estimator. Finally, application of our proposed technique to simulated and real data reveals significant performance gains over existing methods.