Multitaper Analysis of Semi-Stationary Spectra from Multivariate Neuronal Spiking Observations.

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.

Direct extraction of signal and noise correlations from two-photon calcium imaging of ensemble neuronal activity.

Neuronal activity correlations are key to understanding how populations of neurons collectively encode information. While two-photon calcium imaging has created a unique opportunity to record the activity of large populations of neurons, existing methods for inferring correlations from these data face several challenges. First, the observations of spiking activity produced by two-photon imaging are temporally blurred and noisy. Secondly, even if the spiking data were perfectly recovered via deconvolution, inferring network-level features from binary spiking data is a challenging task due to the non-linear relation of neuronal spiking to endogenous and exogenous inputs. In this work, we propose a methodology to explicitly model and directly estimate signal and noise correlations from two-photon fluorescence observations, without requiring intermediate spike deconvolution. We provide theoretical guarantees on the performance of the proposed estimator and demonstrate its utility through applications to simulated and experimentally recorded data from the mouse auditory cortex.