Estimation of Vector Autoregressive Parameters and Granger Causality From Noisy Multichannel Data.

Abstract

The objective of this paper is to estimate the parameters of a multivariate autoregressive process from noisy multichannel data. Using a multivariate generalization of the Cadzow method, we propose a new method for estimating autoregressive parameters from noisy data: the nonlinear Cadzow method. We show that our method outperforms existing multivariate methods such as higher order Yule-Walker method and Kalman EM method on simulated data. We apply our method to estimation of Granger causality from noisy data and again obtain superior results compared to previous methods. Finally, when applied to experimental local field potential data from monkey somatosensory and motor cortical areas, our method produces results consistent with cortical physiology. The proposed nonlinear Cadzow method outperforms existing methods in obtaining denoised estimates of multivariate autoregressive parameters. Since multichannel recordings have become commonplace in biomedical applications ranging from discovering functional connectivity in the brain to speech data analysis and these recordings are inevitably contaminated by measurement noise, we believe our method has the potential for significant impact.