A multivariate phase distribution and its estimation

TL;DR

This paper introduces a new multivariate phase distribution that models joint phase relationships, along with an efficient estimation method, demonstrated on neural data to analyze brain area coupling.

Contribution

It presents a novel multivariate phase distribution and an efficient estimation algorithm suitable for high-dimensional and limited data scenarios.

Findings

Performs well in high dimensions (d=100)

Accurate with as few as 100 samples per dimension

Applicable to neural data analysis for brain coupling

Abstract

Circular variables such as phase or orientation have received considerable attention throughout the scientific and engineering communities and have recently been quite prominent in the field of neuroscience. While many analytic techniques have used phase as an effective representation, there has been little work on techniques that capture the joint statistics of multiple phase variables. In this paper we introduce a distribution that captures empirically observed pair-wise phase relationships. Importantly, we have developed a computationally efficient and accurate technique for estimating the parameters of this distribution from data. We show that the algorithm performs well in high-dimensions (d=100), and in cases with limited data (as few as 100 samples per dimension). We also demonstrate how this technique can be applied to electrocorticography (ECoG) recordings to investigate the coupling of brain areas during different behavioral states. This distribution and estimation technique can be broadly applied to any setting that produces multiple circular variables.