Detection of dependence patterns with delay

TL;DR

This paper extends the Unitary Events method to detect dependence patterns among multiple neurons using a continuous framework, establishing a limit distribution for coincidence counts and proposing an independence test with multiple testing correction.

Contribution

It generalizes the UE method to more than two neurons, deriving the limit distribution of coincidence counts and developing a multiple testing procedure.

Findings

The limit distribution of the coincidence count is established.

The proposed independence test performs well in simulations.

Application to real data demonstrates practical utility.

Abstract

The Unitary Events (UE) method is a popular and efficient method used this last decade to detect dependence patterns of joint spike activity among simultaneously recorded neurons. The first introduced method is based on binned coincidence count \citep{Grun1996} and can be applied on two or more simultaneously recorded neurons. Among the improvements of the methods, a transposition to the continuous framework has recently been proposed in \citep{muino2014frequent} and fully investigated in \citep{MTGAUE} for two neurons. The goal of the present paper is to extend this study to more than two neurons. The main result is the determination of the limit distribution of the coincidence count. This leads to the construction of an independence test between $L\geq 2$ neurons. Finally we propose a multiple test procedure via a Benjamini and Hochberg approach \citep{Benjamini1995}. All the theoretical results are illustrated by a simulation study, and compared to the UE method proposed in \citep{Grun2002}. Furthermore our method is applied on real data.