From the entropy to the statistical structure of spike trains

TL;DR

This paper evaluates various entropy estimators for spike train data, demonstrating their effectiveness in revealing underlying neural structures and testing renewal process models using real and synthetic data.

Contribution

It introduces new theoretical results for entropy estimators and applies them systematically to neural spike train data to infer structural properties and model appropriateness.

Findings

Entropy estimates can detect long-term structure in spike trains.

The hypothesis test assesses the renewal process model fit.

The CTW algorithm reveals underlying neural data structure.

Abstract

We use statistical estimates of the entropy rate of spike train data in order to make inferences about the underlying structure of the spike train itself. We first examine a number of different parametric and nonparametric estimators (some known and some new), including the ``plug-in'' method, several versions of Lempel-Ziv-based compression algorithms, a maximum likelihood estimator tailored to renewal processes, and the natural estimator derived from the Context-Tree Weighting method (CTW). The theoretical properties of these estimators are examined, several new theoretical results are developed, and all estimators are systematically applied to various types of synthetic data and under different conditions. Our main focus is on the performance of these entropy estimators on the (binary) spike trains of 28 neurons recorded simultaneously for a one-hour period from the primary motor and dorsal premotor cortices of a monkey. We show how the entropy estimates can be used to test for the existence of long-term structure in the data, and we construct a hypothesis test for whether the renewal process model is appropriate for these spike trains. Further, by applying the CTW algorithm we derive the maximum a posterior (MAP) tree model of our empirical data, and comment on the underlying structure it reveals.