Bayes Risk Consistency of Nonparametric Classification Rules for Spike Trains Data

TL;DR

This paper investigates the theoretical properties of nonparametric classifiers for spike train data, establishing their convergence to the optimal Bayes rule and supporting findings with simulation studies.

Contribution

It derives the Bayes rule for nonparametric spike train classification and proves the convergence of the kernel classifier to this optimal rule.

Findings

Kernel classifier converges to the Bayes rule asymptotically

Theoretical results are supported by finite sample simulations

Optimal Bayes rule is explicitly derived for nonparametric spike train data

Abstract

Spike trains data find a growing list of applications in computational neuroscience, imaging, streaming data and finance. Machine learning strategies for spike trains are based on various neural network and probabilistic models. The probabilistic approach is relying on parametric or nonparametric specifications of the underlying spike generation model. In this paper we consider the two-class statistical classification problem for a class of spike train data characterized by nonparametrically specified intensity functions. We derive the optimal Bayes rule and next form the plug-in nonparametric kernel classifier. Asymptotical properties of the rules are established including the limit with respect to the increasing recording time interval and the size of a training set. In particular the convergence of the kernel classifier to the Bayes rule is proved. The obtained results are supported by a finite sample simulation studies.