Bayes Risk Consistency of Nonparametric Classification Rules for Spike
  Trains Data
Mirosław Pawlak Mateusz Pabian Dominik Rzepka
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.