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.

翻译：尖峰列车数据在计算神经科学、成像、流数据及金融领域中的应用日益广泛。针对尖峰列车的机器学习策略基于各类神经网络与概率模型，其中概率方法依赖于对潜在尖峰生成模型的参数或非参数规范。本文考虑一类由非参数化强度函数刻画的尖峰列车数据的两类统计分类问题。我们推导出最优贝叶斯规则，进而构建代入式非参数核分类器。建立了规则渐近性质，包括记录时间区间延长与训练集规模增大条件下的极限特性，特别证明了核分类器收敛至贝叶斯规则。有限样本仿真研究验证了所得结论。