Point processes are finding growing applications in numerous fields, such as neuroscience, high frequency finance and social media. So classic problems of classification and clustering are of increasing interest. However, analytic study of misclassification error probability in multi-class classification has barely begun. In this paper, we tackle the multi-class likelihood classification problem for point processes and develop, for the first time, both asymptotic upper and lower bounds on the error rate in terms of computable pair-wise affinities. We apply these general results to classifying renewal processes. Under some technical conditions, we show that the bounds have exponential decay and give explicit associated constants. The results are illustrated with a non-trivial simulation.

翻译：点过程在神经科学、高频金融和社交媒体等众多领域中的应用日益广泛，因此分类和聚类等经典问题正受到越来越多的关注。然而，关于多类分类中误分类错误概率的解析研究才刚刚起步。本文针对点过程的多类似然分类问题展开研究，并首次基于可计算的成对亲和度推导了错误率的渐近上界和下界。我们将这些一般性结果应用于更新过程的分类。在特定技术条件下，我们证明了这些界具有指数衰减特性，并给出了显式的相关常数。通过一项非平凡的模拟实验对结果进行了验证。