Cox process functional learning

TL;DR

This paper introduces a new method for classifying Cox process trajectories based on their intensity functions, achieving consistency and adaptive convergence rates using a regularized empirical risk minimization approach.

Contribution

It proposes a novel classification algorithm for Cox process trajectories with theoretical guarantees of consistency and adaptive convergence rates.

Findings

The classifier is Bayes-risk consistent.

The convergence rate adapts to the unknown regularity of the intensity process.

The method leverages martingale and stochastic calculus techniques.

Abstract

This article addresses the problem of functional supervised classification of Cox process trajectories, whose random intensity is driven by some exogenous random covariable. The classification task is achieved through a regularized convex empirical risk minimization procedure, and a nonasymptotic oracle inequality is derived. We show that the algorithm provides a Bayes-risk consistent classifier. Furthermore, it is proved that the classifier converges at a rate which adapts to the unknown regularity of the intensity process. Our results are obtained by taking advantage of martingale and stochastic calculus arguments, which are natural in this context and fully exploit the functional nature of the problem.