Nonparametric plug-in classifier for multiclass classification of S.D.E. paths

TL;DR

This paper introduces a nonparametric plug-in classifier for multiclass classification of diffusion process paths, estimating drift and diffusion functions to discriminate classes with proven consistency and convergence rates.

Contribution

It develops a novel nonparametric classification method for diffusion paths, with theoretical guarantees and practical validation, addressing unknown diffusion coefficients.

Findings

Classifier is consistent under mild conditions.

Convergence rates are established under various assumptions.

Numerical experiments support theoretical results.

Abstract

We study the multiclass classification problem where the features come from the mixture of time-homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown. In this framework, we build a plug-in classifier which relies on nonparametric estimators of the drift and diffusion functions. We first establish the consistency of our classification procedure under mild assumptions and then provide rates of cnvergence under different set of assumptions. Finally, a numerical study supports our theoretical findings.