Plug-In Classification of Drift Functions in Diffusion Processes Using Neural Networks

TL;DR

This paper introduces a neural network-based plug-in classifier for multiclass diffusion processes, leveraging drift function estimation to improve classification accuracy and theoretical guarantees.

Contribution

It develops a novel classification method using neural networks to estimate drift functions, with convergence analysis and advantages over existing trajectory-based classifiers.

Findings

Achieves better classification performance than previous methods in one dimension.

Remains effective in higher dimensions with compositional drift functions.

Outperforms end-to-end neural classifiers trained directly on trajectories.

Abstract

We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then construct a plug-in classifier by estimating the class-specific drifts with neural networks. Under standard regularity assumptions, we establish convergence rates for the excess misclassification risk, making explicit the contributions of drift estimation, time discretization, and dimension. Our analysis also highlights the benefit of exploiting the diffusion structure: the drift is learned from all observed increments, leading to sharper guarantees than direct trajectory-based neural classifiers in the considered setting. Numerical experiments support the theory: the proposed method achieves better classification performance than Denis et al. (2024) in dimension one, remains effective in higher dimensions when the drift functions admit a compositional structure, and outperforms end-to-end neural classifiers trained directly on trajectories, as in Bos & Schmidt-Hieber (2022).