Empirical risk minimization algorithm for multiclass classification of S.D.E. paths

• URL: http://arxiv.org/abs/2503.14045v1
• Date: Tue, 18 Mar 2025 09:06:19 GMT
• Title: Empirical risk minimization algorithm for multiclass classification of S.D.E. paths
• Authors: Christophe Denis, Eddy Ella Mintsa,
• Abstract summary: We propose a classification algorithm that relies on the minimization of the L 2 risk.<n>We establish rates of convergence for the resulting predictor.<n>A simulation study highlights the numerical performance of our classification algorithm.
• Score: 2.3940819037450987
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address the multiclass classification problem for stochastic diffusion paths, assuming that the classes are distinguished by their drift functions, while the diffusion coefficient remains common across all classes. In this setting, we propose a classification algorithm that relies on the minimization of the L 2 risk. We establish rates of convergence for the resulting predictor. Notably, we introduce a margin assumption under which we show that our procedure can achieve fast rates of convergence. Finally, a simulation study highlights the numerical performance of our classification algorithm.

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