Empirical risk minimization algorithm for multiclass classification of S.D.E. paths
This work addresses classification problems in stochastic processes, likely for applications in finance or physics, but appears incremental as it builds on existing risk minimization methods.
The paper tackles multiclass classification of stochastic diffusion paths by distinguishing classes based on drift functions, proposing an algorithm that minimizes L2 risk and establishing convergence rates, with a simulation study demonstrating numerical performance.
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.