Conference Agenda
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High-dimensional statistics and learning Location: 1.012 Session Chair: Martin Wahl | |
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Supervised classification for Ornstein-Uhlenbeck diffusions with separation condition Humboldt University of Berlin, Germany We study binary supervised classification based on repeated independent observations of continuous sample paths. Our focus is a diffusion classification model in which the features follow an Ornstein-Uhlenbeck process with class-dependent drifts. We consider plug-in classifiers constructed from drift estimators and analyze the performance via the excess risk. Under a separation condition on the drift parameters, we establish upper bounds of the excess risk, which are explicitly parametrized by the separation distance quantifying the difficulty of the problem. Specifically, when the drift distance is bounded away from zero, the plug-in classifiers achieve a fast convergence rate of order n-1 (up to logarithmic factors) in the constant drift scenario. Furthermore, we discuss extensions of this framework to time-inhomogeneous drift functions. The theoretical approach utilizes the Wiener chaos representation and spectral theory to characterize the log-likelihood ratio as a quadratic form of Gaussian random variables, enabling a precise analysis of margin properties and concentration results. This extends the fast-rate results from classification problems with linear and Gaussian white noise models to dynamical diffusion systems with Gaussian structure under separation conditions. | |
