Learning the Infinitesimal Generator of Stochastic Diffusion Processes

Autor:	Kostic, Vladimir R., Lounici, Karim, Halconruy, Helene, Devergne, Timothee, Pontil, Massimiliano
Rok vydání:	2024
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning Mathematics - Probability 62M15
Druh dokumentu:	Working Paper
Popis:	We address data-driven learning of the infinitesimal generator of stochastic diffusion processes, essential for understanding numerical simulations of natural and physical systems. The unbounded nature of the generator poses significant challenges, rendering conventional analysis techniques for Hilbert-Schmidt operators ineffective. To overcome this, we introduce a novel framework based on the energy functional for these stochastic processes. Our approach integrates physical priors through an energy-based risk metric in both full and partial knowledge settings. We evaluate the statistical performance of a reduced-rank estimator in reproducing kernel Hilbert spaces (RKHS) in the partial knowledge setting. Notably, our approach provides learning bounds independent of the state space dimension and ensures non-spurious spectral estimation. Additionally, we elucidate how the distortion between the intrinsic energy-induced metric of the stochastic diffusion and the RKHS metric used for generator estimation impacts the spectral learning bounds. Comment: 38 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.12940 Zobrazit plný text záznamu View this record from Arxiv