2024/10/18 by Vladimir Kostić, Kostic, Vladimir R., Karim Lounici +9 · 2 citations
Computer Science · Engineering · #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2410.14477
openalex publication_date 2024/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov semigroup. The unbounded nature of IGs complicates traditional methods such as vector-valued regression and Hilbert-Schmidt operator analysis. Existing techniques, including physics-informed kernel regression, are computationally expensive and limited in scope, with no recovery guarantees for transfer operator methods when the time-lag is small. We propose a novel method that leverages the IG's resolvent, characterized by the Laplace transform of transfer operators. This approach is robust to time-lag variations, ensuring accurate eigenvalue learning even for small time-lags. Our statistical analysis applies to a broader class of Markov processes than current methods while reducing computational complexity from quadratic to linear in the state dimension. Finally, we illustrate the behaviour of our method in two experiments.