2023/12/03 by Zhengqi Lin, Lin, Zhengqi, Andrzej Ruszczyński +1 · 2 citations
Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Tensor decomposition and applications #Traffic Prediction and Management Techniques
paper · pdf · doi:10.48550/arxiv.2312.01432
openalex publication_date 2023/12/03 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique, enabling the replacement of the original system's kernel with a kernel with a discrete support of limited cardinality. To facilitate practical implementation, we present a specialized dual algorithm capable of constructing these approximate kernels quickly and efficiently, without requiring computationally expensive matrix operations. Finally, we demonstrate the efficacy of our method through several illustrative examples, showcasing its utility in practical scenarios. This advancement offers new possibilities for the streamlined analysis and manipulation of stochastic systems represented by kernels.