Fast Stochastic Kernel Approximation by Dual Wasserstein Distance Method
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Keywords: Markov System, Kernel Distance, Wasserstein Distance, Dual Subgradient Method
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TL;DR: We show how to use a novel kernel metric to approximate Markov systems with simpler systems, and how to calculate the approximate kernels by a dual subgradient method.
Abstract: We introduce a generalization of the Wasserstein metric, originally designed for probability measures, to establish a novel distance between probability kernels of Markov systems. We illustrate how this kernel metric may serve 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 effectiveness of our method through several illustrative examples, showcasing its utility in diverse practical scenarios, including dynamic risk estimation. This advancement offers new possibilities for the streamlined analysis and manipulation of Markov systems represented by kernels.
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Submission Number: 6150
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