A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming⁎This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 798321, the German Federal Ministry for Economic Affairs and Energy (BMWi) via eco4wind (0324125B) and DyConPV (0324166B), and by DFG via Research Unit FOR 2401. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Zhu, Jia-Jie; Muandet, Krikamol; Diehl, Moritz; Schölkopf, Bernhard
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 7240
• Page End: 7247
• Publication Date: 2020
• Subjects: Uncertainty Quantification -- Machine Learning -- Kernel Methods -- Nonparametric Methods -- Stochastic System Identification -- Robust Control -- Randomized Algorithms; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.557
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in functional analysis and wide applicability as demonstrated in distinct numerical examples. The implication of this new concept is a new mode of thinking about the statistical nature of uncertainty in dynamical systems.