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GP3 A Sampling-based Analysis Framework for Gaussian Processes

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Document pages: 6 pages

Abstract: Although machine learning is increasingly applied in control approaches, onlyfew methods guarantee certifiable safety, which is necessary for real worldapplications. These approaches typically rely on well-understood learningalgorithms, which allow formal theoretical analysis. Gaussian processregression is a prominent example among those methods, which attracts growingattention due to its strong Bayesian foundations. Even though many problemsregarding the analysis of Gaussian processes have a similar structure, specificapproaches are typically tailored for them individually, without strong focuson computational efficiency. Thereby, the practical applicability andperformance of these approaches is limited. In order to overcome this issue, wepropose a novel framework called GP3, general purpose computation on graphicsprocessing units for Gaussian processes, which allows to solve many of theexisting problems efficiently. By employing interval analysis, local Lipschitzconstants are computed in order to extend properties verified on a grid tocontinuous state spaces. Since the computation is completely parallelizable,the computational benefits of GPU processing are exploited in combination withmulti-resolution sampling in order to allow high resolution analysis.

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