Their flexibility to learn general function classes renders nonparametric regression algorithms particularly attractive in system identification and data-based control settings, where little a priori knowledge about a dynamical system is to be presumed. Building on approaches known as NSMor Lipschitz regression, we propose a new nonparametic machine learning approach. While it inherits theoretical learning guarantees from the methods it is built upon, it is designed to limit the computational effort both for learning and for generating predictions. This renders our method applicable to online system identification and control settings where the desired sample frequency precludes previous nonparametric approaches from being deployed. Apart from deriving a guarantee on the ability of our method to learn any continuous function, we illustrate some of its practical merits on a number of benchmark comparison problems.
We propose SLAC, a sparse approximation to a Lipschitz constant estimator that can be utilised to obtain uncertainty bounds around predictions of a regression method. As we demonstrate in a series of experiments on real-world and synthetic data, this approach can yield fast and robust predictive uncertainty bounds that are as reliable as those of Gaussian Processes or Bayesian Neural Networks, while reducing computational effort markedly.
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