Reduced-Rank Online Gaussian Process Modeling With Uncertain Inputs

Jade Coulin, Mohamed Ouerfelli, Richard Guillemard, Vincent Gay-Bellile, Cyril JOLY, Arnaud de La Fortelle

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Keywords: Gaussian process, reduced-rank, uncertainty, input noise

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Abstract: Gaussian Process (GP) is an increasingly popular modeling approach. In its classical formulation, the inputs are supposed to be perfectly known. However, in some use cases, this assumption is not true: the inputs as well as the outputs can be corrupted by noise. Some methods already insert these uncertainties in GP modeling but the only currently existing online algorithm (i.e. that incrementally updates the model each time a measure is acquired) still lacks in robustness and precision. In this article we propose a novel online Gaussian Process (GP) modeling approach for vector field mapping with uncertain inputs. They are included into the GP through a complete second-order Taylor approximation with a better estimation of variances. Our experiments prove that our algorithm is more accurate and robust than the previous online method for a shorter computing time. Moreover, for high input uncertainties, our method achieves better performance than both online and offline state of the art methods on simulated data. This algorithm can also be applied to diverse real scenarios which require precise estimation of unknown functions from a small set of corrupted datapoints, as we show in the challenging problem of indoor localization, mapping magnetic fields.

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Submission Number: 7954