  Techniques known as Nonlinear Set Membership prediction, Kinky Inference or
Lipschitz Interpolation are fast and numerically robust approaches to
nonparametric machine learning that have been proposed to be utilised in the
context of system identification and learning-based control. They utilise
presupposed Lipschitz properties in order to compute inferences over unobserved
function values. Unfortunately, most of these approaches rely on exact
knowledge about the input space metric as well as about the Lipschitz constant.
Furthermore, existing techniques to estimate the Lipschitz constants from the
data are not robust to noise or seem to be ad-hoc and typically are decoupled
from the ultimate learning and prediction task. To overcome these limitations,
we propose an approach for optimising parameters of the presupposed metrics by
minimising validation set prediction errors. To avoid poor performance due to
local minima, we propose to utilise Lipschitz properties of the optimisation
objective to ensure global optimisation success. The resulting approach is a
new flexible method for nonparametric black-box learning. We provide
experimental evidence of the competitiveness of our approach on artificial as
well as on real data.
