  Probabilistic regression techniques in control and robotics applications have
to fulfill different criteria of data-driven adaptability, computational
efficiency, scalability to high dimensions, and the capacity to deal with
different modalities in the data. Classical regressors usually fulfill only a
subset of these properties. In this work, we extend seminal work on Bayesian
nonparametric mixtures and derive an efficient variational Bayes inference
technique for infinite mixtures of probabilistic local polynomial models with
well-calibrated certainty quantification. We highlight the model's power in
combining data-driven complexity adaptation, fast prediction and the ability to
deal with discontinuous functions and heteroscedastic noise. We benchmark this
technique on a range of large real inverse dynamics datasets, showing that the
infinite mixture formulation is competitive with classical Local Learning
methods and regularizes model complexity by adapting the number of components
based on data and without relying on heuristics. Moreover, to showcase the
practicality of the approach, we use the learned models for online inverse
dynamics control of a Barrett-WAM manipulator, significantly improving the
trajectory tracking performance.
