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Well-calibrated probabilistic regression models are a crucial learningcomponent in robotics applications as datasets grow rapidly and tasks becomemore complex. Unfortunately, classical regression models are usually eitherprobabilistic kernel machines with a flexible structure that does not scalegracefully with data or deterministic and vastly scalable automata, albeit witha restrictive parametric form and poor regularization. In this paper, weconsider a probabilistic hierarchical modeling paradigm that combines thebenefits of both worlds to deliver computationally efficient representationswith inherent complexity regularization. The presented approaches areprobabilistic interpretations of local regression techniques that approximatenonlinear functions through a set of local linear or polynomial units.Importantly, we rely on principles from Bayesian nonparametrics to formulateflexible models that adapt their complexity to the data and can potentiallyencompass an infinite number of components. We derive two efficient variationalinference techniques to learn these representations and highlight theadvantages of hierarchical infinite local regression models, such as dealingwith non-smooth functions, mitigating catastrophic forgetting, and enablingparameter sharing and fast predictions. Finally, we validate this approach onlarge inverse dynamics datasets and test the learned models in real-worldcontrol scenarios.

Variational Hierarchical Mixtures for Probabilistic Learning of Inverse Dynamics