Variational Hierarchical Mixtures for Probabilistic Learning of Inverse Dynamics

Hany Abdulsamad, Peter Nickl, Pascal Klink, Jan Peters

Research output: Contribution to journalArticleScientificpeer-review


Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic kernel machines with a flexible structure that does not scale gracefully with data or deterministic and vastly scalable automata, albeit with a restrictive parametric form and poor regularization. In this paper, we consider a probabilistic hierarchical modeling paradigm that combines the benefits of both worlds to deliver computationally efficient representations with inherent complexity regularization. The presented approaches are probabilistic interpretations of local regression techniques that approximate nonlinear functions through a set of local linear or polynomial units. Importantly, we rely on principles from Bayesian nonparametrics to formulate flexible models that adapt their complexity to the data and can potentially encompass an infinite number of components. We derive two efficient variational inference techniques to learn these representations and highlight the advantages of hierarchical infinite local regression models, such as dealing with non-smooth functions, mitigating catastrophic forgetting, and enabling parameter sharing and fast predictions. Finally, we validate this approach on large inverse dynamics datasets and test the learned models in real-world control scenarios.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Publication statusE-pub ahead of print - 2023
MoE publication typeA1 Journal article-refereed


  • Bayes methods
  • Computational modeling
  • Data models
  • Dirichlet Process Mixtures
  • Generative Models
  • Hierarchical Local Regression
  • Inverse Dynamics Control
  • Manipulator dynamics
  • Mixture models
  • Neural networks
  • Uncertainty


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