A Variational Infinite Mixture for Probabilistic Inverse Dynamics Learning

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-world 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.

Authors

• Hany Abdulsamad
• Peter Nickl
• Pascal Klink
• Jan Peters 0001

Keywords

• Adaptation models
• Uncertainty
• Trajectory tracking
• Scalability
• Process control
• Probabilistic logic
• Complexity theory
• Inverse Dynamics
• Infinite Mixture
• Benchmark
• Learning Models
• Computational Efficiency
• Regression Techniques
• Variational Inference
• Subset Of Properties
• Random Variables
• Artificial Neural Network
• Mixture Model
• Markov Chain Monte Carlo
• Kriging
• Gaussian Mixture Model
• Incremental Learning
• Range Of Tasks
• Concentration Parameters
• Input Space
• Bayesian Regression
• Discrete Random Variable
• Normalized Mean Square Error
• Dirichlet Process
• Precision Matrix
• Universal Approximation
• Catastrophic Forgetting
• Bayesian Neural Network
• Mixing Weight
• Beta Distribution
• Conjugate Prior
• Hierarchical Local Regression
• Inverse Dynamics Control
• Fully Generative Models
• Dirichlet Process Mixtures