Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. 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 a set of large inverse dynamics datasets and test the learned models in real-world control scenarios.

这篇论文介绍了一种层级建模范式，结合了概率回归模型和贝叶斯非参数方法，采用了一种逼近非线性函数的局部回归技术，提出了两种有效的变分推理技术来学习这些模型，此方法可适应数据并涵盖无限数量的组件，本文对大型逆动力学数据集进行了验证和测试。

层次变分混合模型用于学习动力学概率反演