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.

翻译：良好校准的概率回归模型是机器人应用中的关键学习组件，因为数据集迅速增长且任务变得更加复杂。不幸的是，经典回归模型通常是具有灵活结构但无法随数据优雅扩展的概率核机器，或是具有限制性参数形式和较差正则化的确定性且高度可扩展的自动机。在本文中，我们考虑了一种概率层次建模范式，它结合了两种方法的优点，以提供具有内在复杂性正则化的计算高效表示。所提出的方法是对局部回归技术的概率解释，通过一组局部线性或多项式单元来逼近非线性函数。重要的是，我们依赖贝叶斯非参数原理来制定灵活的模型，这些模型能够根据数据调整其复杂性，并且可能包含无限数量的组件。我们推导了两种高效变分推理技术来学习这些表示，并突出了层次无限局部回归模型的优势，例如处理非光滑函数、缓解灾难性遗忘、实现参数共享和快速预测。最后，我们在大型逆动力数据集上验证了该方法，并在真实世界控制场景中测试了学习到的模型。