论文标题
通过非线性复发系统表征深层的高斯过程
Characterizing Deep Gaussian Processes via Nonlinear Recurrence Systems
论文作者
论文摘要
深层高斯过程（DGP）的最新进展表明，具有比传统高斯工艺（GPS）的表达性更高的潜力。但是，存在深层过程的病理学，即当层数增加时，其学习能力会大大降低。在本文中，我们通过研究其相应的非线性动态系统来解释该问题，在DGP中介绍了新的分析。现有工作报告了平方指数内核功能的病理。我们将研究扩展到四种类型的常见固定核函数。层之间的复发关系是分析得出的，提供了更严格的界限和动态系统的收敛速率。我们通过许多实验结果证明了我们的发现。
Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). However, there exists a pathology of deep Gaussian processes that their learning capacities reduce significantly when the number of layers increases. In this paper, we present a new analysis in DGPs by studying its corresponding nonlinear dynamic systems to explain the issue. Existing work reports the pathology for the squared exponential kernel function. We extend our investigation to four types of common stationary kernel functions. The recurrence relations between layers are analytically derived, providing a tighter bound and the rate of convergence of the dynamic systems. We demonstrate our finding with a number of experimental results.
