论文标题
州空间高斯流程模型中的快速变分学习
Fast Variational Learning in State-Space Gaussian Process Models
论文作者
论文摘要
通常可以通过随机微分方程公式在线性时间内执行具有1D输入的高斯过程（GP）回归。但是，对于非高斯的可能性，这需要应用近似推理方法，这可能使实施变得困难，例如，期望传播在数值上可能是不稳定的，并且变异推断可以在计算上效率低下。在本文中，我们提出了一种消除这种困难的新方法。我们的方法基于一种称为共轭兼容的变量推理的现有方法，可以通过卡尔曼递归递归进行线性推理，同时避免数值不稳定性和收敛问题。我们提供有效的JAX实现，该实现利用了即时的汇编，并允许通过大型陆面进行快速自动差异化。总体而言，我们的方法会导致状态空间GP模型的快速和稳定的变异推断，这些推断可以将其缩放到数百万个数据点的时间序列。
Gaussian process (GP) regression with 1D inputs can often be performed in linear time via a stochastic differential equation formulation. However, for non-Gaussian likelihoods, this requires application of approximate inference methods which can make the implementation difficult, e.g., expectation propagation can be numerically unstable and variational inference can be computationally inefficient. In this paper, we propose a new method that removes such difficulties. Building upon an existing method called conjugate-computation variational inference, our approach enables linear-time inference via Kalman recursions while avoiding numerical instabilities and convergence issues. We provide an efficient JAX implementation which exploits just-in-time compilation and allows for fast automatic differentiation through large for-loops. Overall, our approach leads to fast and stable variational inference in state-space GP models that can be scaled to time series with millions of data points.
