论文标题
Sleipnir：具有衍生物的高斯过程回归的确定性和可证明的特征扩展
SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives
论文作者
论文摘要
高斯过程是具有出色分析特性的重要回归工具，可以直接整合衍生观测。但是，香草GP方法在观察量中立方扩展。在这项工作中，我们提出了一种基于正交傅立叶特征的衍生物来缩放GP回归的新方法。然后，我们证明了确定性，非反应和指数快速衰减的误差边界，这些误差范围均适用于近似内核和近似后部。此外，为了说明我们方法的实际适用性，然后将其应用于Odin，这是最近开发的ODE参数推断算法。在广泛的实验部分中，所有结果均经过经验验证，证明了这种方法的速度，准确性和实际适用性。
Gaussian processes are an important regression tool with excellent analytic properties which allow for direct integration of derivative observations. However, vanilla GP methods scale cubically in the amount of observations. In this work, we propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We then prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior. To furthermore illustrate the practical applicability of our method, we then apply it to ODIN, a recently developed algorithm for ODE parameter inference. In an extensive experiments section, all results are empirically validated, demonstrating the speed, accuracy, and practical applicability of this approach.
