标题： SLEIPNIR：具有导数的高斯过程回归的确定性和可证明准确的特征扩展 显示英文标题

标题： SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives

摘要： 高斯过程是一种重要的回归工具，具有优异的解析性质，允许直接整合导数观测值。 然而，传统的GP方法在观测数量上呈立方级增长。 在这项工作中，我们提出了一种基于积分傅里叶特征的新方法，用于扩展带有导数的GP回归。 然后，我们证明了确定性的、非渐近的且指数衰减的误差界限，这些界限适用于近似核以及近似后验。 为了进一步说明我们方法的实际适用性，我们将其应用于ODIN，这是一种最近开发的用于ODE参数推断的算法。 在广泛的实验部分，所有结果都经过实证验证，展示了该方法的速度、准确性和实际适用性。 显示英文摘要

摘要： 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.