论文标题
连续时间回归的内核方法在子集和歧管上
Kernel Methods for Regression in Continuous Time over Subsets and Manifolds
论文作者
论文摘要
本文在某些类型的riemannian流形的子集上得出了连续时间回归的误差范围。回归问题通常是由非线性进化定律对歧管的值驱动的，并且它被视为复制的内核希尔伯特空间（RKHS）的最佳估计之一。在歧管上定义了一个新的激发持续性（PE）概念，并使用PE条件得出了连续时间估计的收敛速率。我们讨论并分析了确切回归解决方案的两种近似方法。然后，我们用一些数值模拟结束了论文，这些模拟说明了计算函数估计的定性特征。介绍了在洛伦兹系统轨迹上产生的函数估计值的数值结果。此外，我们使用运动捕获数据分析了两种近似方法的实现。
This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as one of optimal estimation in a reproducing kernel Hilbert space (RKHS). A new notion of persistency of excitation (PE) is defined for the estimation problem over the manifold, and rates of convergence of the continuous time estimates are derived using the PE condition. We discuss and analyze two approximation methods of the exact regression solution. We then conclude the paper with some numerical simulations that illustrate the qualitative character of the computed function estimates. Numerical results from function estimates generated over a trajectory of the Lorenz system are presented. Additionally, we analyze an implementation of the two approximation methods using motion capture data.
