L1控制理论平滑样条
L1 Control Theoretic Smoothing Splines
AI总结：
本文提出基于L1最优性的控制理论平滑样条，用于减少描述拟合曲线的参数数量并去除异常数据。通过线性动态系统生成控制理论样条，利用L1范数进行正则化和经验风险项优化，有效提升鲁棒性。
摘要：
本文提出一种基于L1最优性的控制理论平滑样条，旨在减少描述拟合曲线的参数数量并去除异常数据。控制理论样条是通过给定线性动态系统生成的平滑样条。传统设计需要与数据数量相同的基函数，结果对异常值不鲁棒。为解决这些问题，本文提出使用L1最优性，即使用L1范数作为正则化项和/或经验风险项。优化过程描述为凸优化问题，可通过数值优化软件高效求解。数值示例展示了所提方法的有效性。
英文摘要：
In this paper, we propose control theoretic smoothing splines with L1 optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the result is not robust against outliers. To solve these problems, we propose to use L1 optimality, that is, we use the L1 norm for the regularization term and/or the empirical risk term. The optimization is described by a convex optimization, which can be efficiently solved via a numerical optimization software. A numerical example shows the effectiveness of the proposed method.
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