L1-Optimal Splines for Outlier Rejection

TL;DR

This paper introduces L1-optimized control theoretic splines to improve outlier rejection in data fitting, enhancing robustness over traditional L2-based methods, demonstrated through a numerical example.

Contribution

The paper proposes a novel L1 optimization approach for control theoretic splines to robustly reject outliers, extending spline regression techniques.

Findings

L1-optimized splines effectively reject outliers in data.

The method outperforms traditional L2-based splines in robustness.

Numerical example demonstrates improved outlier handling.

Abstract

In this article, we consider control theoretic splines with L1 optimization for rejecting outliers in data. Control theoretic splines are either interpolating or smoothing splines, depending on a cost function with a constraint defined by linear differential equations. Control theoretic splines are effective for Gaussian noise in data since the estimation is based on L2 optimization. However, in practice, there may be outliers in data, which may occur with vanishingly small probability under the Gaussian assumption of noise, to which L2-optimized spline regression may be very sensitive. To achieve robustness against outliers, we propose to use L1 optimality, which is also used in support vector regression. A numerical example shows the effectiveness of the proposed method.