The Hinges model: A one-dimensional continuous piecewise polynomial model

Abstract

In this article we propose an efficient approach to flexible and robust one-dimensional curve fitting under stringent high noise conditions. This is an important subproblem arising in many automatic learning tasks. The proposed algorithm combines the noise filtering feature of an existing scatterplot smoothing algorithm (the Supersmoother) with the flexibility and computational efficiency of piecewise linear hinges models. The former is used in order to provide a first approximation of the noise in the data, in a pre-processing step. Then, the latter are used in order to provide a closed form approximation of the underlying curve and further to reduce bias of the Supersmoother thanks to an efficient refitting algorithm, using updating formulas. The proposed technique is assessed on a synthetic test problem and one closer to real world data.