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

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 preprocessing
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.