Section: New Results
Iterative isotone regression
Participants : Arnaud Guyader, Nicolas Jégou.
This is a collaboration with Nicolas Hengartner (Los Alamos) and Eric Matzner–Løber (université de Rennes 2), and with Alexander B. Németh (Babeş Bolyai University) and Sándor Z. Németh (University of Birmingham).
The current collaboration on nonparametric regression focuses on a novel nonparametric regression technique that applies ideas borrowed from iterative bias reduction to estimating functions of bounded variations. This work has emerged from the joint supervision of Nicolas Jégou's PhD thesis by Arnaud Guyader, Nick Hengartner and Eric Matzner-Løber.
A geometric approach has been investigated, as an extension of some ideas developed in the thesis. The current work  proposes and analyzes a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic regression and the estimation of additive models. A geometrical interpretation enables us to link this iterative method with Von Neumann's algorithm. Moreover, making a connection with the general property of isotonicity of projection onto convex cones, we derive another equivalent algorithm and go further in the analysis. As iterating the algorithm leads to overfitting, several practical stopping criteria are also presented and discussed.