In this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-constrained minimax classifier is obtained from the computation of the least favorable prior which maximizes the minimum empirical risk of error over the box-constrained region. After studying the discrete empirical Bayes risk over the probabilistic simplex, we consider a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain. The convergence of our algorithm is established.
1
University of Côte d’Azur, CNRS, I3S laboratory, Sophia-Antipolis, France
2
University of Côte d’Azur, CNRS, laboratory IPMC, Sophia-Antipolis, France
@article{EP_2021_71_a9,
author = {Cyprien Gilet and Susana Barbosa and Lionel Fillatre},
title = {Box-constrained optimization for minimax supervised learning},
journal = {ESAIM. Proceedings},
pages = {101--113},
year = {2021},
volume = {71},
doi = {10.1051/proc/202171109},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202171109/}
}
TY - JOUR
AU - Cyprien Gilet
AU - Susana Barbosa
AU - Lionel Fillatre
TI - Box-constrained optimization for minimax supervised learning
JO - ESAIM. Proceedings
PY - 2021
SP - 101
EP - 113
VL - 71
UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202171109/
DO - 10.1051/proc/202171109
LA - en
ID - EP_2021_71_a9
ER -
