Topologically penalized regression on manifolds - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Machine Learning Research Year : 2022

Topologically penalized regression on manifolds

Abstract

We study a regression problem on a compact manifold M. In order to take advantage of the underlying geometry and topology of the data, the regression task is performed on the basis of the first several eigenfunctions of the Laplace-Beltrami operator of the manifold, that are regularized with topological penalties. The proposed penalties are based on the topology of the sub-level sets of either the eigenfunctions or the estimated function. The overall approach is shown to yield promising and competitive performance on various applications to both synthetic and real data sets. We also provide theoretical guarantees on the regression function estimates, on both its prediction error and its smoothness (in a topological sense). Taken together, these results support the relevance of our approach in the case where the targeted function is "topologically smooth".
Fichier principal
Vignette du fichier
tpregression.pdf (6.19 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03402076 , version 1 (25-10-2021)
hal-03402076 , version 2 (07-06-2022)

Identifiers

Cite

Olympio Hacquard, Krishnakumar Balasubramanian, Gilles Blanchard, Clément Levrard, Wolfgang Polonik. Topologically penalized regression on manifolds. Journal of Machine Learning Research, 2022, 23 (161), pp.1-39. ⟨hal-03402076v2⟩
155 View
74 Download

Altmetric

Share

Gmail Facebook X LinkedIn More