Manifold Structured Prediction

Alessandro Rudi (1, 2, 3) , Carlo Ciliberto (4) , Gian Maria Marconi (5, 6) , Lorenzo Rosasco (5, 6)

1 PSL - Université Paris Sciences et Lettres
2 DI-ENS - Département d'informatique - ENS Paris
3 SIERRA - Statistical Machine Learning and Parsimony
4 UCL - University College of London [London]
5 IIT - Istituto Italiano di Tecnologia
6 UniGe - Università degli studi di Genova = University of Genoa

Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we discuss how structured prediction can be extended to a continuous scenario. Specifically, we study a structured prediction approach to manifold valued regression. We characterize a class of problems for which the considered approach is statistically consistent and study how geometric optimization can be used to compute the corresponding estimator. Promising experimental results on both simulated and real data complete our study.

Domaines: Apprentissage [cs.LG]

Alessandro Rudi, Carlo Ciliberto, Gian Maria Marconi, Lorenzo Rosasco. Manifold Structured Prediction. NIPS 2018 - Neural Information Processing Systems Conference, Dec 2018, Montreal, Canada. pp.5615-5626. ⟨hal-01958900⟩