Manifold Structured Prediction

Authors:
Alessandro Rudi INRIA, Ecole Normale Superieure
Carlo Ciliberto Imperial College London
GianMaria Marconi Italian Institute of Technology
Lorenzo Rosasco University of Genova- MIT - IIT

Introduction:

Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure.Specifically, the authors study a structured prediction approach to manifold-valued regression.

Abstract:

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.

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