Manifold Structured Prediction
This work addresses the challenge of structured prediction for continuous outputs, which is incremental as it builds on classical finite-output methods.
The paper tackles the problem of extending structured prediction to continuous, manifold-valued outputs, providing a statistically consistent approach and demonstrating promising experimental results on simulated and real data.
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.