Robust Nonparametric Regression with Metric-Space Valued Output

Part of Advances in Neural Information Processing Systems 22 (NIPS 2009)

Bibtex »Metadata »Paper »Supplemental »

Authors

Matthias Hein

Abstract

<p>Motivated by recent developments in manifold-valued regression we propose a family of nonparametric kernel-smoothing estimators with metric-space valued output including a robust median type estimator and the classical Frechet mean. Depending on the choice of the output space and the chosen metric the estimator reduces to partially well-known procedures for multi-class classification, multivariate regression in Euclidean space, regression with manifold-valued output and even some cases of structured output learning. In this paper we focus on the case of regression with manifold-valued input and output. We show pointwise and Bayes consistency for all estimators in the family for the case of manifold-valued output and illustrate the robustness properties of the estimator with experiments.</p>