Semi-supervised Fréchet Regression
Rui Qiu Zhou Yu Zhenhua Lin
This paper explores the field of semi-supervised Fr\'echet regression, driven
by the significant costs associated with obtaining non-Euclidean labels.
Methodologically, we propose two novel methods: semi-supervised NW Fr\'echet
regression and semi-supervised kNN Fr\'echet regression, both based on graph
distance acquired from all feature instances. These methods extend the scope of
existing semi-supervised Euclidean regression methods. We establish their
convergence rates with limited labeled data and large amounts of unlabeled
data, taking into account the low-dimensional manifold structure of the feature
space. Through comprehensive simulations across diverse settings and
applications to real data, we demonstrate the superior performance of our
methods over their supervised counterparts. This study addresses existing
research gaps and paves the way for further exploration and advancements in the
field of semi-supervised Fr\'echet regression.