Semi-supervised Fréchet Regression
It addresses the cost issue for researchers in semi-supervised learning with non-Euclidean data, but appears incremental as it extends existing Euclidean methods.
This paper tackles the problem of high costs in obtaining non-Euclidean labels by proposing semi-supervised Fréchet regression methods, demonstrating superior performance over supervised counterparts in simulations and real data.
This paper explores the field of semi-supervised Fréchet regression, driven by the significant costs associated with obtaining non-Euclidean labels. Methodologically, we propose two novel methods: semi-supervised NW Fréchet regression and semi-supervised kNN Fréchet 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 Fréchet regression.