Skeleton Regression: A Graph-Based Approach to Estimation with Manifold Structure

arXiv:2303.11786v2 Announce Type: replace
Abstract: We introduce a new regression framework designed to deal with large-scale, complex data that lies around a low-dimensional manifold with noises. Our approach first constructs a graph representation, referred to as the skeleton, to capture the underlying geometric structure. We then define metrics on the skeleton graph and apply nonparametric regression techniques, along with feature transformations based on the graph, to estimate the regression function. We also discuss the limitations of some nonparametric regressors with …

abstract arxiv cs.lg data deal framework graph graph-based graph representation lies low manifold metrics regression representation scale stat.me stat.ml type