Wasserstein Soft Label Propagation on Hypergraphs: Algorithm and Generalization Error Bounds

  • Tingran Gao University of Chicago
  • Shahab Asoodeh University of Chicago
  • Yi Huang University of Chicago
  • James Evans University of Chicago

Abstract

Inspired by recent interests of developing machine learning and data mining algorithms on hypergraphs, we investigate in this paper the semi-supervised learning algorithm of propagating ”soft labels” (e.g. probability distributions, class membership scores) over hypergraphs, by means of optimal transportation. Borrowing insights from Wasserstein propagation on graphs [Solomon et al. 2014], we re-formulate the label propagation procedure as a message-passing algorithm, which renders itself naturally to a generalization applicable to hypergraphs through Wasserstein barycenters. Furthermore, in a PAC learning framework, we provide generalization error bounds for propagating one-dimensional distributions on graphs and hypergraphs using 2-Wasserstein distance, by establishing the algorithmic stability of the proposed semisupervised learning algorithm. These theoretical results also shed new lights upon deeper understandings of the Wasserstein propagation on graphs.

Published
2019-07-17