Sample compression schemes for balls in graphs

Abstract

One of the open problems in machine learning is whether any set-family of VC-dimension d admits a sample compression scheme of size O ( d ). In this paper, we study this problem for balls in graphs. For balls of arbitrary radius r , we design proper sample compression schemes of size 4 for interval graphs, of size 6 for trees of cycles, and of size 22 for cube-free median graphs. We also design approximate sample compression schemes of size 2 for balls of δ -hyperbolic graphs.