Sample compression schemes for balls in graphs

arXiv:2206.13254v2 Announce Type: replace-cross
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 a ball $B=B_r(x)$ of a graph $G=(V,E)$, a realizable sample for $B$ is a signed subset $X=(X^+,X^-)$ of $V$ such that $B$ contains $X^+$ and is disjoint from $X^-$. A proper sample compression scheme of size $k$ consists of a …

abstract arxiv compression cs.dm cs.lg family graph graphs machine machine learning paper sample set study type