{"paper":{"title":"Sample compression schemes for balls in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DM","authors_text":"Fionn Mc Inerney, J\\'er\\'emie Chalopin, S\\'ebastien Ratel, Victor Chepoi, Yann Vax\\`es","submitted_at":"2022-06-27T12:39:36Z","abstract_excerpt":"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 compressor and a reconstructor. The compressor maps any realizable sample $X$ to a subsample $X'$ of size at most $k$. The reconstructor maps each such subsample $X'$ to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.13254","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.13254/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}