Unlabeled Sample Compression Schemes and Corner Peelings for Ample and Maximum Classes

Jérémie Chalopin 1 Victor Chepoi 2 Shay Moran 3 Manfred Warmuth 4
1 DALGO - Algorithmique Distribuée
LIS - Laboratoire d'Informatique et Systèmes
2 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
LIS - Laboratoire d'Informatique et Systèmes
3 Princeton University
4 UCSC - University of California [Santa Cruz]
Abstract : We examine connections between combinatorial notions that arise in machine learning and topological notions in cubical/simplicial geometry. These connections enable to export results from geometry to machine learning. Our first main result is based on a geometric construction by H. Tracy Hall (2004) of a partial shelling of the cross-polytope which can not be extended. We use it to derive a maximum class of VC dimension 3 that has no corners. This refutes several previous works in machine learning from the past 11 years. In particular, it implies that the previous constructions of optimal unlabeled compression schemes for maximum classes are erroneous. On the positive side we present a new construction of an optimal unlabeled compression scheme for maximum classes. We leave as open whether our unlabeled compression scheme extends to ample (a.k.a. lopsided or extremal) classes, which represent a natural and far-reaching generalization of maximum classes. Towards resolving this question, we provide a geometric characterization in terms of unique sink orientations of the 1-skeletons of associated cubical complexes.
Keywords : VC-dimension sample compression Sauer-Shelah-Perles lemma Sandwich lemma maximum class ample/extremal class corner peeling unique sink orientation
Document type :
Conference papers
Complete list of metadatas

Cited literature [38 references]  Display  Hide  Download
https://hal.archives-ouvertes.fr/hal-02269141
Contributor : Victor Chepoi <>
Submitted on : Thursday, August 22, 2019 - 12:53:48 PM
Last modification on : Friday, August 23, 2019 - 1:18:48 AM

File

LIPIcs-ICALP-2019-34.pdf
Publisher files allowed on an open archive

Identifiers

Collections

INSMI | CNRS | LIS-LAB | UNIV-TLN | UNIV-AMU

Citation

Jérémie Chalopin, Victor Chepoi, Shay Moran, Manfred Warmuth. Unlabeled Sample Compression Schemes and Corner Peelings for Ample and Maximum Classes. 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), 2019, Patras, Greece. pp.34:1--34:15, ⟨10.4230/LIPIcs.ICALP.2019.34⟩. ⟨hal-02269141⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

50

Files downloads

7

Contact

CCSD