2026-07-20T07:27:33Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7461 2024-03-06T10:40:19Z ddc:004 open_access

Correlated Rounding of Multiple Uniform Matroids and Multi-Label Classification Chen, Shahar Di Castro, Dotan Karnin, Zohar Lewin-Eytan, Liane Naor, Joseph (Seffi) Schwartz, Roy approximation algorithms randomized rounding dependent rounding metric labeling classification We introduce correlated randomized dependent rounding where, given multiple points y^1,...,y^n in some polytope P\subseteq [0,1]^k, the goal is to simultaneously round each y^i to some integral z^i in P while preserving both marginal values and expected distances between the points. In addition to being a natural question in its own right, the correlated randomized dependent rounding problem is motivated by multi-label classification applications that arise in machine learning, e.g., classification of web pages, semantic tagging of images, and functional genomics. The results of this work can be summarized as follows: (1) we present an algorithm for solving the correlated randomized dependent rounding problem in uniform matroids while losing only a factor of O(log{k}) in the distances (k is the size of the ground set); (2) we introduce a novel multi-label classification problem, the metric multi-labeling problem, which captures the above applications. We present a (true) O(log{k})-approximation for the general case of metric multi-labeling and a tight 2-approximation for the special case where there is no limit on the number of labels that can be assigned to an object. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shahar Chen and Dotan Di Castro and Zohar Karnin and Liane Lewin-Eytan and Joseph (Seffi) Naor and Roy Schwartz 2017 Is Part Of LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2017.34 urn:nbn:de:0030-drops-74612 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.34 eng https://creativecommons.org/licenses/by/3.0/legalcode