文章基本信息

标题：Correlated Rounding of Multiple Uniform Matroids and Multi-Label Classification
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作者：Shahar Chen ; Dotan Di Castro ; Zohar Karnin 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：80
页码：34:1-34:15
DOI：10.4230/LIPIcs.ICALP.2017.34
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：approximation algorithms; randomized rounding; dependent rounding; metric labeling; classification