When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2017.34
URN: urn:nbn:de:0030-drops-74612
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7461/
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### Correlated Rounding of Multiple Uniform Matroids and Multi-Label Classification

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### Abstract

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.

### BibTeX - Entry

```@InProceedings{chen_et_al:LIPIcs:2017:7461,
author =	{Shahar Chen and Dotan Di Castro and Zohar Karnin and Liane Lewin-Eytan and Joseph (Seffi) Naor and Roy Schwartz},
title =	{{Correlated Rounding of Multiple Uniform Matroids and Multi-Label Classification}},
booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages =	{34:1--34:15},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-041-5},
ISSN =	{1868-8969},
year =	{2017},
volume =	{80},
editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address =	{Dagstuhl, Germany},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7461},
URN =		{urn:nbn:de:0030-drops-74612},
doi =		{10.4230/LIPIcs.ICALP.2017.34},
annote =	{Keywords: approximation algorithms, randomized rounding, dependent rounding, metric labeling, classification}
}
```

 Keywords: approximation algorithms, randomized rounding, dependent rounding, metric labeling, classification Seminar: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) Issue Date: 2017 Date of publication: 06.07.2017

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