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arXiv · 1511.02163

Submodular Hamming Metrics

Jennifer Gillenwater·Rishabh Iyer·Bethany Lusch·Rahul Kidambi·Jeff Bilmes
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Abstract

We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tractable to optimize over. By exploiting submodularity, we are able to give hardness results and approximation algorithms for optimizing over such metrics. Additionally, we demonstrate empirically the effectiveness of these metrics and associated algorithms on both a metric minimization task (a form of clustering) and also a metric maximization task (generating diverse k-best lists).

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BibTeXRIS

Jennifer Gillenwater, Rishabh Iyer, Bethany Lusch, Rahul Kidambi, Jeff Bilmes. 2015-11-06. Submodular Hamming Metrics. https://arxiv.org/abs/1511.02163

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