Submodular Hamming Metrics
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).
Cite
Text
Gillenwater et al. "Submodular Hamming Metrics." Neural Information Processing Systems, 2015.Markdown
[Gillenwater et al. "Submodular Hamming Metrics." Neural Information Processing Systems, 2015.](https://mlanthology.org/neurips/2015/gillenwater2015neurips-submodular/)BibTeX
@inproceedings{gillenwater2015neurips-submodular,
title = {{Submodular Hamming Metrics}},
author = {Gillenwater, Jennifer A and Iyer, Rishabh K and Lusch, Bethany and Kidambi, Rahul and Bilmes, Jeff A.},
booktitle = {Neural Information Processing Systems},
year = {2015},
pages = {3141-3149},
url = {https://mlanthology.org/neurips/2015/gillenwater2015neurips-submodular/}
}