Beyond $1/2$-Approximation for Submodular Maximization on Massive Data Streams
Abstract
Many tasks in machine learning and data mining, such as data diversification, non-parametric learning, kernel machines, clustering etc., require extracting a small but representative summary from a massive dataset. Often, such problems can be posed as maximizing a submodular set function subject to a cardinality constraint. We consider this question in the streaming setting, where elements arrive over time at a fast pace and thus we need to design an efficient, low-memory algorithm. One such method, proposed by Badanidiyuru et al. (2014), always finds a -approximate solution. Can this approximation factor be improved? We answer this question affirmatively by designing a new algorithm SALSA for streaming submodular maximization. It is the first low-memory, single-pass algorithm that improves the factor , under the natural assumption that elements arrive in a random order. We also show that this assumption is necessary, i.e., that there is no such algorithm with better than -approximation when elements arrive in arbitrary order. Our experiments demonstrate that SALSA significantly outperforms the state of the art in applications related to exemplar-based clustering, social graph analysis, and recommender systems.
Cite
@article{arxiv.1808.01842,
title = {Beyond $1/2$-Approximation for Submodular Maximization on Massive Data Streams},
author = {Ashkan Norouzi-Fard and Jakub Tarnawski and Slobodan Mitrović and Amir Zandieh and Aida Mousavifar and Ola Svensson},
journal= {arXiv preprint arXiv:1808.01842},
year = {2018}
}