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Deletion Robust Submodular Maximization over Matroids
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:5671-5693, 2022.
Abstract
Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the dataset that contains a high value independent set even after an adversary deleted some elements. We present constant-factor approximation algorithms, whose space complexity depends on the rank k of the matroid and the number d of deleted elements. In the centralized setting we present a (3.582+O(ε))-approximation algorithm with summary size O(k+d\eps2logk\eps). In the streaming setting we provide a (5.582+O(ε))-approximation algorithm with summary size and memory O(k+d\eps2logk\eps). We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets.