Deletion Robust Submodular Maximization over Matroids

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 + εd2 log kε ). In the streaming setting we provide a (5.582 + O(ε))approximation algorithm with summary size and memory O(k + εd2 log kε ). We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets.