Deletion Robust Submodular Maximization over Matroids
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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 log k/ε^2). In the streaming setting we provide a (5.582+O(ε))-approximation algorithm with summary size and memory O(k + d log k/ε^2). We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets.
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