Deletion Robust Submodular Maximization over Matroids
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866909111122132992 |
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| author | Dütting, Paul Fusco, Federico Lattanzi, Silvio Norouzi-Fard, Ashkan Zadimoghaddam, Morteza |
| author_facet | Dütting, Paul Fusco, Federico Lattanzi, Silvio Norouzi-Fard, Ashkan Zadimoghaddam, Morteza |
| contents | 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 $(3.582+O(\varepsilon))$-approximation algorithm with summary size $O(k + \frac{d \log k}{\varepsilon^2})$. In the streaming setting we provide a $(5.582+O(\varepsilon))$-approximation algorithm with summary size and memory $O(k + \frac{d \log k}{\varepsilon^2})$. We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_13128 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Deletion Robust Submodular Maximization over Matroids Dütting, Paul Fusco, Federico Lattanzi, Silvio Norouzi-Fard, Ashkan Zadimoghaddam, Morteza Data Structures and Algorithms Machine Learning 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 $(3.582+O(\varepsilon))$-approximation algorithm with summary size $O(k + \frac{d \log k}{\varepsilon^2})$. In the streaming setting we provide a $(5.582+O(\varepsilon))$-approximation algorithm with summary size and memory $O(k + \frac{d \log k}{\varepsilon^2})$. We complement our theoretical results with an in-depth experimental analysis showing the effectiveness of our algorithms on real-world datasets. |
| title | Deletion Robust Submodular Maximization over Matroids |
| topic | Data Structures and Algorithms Machine Learning |
| url | https://arxiv.org/abs/2201.13128 |