← 研踪 PaperTrailarXiv:2405.18754 · v3
GIST: Greedy Independent Set Thresholding for Max-Min Diversification with Submodular Utility
首次提交 2024-05-29 12:39
版本更新 2025-10-20 21:56
雷达观测 2026-11-01 22:43
摘要
This work studies a novel subset selection problem called max-min diversification with monotone submodular utility ($\textsf{MDMS}$), which has a wide range of applications in machine learning, e.g., data sampling and feature selection. Given a set of points in a metric space, the goal of $\textsf{MDMS}$ is to maximize $f(S) = g(S) + λ\cdot \texttt{div}(S)$ subject to a cardinality constraint $|S| \le k$, where $g(S)$ is a monotone submodular function and $\texttt{div}(S) = \min_{u,v \in S : u \ne v} \text{dist}(u,v)$ is the max-min diversity objective. We propose the $\texttt{GIST}$ algorithm, which gives a $\frac{1}{2}$-approximation guarantee for $\textsf{MDMS}$ by approximating a series of maximum independent set problems with a bicriteria greedy algorithm. We also prove that it is NP-hard to approximate within a factor of $0.5584$. Finally, we show in our empirical study that $\texttt{GIST}$ outperforms state-of-the-art benchmarks for a single-shot data sampling task on ImageNet.
作者备注：21 pages, 3 figures
期刊信息：Proceedings of the 39th Annual Conference on Neural Information Processing Systems (NeurIPS 2025)
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v3 · 2025-10-20 21:56 · 最新观测版本
GIST: Greedy Independent Set Thresholding for Max-Min Diversification with Submodular Utility
This work studies a novel subset selection problem called max-min diversification with monotone submodular utility ($\textsf{MDMS}$), which has a wide range of applications in machine learning, e.g., data sampling and feature selection. Given a set of points in a metric space, the goal of $\textsf{MDMS}$ is to maximize $f(S) = g(S) + λ\cdot \texttt{div}(S)$ subject to a cardinality constraint $|S| \le k$, where $g(S)$ is a monotone submodular function and $\texttt{div}(S) = \min_{u,v \in S : u \ne v} \text{dist}(u,v)$ is the max-min diversity objective. We propose the $\texttt{GIST}$ algorithm, which gives a $\frac{1}{2}$-approximation guarantee for $\textsf{MDMS}$ by approximating a series of maximum independent set problems with a bicriteria greedy algorithm. We also prove that it is NP-hard to approximate within a factor of $0.5584$. Finally, we show in our empirical study that $\texttt{GIST}$ outperforms state-of-the-art benchmarks for a single-shot data sampling task on ImageNet.
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