GIST: Greedy Independent Set Thresholding for Diverse Data Summarization

• URL: http://arxiv.org/abs/2405.18754v1
• Date: Wed, 29 May 2024 04:39:24 GMT
• Title: GIST: Greedy Independent Set Thresholding for Diverse Data Summarization
• Authors: Matthew Fahrbach, Srikumar Ramalingam, Morteza Zadimoghaddam, Sara Ahmadian, Gui Citovsky, Giulia DeSalvo,
• Abstract summary: We propose a novel subset selection task called min-distance diverse data summarization ($textsfMDDS$) The goal is to maximize an objective that combines the total utility of the points and a diversity term that captures the minimum distance between any pair of selected points. This work presents the $textttGIST$ algorithm, which achieves a $frac23$-approximation guarantee for $textsfMDDS$.
• Score: 21.69260104523751
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a novel subset selection task called min-distance diverse data summarization ($\textsf{MDDS}$), which has a wide variety of applications in machine learning, e.g., data sampling and feature selection. Given a set of points in a metric space, the goal is to maximize an objective that combines the total utility of the points and a diversity term that captures the minimum distance between any pair of selected points, subject to the constraint $|S| \le k$. For example, the points may correspond to training examples in a data sampling problem, e.g., learned embeddings of images extracted from a deep neural network. This work presents the $\texttt{GIST}$ algorithm, which achieves a $\frac{2}{3}$-approximation guarantee for $\textsf{MDDS}$ by approximating a series of maximum independent set problems with a bicriteria greedy algorithm. We also prove a complementary $(\frac{2}{3}+\varepsilon)$-hardness of approximation, for any $\varepsilon > 0$. Finally, we provide an empirical study that demonstrates $\texttt{GIST}$ outperforms existing methods for $\textsf{MDDS}$ on synthetic data, and also for a real-world image classification experiment the studies single-shot subset selection for ImageNet.

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