Very Fast Streaming Submodular Function Maximization

TL;DR

This paper introduces ThreeSieves, a fast streaming algorithm for submodular maximization that performs well in practice, especially on well-behaved data, with lower resource usage and strong theoretical guarantees.

Contribution

The paper presents a novel streaming algorithm, ThreeSieves, which bypasses worst-case assumptions to efficiently maximize submodular functions with high probability.

Findings

Outperforms six existing methods on eight datasets.

Uses fewer computational resources than state-of-the-art algorithms.

Effective in real-world data summarization, demonstrated in gamma-ray astronomy.

Abstract

Data summarization has become a valuable tool in understanding even terabytes of data. Due to their compelling theoretical properties, submodular functions have been in the focus of summarization algorithms. These algorithms offer worst-case approximations guarantees to the expense of higher computation and memory requirements. However, many practical applications do not fall under this worst-case, but are usually much more well-behaved. In this paper, we propose a new submodular function maximization algorithm called ThreeSieves, which ignores the worst-case, but delivers a good solution in high probability. It selects the most informative items from a data-stream on the fly and maintains a provable performance on a fixed memory budget. In an extensive evaluation, we compare our method against $6$ other methods on $8$ different datasets with and without concept drift. We show that our algorithm outperforms current state-of-the-art algorithms and, at the same time, uses fewer resources. Last, we highlight a real-world use-case of our algorithm for data summarization in gamma-ray astronomy. We make our code publicly available at https://github.com/sbuschjaeger/SubmodularStreamingMaximization.