arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2406.02891cs.IRcs.DScs.LG
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一种用于快速相似性搜索的双度量框架

A Bi-metric Framework for Fast Similarity Search

MIT(麻省理工学院)

Haike Xu, Sandeep Silwal, Piotr Indyk

AI总结:

本文提出双度量框架,用廉价代理度量构建最近邻数据结构,查询时以有限次调用达到昂贵真实度量的准确性,并在DiskANN、Cover Tree及MTEB文本检索上验证了显著的精度-效率优势。

摘要:

我们提出了一种新的“双度量”框架,用于设计最近邻数据结构。该框架假设存在两种不相似度函数:一种是真实度量,准确但计算代价高昂;另一种是代理度量,计算成本较低但准确性较差。在理论和实践两方面,我们展示了如何仅使用代理度量来构建数据结构,使得查询过程能够达到昂贵度量的准确性,同时仅对两种度量进行有限次数的调用。我们的理论结果将该框架实例化到两种流行的最近邻搜索算法:DiskANN和Cover Tree。在这两种情况下,我们证明,只要用于构建数据结构的代理度量在有限因子范围内近似真实度量,我们的数据结构就能相对于真实度量实现任意好的近似保证。在实证方面,我们将该框架应用于文本检索问题,使用由计算成本差异巨大的机器学习模型评估的两种不相似度函数。我们观察到,对于MTEB基准中的几乎所有数据集,与重排序等替代方法相比,我们的方法在准确性与效率的权衡上取得了显著更好的效果。

英文摘要:

We propose a new "bi-metric" framework for designing nearest neighbor data structures. Our framework assumes two dissimilarity functions: a ground-truth metric that is accurate but expensive to compute, and a proxy metric that is cheaper but less accurate. In both theory and practice, we show how to construct data structures using only the proxy metric such that the query procedure achieves the accuracy of the expensive metric, while only using a limited number of calls to both metrics. Our theoretical results instantiate this framework for two popular nearest neighbor search algorithms: DiskANN and Cover Tree. In both cases we show that, as long as the proxy metric used to construct the data structure approximates the ground-truth metric up to a bounded factor, our data structure achieves arbitrarily good approximation guarantees with respect to the ground-truth metric. On the empirical side, we apply the framework to the text retrieval problem with two dissimilarity functions evaluated by ML models with vastly different computational costs. We observe that for almost all data sets in the MTEB benchmark, our approach achieves a considerably better accuracy-efficiency tradeoff than the alternatives, such as re-ranking.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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