🤖 AI Summary
本文通过将TF-IDF和BM25解释为两种概率模型之间的KL散度，解决了这两种查询文档相关性评分方法缺乏统一统计理论基础的问题。
📝 Abstract
TF-IDF and BM25 are two of the most widely used methods for scoring query-document relevance, yet neither has a standard probabilistic derivation that justifies it as a statistical method within a unified framework. We address this gap by showing that both scoring methods admit an exact interpretation as Kullback-Leibler divergences between two probability models. We treat the BM25 variant that includes the plus 1 correction in the IDF term, which is the one used in practice, and also discuss the original BM25 formulation without that correction. The resulting framework provides a common theoretical basis for TF-IDF and BM25, clarifies what they measure, and allows them to be compared theoretically with other information retrieval methods rather than only experimentally.