Common TF-IDF variants arise as key components in the test statistic of a penalized likelihood-ratio test for word burstiness

2026-04-01

AI Summary

This work addresses the lack of a solid statistical foundation in traditional TF-IDF and its inability to capture term burstiness. The authors propose a statistical framework based on a penalized likelihood ratio test, modeling term frequencies with a Beta-Binomial distribution and incorporating a Gamma prior as a regularizer. This formulation yields a term-weighting statistic that aligns with existing TF-IDF variants. Notably, the study provides the first theoretical interpretation of TF-IDF from a hypothesis testing perspective, uncovering its intrinsic connection to burstiness modeling. Experimental results on document classification tasks demonstrate that the proposed method achieves performance comparable to classical TF-IDF, thereby validating the effectiveness and soundness of the proposed statistical framework.

Abstract

TF-IDF is a classical formula that is widely used for identifying important terms within documents. We show that TF-IDF-like scores arise naturally from the test statistic of a penalized likelihood-ratio test setup capturing word burstiness (also known as word over-dispersion). In our framework, the alternative hypothesis captures word burstiness by modeling a collection of documents according to a family of beta-binomial distributions with a gamma penalty term on the precision parameter. In contrast, the null hypothesis assumes that words are binomially distributed in collection documents, a modeling approach that fails to account for word burstiness. We find that a term-weighting scheme given rise to by this test statistic performs comparably to TF-IDF on document classification tasks. This paper provides insights into TF-IDF from a statistical perspective and underscores the potential of hypothesis testing frameworks for advancing term-weighting scheme development.

Problem

• TF-IDF
• word burstiness
• term weighting
• likelihood-ratio test
• over-dispersion

Innovation

• penalized likelihood-ratio test
• word burstiness
• beta-binomial distribution
• term weighting
• TF-IDF