Aitazaz A. Farooque

Zeyad Ahmed, Paul Sheridan, Michael McIsaac et al.

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.

Paul Sheridan, Zeyad Ahmed, Aitazaz A. Farooque

Term frequency-inverse document frequency, or TF-IDF for short, is arguably the most celebrated mathematical expression in the history of information retrieval. Conceived as a simple heuristic quantifying the extent to which a given term's occurrences are concentrated in any one given document out of many, TF-IDF and its many variants are routinely used as term-weighting schemes in diverse text analysis applications. There is a growing body of scholarship dedicated to placing TF-IDF on a sound theoretical foundation. Building on that tradition, this paper justifies the use of TF-IDF to the statistics community by demonstrating how the famed expression can be understood from a significance testing perspective. We show that the common TF-IDF variant TF-ICF is, under mild regularity conditions, closely related to the negative logarithm of the $p$-value from a one-tailed version of Fisher's exact test of statistical significance. As a corollary, we establish a connection between TF-IDF and the said negative log-transformed $p$-value under certain idealized assumptions. We further demonstrate, as a limiting case, that this same quantity converges to TF-IDF in the limit of an infinitely large document collection. The Fisher's exact test justification of TF-IDF equips the working statistician with a ready explanation of the term-weighting scheme's long-established effectiveness.