A Fisher's exact test justification of the TF-IDF term-weighting scheme
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| Format: | Preprint |
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2025
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| author | Sheridan, Paul Ahmed, Zeyad Farooque, Aitazaz A. |
| author_facet | Sheridan, Paul Ahmed, Zeyad Farooque, Aitazaz A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_15742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fisher's exact test justification of the TF-IDF term-weighting scheme Sheridan, Paul Ahmed, Zeyad Farooque, Aitazaz A. Computation and Language Information Retrieval Statistics Theory 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. |
| title | A Fisher's exact test justification of the TF-IDF term-weighting scheme |
| topic | Computation and Language Information Retrieval Statistics Theory |
| url | https://arxiv.org/abs/2507.15742 |