A Fisher’s Exact Test Justification of the TF–IDF Term-Weighting Scheme
Why this work is in the frame
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Bibliographic record
Abstract
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.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.044 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it