precision, recall concept

Definition	The fraction of predicted positives that are truly positive, and the fraction of true positives that were predicted. Equation 0.28. Also precision.
Example	Ten rows called positive, six of them correct, out of eight true positives, is precision 0.6 and recall 0.75.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `precision-recall`, kind concept.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 0.28.
Assumptions and scope	The fraction of predicted positives that are truly positive, and the fraction of true positives that were predicted, both in the unit interval. F1 is their harmonic mean, between the smaller of the two and their arithmetic mean, equal to both when they agree, and zero when either is zero. In counts F1 is twice the true positives over twice the true positives plus the false positives and false negatives, the form the Youden ceiling bounds.
Prior art	none recorded
Evidence	`gtc-prototype/docs/SPECTRUM_FINDINGS.md:84-88`, `lean/DataMiningAsObservation/PrecisionRecall.lean`
Reviewed	not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.

Of the rows called positive, how many are, and of the positives, how many are called.

Equation

Book equation 0.28.

\[P=\frac{TP}{TP+FP},\qquad R=\frac{TP}{TP+FN},\qquad F_1=\frac{2PR}{P+R}.\]

Conditions

The fraction of predicted positives that are truly positive, and the fraction of true positives that were predicted, both in the unit interval. F1 is their harmonic mean, between the smaller of the two and their arithmetic mean, equal to both when they agree, and zero when either is zero.
In counts F1 is twice the true positives over twice the true positives plus the false positives and false negatives, the form the Youden ceiling bounds.

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Chapter 0 section 0.14 of Data Mining as Observation, with the program’s precision targets in gtc-prototype/docs/SPECTRUM_FINDINGS.md:84-88.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 14 section 14.7	51 percent moderated at 80 and 95 percent precision on the balanced set	`gtc-prototype/docs/SPECTRUM_FINDINGS.md:84-88`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/PrecisionRecall.lean, theorems precision_mem_unit, recall_mem_unit, f1_le_mean, min_le_f1, f1_self, f1_zero, f1_counts, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation primer S, chapters 0, 1, 4, 6, 8, 9, 10, 11, 12, 14.

F1; threshold; recall at k; Youden F1 bound.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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