AUROC concept
| Definition | The area under the receiver operating characteristic curve, equal to the probability that a random positive scores above a random negative, ties counted as one half. A strictly increasing transform of the score leaves it unchanged and a strictly decreasing one sends it to one minus itself. Equation 0.16. |
|---|---|
| Example | Positives scoring 0.9 and 0.7 against negatives scoring 0.8 and 0.2 win three of the four pairs, so the AUROC is 0.75. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id auroc, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.16. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Auroc.lean |
| Reviewed | semantic review 2026-09-06; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.16.
\[\mathrm{AUROC}=\Pr\big[s^{+}>s^{-}\big]\ +\ \tfrac12\Pr\big[s^{+}=s^{-}\big].\]
Book equation 0.38.
\[w=\max\big(0,\ 2\cdot\mathrm{AUROC}-1\big).\]
Book equation 12.3.
\[\text{validated}\iff \mathrm{AUROC}_{\text{cross}}-\max\big(\mathrm{AUROC}_{\text{untrained}},\ \mathrm{AUROC}_{\text{BoW}}\big)\ \ge\ 0.10.\]
Conditions
- The area under the ROC curve, the probability that a random positive scores above a random negative with ties counted as one half. It lies in the unit interval, is one half for a constant score, one for a perfect ranking, and zero for a perfectly reversed one.
- A strictly increasing transform of the score leaves it unchanged. A strictly decreasing transform reverses every ranking and sends A to 1 minus A, so the AUROC is not free of orientation, and an authority that should ignore orientation reads the larger of A and 1 minus A.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.8 of Data Mining as Observation, the pairwise definition with ties counted one half, and the held-out AUROC of every encoder gate and flip in the program.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Auroc.lean,
theorems pair_nonneg, auroc_nonneg,
auroc_le_one, auroc_perfect,
auroc_reversed, auroc_chance,
auroc_monotone_invariant, 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, 5, 6, 8, 11, 12, 14.
Related
Monotone Invariance Theorem; reliability weight; chance level; Youden F1 bound; cross-corpus gate.
See also
Ledger rows that cite the entry’s records without naming it: GO-B-legal (035→036), GO-B-whale (038).
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.