balanced accuracy concept
| Definition | The mean of the per-class recalls, so that a large class cannot hide a small one. Equation 0.34. |
|---|---|
| Example | Recalls of 0.90 on class A and 0.30 on class B give balanced accuracy 0.60, whatever the class sizes. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id balanced-accuracy, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.34. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/BalancedAccuracy.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.34.
\[\mathrm{BA}=\frac1K\sum_{k=1}^{K}\frac{\text{correct in class }k}{\text{rows in class }k}.\]
Conditions
- The mean of the per-class recalls, between the worst class and the best. Plain accuracy is the size-weighted mean of the same recalls, so a class of 990 rows recalled perfectly and a class of 10 never recalled give accuracy 0.99 and balanced accuracy 0.5.
- The book prefers the min over classes to the mean where a verdict is at stake, since a mean can still hide one failing class among many.
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 use in the anti-hub category table,
openvector-bench/results/R13_STAGE1_RESULTS.md.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 10 section 10.2 | five kinds, balanced accuracy 0.611, 0.718, 0.684, the category table, per-category 0.57 to 0.82, the sweep, pigeonhole floor | openvector-bench/results/R13_STAGE1_RESULT.md:40-75 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/BalancedAccuracy.lean,
theorems min_le_balanced, balanced_le_max,
hidden_class, at observation-data-mining f3914f0; what the
check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 0, 10.
Related
min-over-strata; anti-hub; abstention; harness.
See also
Book equations stated beside the entry’s terms, not defining it: 10.7.
Ledger rows that cite the entry’s records without naming it: NEG-11.
Sources-table rows that share a record with the entry without naming it: chapter 3 section 3.5, chapter 10 section 10.2, chapter 11 section 11.6.
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.