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min-over-strata concept

DefinitionThe rule that a verdict over several groups is the worst group's verdict, with abstention counted as a verdict, never the average. Chapter 10. Also abstention, abstain.
ExampleStrata at 0.95, 0.93, 0.97, and 0.66 have a mean of 0.878 and a minimum of 0.66, and the minimum is the verdict.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id min-over-strata, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equation

Book equation 10.7.

Assumptions and scope
  • A verdict over several groups is the worst group’s verdict, with a group too small to score counted as an abstention and reported, never averaged away.
  • The first stratified run made two wrong predictions, and the record carries them at the size of the result.
Prior artnone recorded
Evidenceturboquant-pro/docs/STRATA_RFC.md:24-98, turboquant-pro/docs/RESULTS_multilingual_strata.md:1-55, lean/DataMiningAsObservation/Certificate.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
00.51stratumscores1s2s3s4s5s6s7barmean passes, the minimum fails
The worst stratum is the verdict.

Equation

Book equation 10.7.

\[\text{verdict}=\min_{i:\ n_i\ge n_{\min},\ |Q_i|\ge q_{\min}}\ \mathrm{score}_i,\qquad \text{ABSTAIN otherwise}.\]

Book equation 14.5.

\[\mathrm{FC}_g=\Pr\big[y=\text{violation}\ \big|\ \hat y=\text{clear},\ g\big],\qquad \text{verdict}=\max_{g:\ n_g\ge n_{\min}}\mathrm{FC}_g,\qquad \text{ABSTAIN otherwise}.\]

Conditions

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

Ledger

none

First stated

The compression program’s stratified evaluation, STRATA, in turboquant-pro, DOI 10.5281/zenodo.20660087, and chapter 10 section 10.4 of Data Mining as Observation.

Measurements

Where the book states it Numbers, as the book’s sources table records them Source
chapter 10 section 10.4 area map, boundary rule, hash, refuse not warn, intra and transit counts, area classes, abstention rule turboquant-pro/docs/STRATA_RFC.md:24-98
chapter 10 section 10.4 first run, 350000 of 2391361 rows, 7 of 14 eligible, abstentions with 2 and 1 rows, Robin Hood 0.3447 to 0.4469 ratio 1.30 against 1.5, skew 2.68 to 4.40 ratio 1.64 against 3, 63 times sample range turboquant-pro/docs/RESULTS_multilingual_strata.md:1-55

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Certificate.lean, theorems falseClear_mul_coverage, coverage_empty, falseClear_mem_unit, minOverStrata_passes_iff, minOverStrata_le_weighted_mean, 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, 10, 11, 14.

Related

false-clear rate; coverage; hubness; certificate.

See also

Ledger rows that cite the entry’s records without naming it: NEG-14.

Sources-table rows that share a record with the entry without naming it: chapter 2 section 2.6, chapter 3 section 3.5, chapter 8 section 8.1, chapter 8 section 8.4, chapter 8 section 8.7, chapter 8 section 8.10, chapter 10 section 10.2, chapter 10 section 10.4, chapter 10 section 10.5, chapter 11 section 11.4, chapter 11 section 11.6, chapter 12 section 12.2, chapter 12 section 12.4, chapter 13 section 13.1.

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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