ensemble instrument
| Definition | A scorer that averages or votes several scorers. Its average lies between its members and its squared error is at most their mean squared error. Chapter 7. Also bagging, random forest. |
|---|---|
| Example | Scores 0.6, 0.7, and 0.8 average 0.7, and the average’s squared error is at most the mean of the three squared errors. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id ensemble, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Ensemble.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A scorer that averages or votes several scorers. Its average lies between the smallest and the largest member, its squared error is at most the mean of the members’ squared errors, and a constant ensemble is its constant. That arithmetic is why bagging reduces variance.
- Whether an ensemble beats a formula is a measured question and not a principle, and the comparison is fair only inside one fold protocol with the Nadeau and Bengio correction applied, where nine wins to three became three wins, seventeen ties, and eleven losses.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Breiman, bagging predictors, 1996, as chapter 7 section 7.1 of
Data Mining as Observation reads it, with the fair comparison
in constraint-gap/review/INDETERMINATES.md:1-40.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 7 section 7.1 | bagging variance, out-of-bag estimation, random forests, importances, AdaBoost | Hastie, Tibshirani, Friedman, ESL 2e chapters 15 and 10.1; TSK 2e 4.10 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Ensemble.lean,
theorems average_between, sq_average_le,
average_const, 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, 6, 7.
Related
boosting; decision tree; standard error; Nadeau and Bengio correction.
See also
Book equations stated beside the entry’s terms, not defining it: 6.1, 0.18, 8.2.
Sources-table rows that share a record with the entry without naming it: chapter 6 section 6.3, chapter 7 section 7.3, chapter 7 section 7.4.
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.