bagging instrument
| Definition | Fitting the same model on bootstrap resamples and averaging. The average's squared error is at most the members' mean squared error, which is how it reduces variance. Chapter 7. Also bootstrap aggregat. |
|---|---|
| Example | Ten trees fit on ten bootstrap resamples and averaged have at most the mean squared error of the ten members. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id bagging, 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, lean/DataMiningAsObservation/Bootstrap.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- Fitting the same model on bootstrap resamples of the rows and averaging. The average’s squared error is at most the mean of the members’ squared errors, which is the arithmetic by which bagging reduces variance, and the reduction is largest when the members covary least.
- Bagging reduces variance and boosting reduces bias, and neither changes what the base model reads.
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.
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.
lean/DataMiningAsObservation/Bootstrap.lean,
theorems mean_sub, var_sub,
paired_lt_iff, cov_comm, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation chapters 7.
Related
ensemble; bootstrap; random forest; standard error; variance.
See also
Book equations stated beside the entry’s terms, not defining it: 0.18, 8.2.
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.