random forest instrument
| Definition | An ensemble of decision trees, each fit on a bootstrap sample with a random subset of features at each split. Chapter 7. |
|---|---|
| Example | Five hundred trees, each on a bootstrap sample with 5 of 30 features tried per split, vote. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id random-forest, 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/DecisionTree.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- An ensemble of decision trees, each fit on a bootstrap sample with a random subset of features at each split, that averages or votes. The average lies between its members and its squared error is at most their mean squared error, and each tree is flat within a leaf so the forest’s importances count splits.
- On the five-dataset benchmark the forest and the boosted trees win when the boundary needs many features and lose to a formula when it needs few.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Breiman, random forests, 2001, 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/DecisionTree.lean,
theorems stump_flat_left, stump_flat_right,
split_reads_one_axis, gini_le_half,
gini_eq_zero_iff, at observation-data-mining f3914f0; what
the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 6, 7.
Related
ensemble; decision tree; bagging; importance; boosting.
See also
Book equations stated beside the entry’s terms, not defining it: 6.1, 14.5.
Sources-table rows that share a record with the entry without naming it: chapter 6 section 6.3, chapter 7 section 7.3.
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.