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boosting instrument

DefinitionFitting a sequence of weak scorers, each on the rows the previous ones got wrong, and summing them. Its step size is positive exactly when the weak scorer beats chance, and the reweighting makes the last scorer's weighted error one half. Chapter 7. Also boost.
ExampleA weak scorer with weighted error 0.25 gets step size one half of the log of 3, about 0.549, and after reweighting its error is one half.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id boosting, kind instrument.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • Fitting a sequence of weak scorers, each on the rows the previous ones got wrong, and summing them with a step size set by the weighted error. The step size is positive exactly when the weak scorer beats chance, and after the rows are reweighted the weighted error of the scorer just fitted is one half, so the next scorer must find something new.
  • Gradient boosting reads the loss through its curvature, so the optimizer is a consumer whose read operator is the Hessian, and on the author’s five-dataset benchmark the ensemble wins when the boundary needs many features and a formula wins when it needs few.
Prior artnone recorded
Evidencelean/DataMiningAsObservation/Boosting.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
weightrightrightwrongrightwrongright
Rows the last scorer got wrong are reweighted so that its error becomes one half.

Equation

none

Conditions

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

Ledger

none

First stated

Freund and Schapire, a decision-theoretic generalization of on-line learning, 1997, as chapter 7 section 7.1 of Data Mining as Observation reads it, with the curvature reader in geometric-observation/claims/LEDGER.md row GO-B-optim-D4.

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/Boosting.lean, theorems alpha_pos_iff, alpha_half, reweighted_error_half, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 1, 6, 7, 8.

Related

ensemble; curvature; decision tree; importance.

See also

Book equations stated beside the entry’s terms, not defining it: 6.1, 0.8, 0.9.

Ledger rows that cite the entry’s records without naming it: GO-B-optim-D4 (034 · D4).

Sources-table rows that share a record with the entry without naming it: chapter 6 section 6.3, chapter 7 section 7.2, 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.

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