decision tree instrument
| Definition | A classifier that scores by a sequence of axis-aligned splits, flat within each leaf, so that its sensitivity is zero almost everywhere and its importances count splits. Chapter 6. Also random forest. |
|---|---|
| Example | Split on x1 below 5, then on x2 below 4 in the left branch; a row at x1 equal to 5.1 lands in the right leaf whatever x2 is. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id decision-tree, 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/DecisionTree.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- A classifier that scores by a sequence of axis-aligned splits and is flat within each leaf. Its finite difference is zero at every row that does not straddle a split, a split on one coordinate reads nothing of the others, and the Gini impurity it splits on is at most one half for two classes and zero exactly for a pure leaf.
- Its read subspace is spanned by the coordinates it splits on and a feature that appears in no split is in its nuisance exactly, which is why a finite-difference probe of a tree returns zero at most rows and importances that count splits are the right sensitivity for this reader.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Breiman, Friedman, Olshen, and Stone, classification and regression
trees, 1984, as chapter 6 section 6.1 of Data Mining as
Observation reads it, with the selection-consumer regime in
readscope/readscope/regimes.py:1-60.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
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 0, 4, 5, 6, 7, 8, 9, 11, 14.
Related
classifier; importance; boosting; ensemble; sensitivity.
See also
Book equations stated beside the entry’s terms, not defining it: 6.1, 0.8, 14.5.
Ledger rows that cite the entry’s records without naming it: GO-1.
Sources-table rows that share a record with the entry without naming it: chapter 2 section 2.3, chapter 6 section 6.1, 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.