importance instrument
| Definition | A per-feature score of how much a classifier reads it. For a tree it counts splits, which is the right sensitivity for a reader that is flat within leaves. Permutation importance and partial dependence answer related questions. Chapter 7 and chapter 14. Also permutation importance, partial dependence. |
|---|---|
| Example | A tree that splits on x1 twice and on x3 once and never on x2 gives importances 2, 0, and 1. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id importance, 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/Attribution.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
- A per-feature score of how much a classifier reads it. For a gradient reader the averaged squared sensitivity is the read operator’s diagonal, and for a tree, whose finite difference is zero at every row that does not straddle a split, counting splits is the right sensitivity.
- Permutation importance averages the consumer over rows that may never occur together, and partial dependence reads it at inputs it was never trained on, so the three answer different questions and the report names which.
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 and chapter
14 section 14.5 of Data Mining as Observation read it, with the
selection-consumer regime in
readscope/readscope/regimes.py:1-60.
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/Attribution.lean,
theorems attr_sum_affine, attr_unread,
sq_sensitivity_eq_readOp_diag, 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 0, 4, 6, 7, 14.
Related
attribution; decision tree; sensitivity; read operator; ensemble.
See also
Book equations stated beside the entry’s terms, not defining it: 14.5, 0.9, 6.1.
Ledger rows that cite the entry’s records without naming it: GO-EC-3.
Sources-table rows that share a record with the entry without naming it: chapter 2 section 2.3, chapter 6 section 6.1, chapter 14 section 14.5.
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.