attribution instrument
| Definition | An assignment to each feature of a share of one prediction. The raw gradient is the sensitivity at a row, gradient times input is the share of the change in output, and the averaged squared gradient is a diagonal entry of the read operator, and the three are kept apart. Shapley, permutation, and partial-dependence methods measure other things and are named for them. Chapter 14. Also partial dependence, Shapley. |
|---|---|
| Example | For the affine consumer 3x1 + 2x2, moving from (0, 0) to (1, 1) gives attributions 3 and 2, which sum to the change in output, 5. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id attribution, 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 |
| Reviewed | semantic review 2026-09-06; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- An assignment to each feature of a share of one prediction. Three gradient quantities are kept apart. The raw gradient is the sensitivity at a row. Gradient times input, the sensitivity times the move along a coordinate, sums exactly to the change in output for an affine consumer and is zero on an unread coordinate. The weighted mean of the squared sensitivity is a diagonal entry of the read operator, so an averaged squared gradient estimates the read operator and a single-row attribution does not.
- Shapley, permutation, and partial-dependence methods measure other things and are named for them, and for a tree the sensitivity is zero almost everywhere, so importances that count splits are the right reading and finite differences the wrong one.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Lundberg and Lee, a unified approach to interpreting model
predictions, 2017, as chapter 14 section 14.5 of Data Mining as
Observation reads it, with the program’s contraction formula in
gtc-prototype/docs/SPECTRUM_FINDINGS.md:90-99.
Measurements
none
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.
Used in
Data Mining as Observation primer L, chapters 0, 8, 14.
Related
sensitivity; read operator; finite difference; consumer.
See also
Book equations stated beside the entry’s terms, not defining it: 0.8, 0.9, 14.5.
Ledger rows that cite the entry’s records without naming it: GO-1, GO-EC-3.
Sources-table rows that share a record with the entry without naming it: chapter 11 section 11.7, 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.