linear classifier instrument
| Definition | A classifier that scores by a weighted sum, logistic regression or a linear support vector machine. Its read subspace is the one direction of its weight vector. Chapter 6. Also weighted sum, support vector. |
|---|---|
| Example | The score 2x1 + x2 − 3 reads only the direction (2, 1), and (1, −2) is in its nuisance. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id linear-classifier, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 6.1. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Logistic.lean, lean/DataMiningAsObservation/ReadOperator.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 6.1.
\[s(x)=w\cdot x+b,\qquad P_C=\mathbb E\big[\sigma'(s)^{2}\big]\,w\,w^{\top},\qquad \operatorname{rank}P_C=1.\]
Conditions
- A classifier that scores by a weighted sum, logistic regression or a linear support vector machine. Its decision boundary is the hyperplane where the weighted sum is zero, its read subspace is the one direction of its weight vector, and its read operator is the outer product of that vector with itself, scaled by the score’s slope.
- Its nuisance is everything orthogonal to the weight vector, and a planted linear consumer is the case a probe is tested against before it is trusted on a real model.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 6 section 6.1 of Data Mining as Observation, with
the planted affine consumer in
geometric-observation/claims/LEDGER.md row GO-1.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Logistic.lean,
theorems sigmoid_pos, sigmoid_lt_one,
sigmoid_zero, sigmoid_neg,
sigmoid_strictMono, decision_iff,
decision_linear, at observation-data-mining f3914f0; what
the check covers is stated in the book’s appendix
C.
lean/DataMiningAsObservation/ReadOperator.lean,
theorems rank_one_reads_one_direction,
readOp_mulVec, quad_readOp,
quad_readOp_nonneg, readOp_mulVec_eq_zero_iff,
readOp_diag, readOp_offdiag,
readOp_symm, readOp_neg,
affine_const_along_nuisance, readOp_affine,
readOp_sqLength_basis, 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, 2, 6, 7, 11.
Related
logistic regression; decision boundary; read subspace; margin; planted.
See also
Book equations stated beside the entry’s terms, not defining it: 0.9, 0.28.
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 6 section 6.1, chapter 6 section 6.2, chapter 11 section 11.7.
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.