margin concept
| Definition | How far a row's score sits from the threshold. Chapter 6. |
|---|---|
| Example | Points at distance 0.5 and 0.8 from the boundary on either side give a margin of 0.5. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id margin, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 9.3. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Margin.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 9.3.
\[\hat\mu=\frac{\bar s_{\mathrm{true}}-\bar s_{\mathrm{distr}}}{\sigma_{\mathrm{distr}}},\qquad \mu_{\mathrm{crit}}=\mathbb E\Big[\max_{N-1}\mathcal N(0,1)\Big],\qquad \rho=\frac{\hat\mu}{\mu_{\mathrm{crit}}},\qquad \rho=1\ \text{vacuous}.\]
Conditions
- How far a row’s score sits from the threshold. A perturbation whose length times the weight length is smaller than the margin cannot move a linear classifier’s score across the threshold, by Cauchy–Schwarz, and a step along the weights of exactly that size reaches the boundary.
- The margin is therefore a certificate on a decision, and chapter 9’s margin certificate is the same idea with a noise model in place of a perturbation bound and a vacuity threshold derived from it.
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 margin certificate of chapter 9 section 9.3 and the neighbour margins of chapter 11.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Margin.lean,
theorems score_add, decision_stable,
tight_along_weights, 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, 6, 7, 9, 11, 12, 14.
Related
classifier; decision boundary; vacuity threshold; rank certificate; escalation.
See also
Book equations stated beside the entry’s terms, not defining it: 11.2.
Ledger rows that cite the entry’s records without naming it: GO-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.