score concept
| Definition | The number a classifier produces per row before a threshold turns it into a decision. Chapter 6. |
|---|---|
| Example | A classifier outputs 0.73 for a row; the threshold, not the score, makes the decision. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id score, kind concept. |
| 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/Threshold.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 6.1.
\[s(x)=w\cdot x+b,\qquad P_C=\mathbb E\big[\sigma'(s)^{2}\big]\,w\,w^{\top},\qquad \operatorname{rank}P_C=1.\]
Book equation 6.2.
\[\begin{gathered} \max_{\tau,\ \mathrm{dir}}F_1\!\Big(\mathbf 1\big[\mathrm{dir}\big(g(f(X)),\tau\big)\big],\,y\Big)=\max_{\tau,\ \mathrm{dir}}F_1\!\Big(\mathbf 1\big[\mathrm{dir}\big(f(X),\tau\big)\big],\,y\Big) \\ \text{for every strictly monotone } g. \end{gathered}\]
Conditions
- The number a classifier produces per row before a threshold turns it into a decision. Every decision at every threshold is a function of the scores’ ordering, so a strictly increasing recalibration of the scores with the matching recalibration of the threshold changes no decision.
- What a recalibration can change is calibration, which is why the reliability weight reads the ordering and the expected calibration error reads the values, and neither stands in for the other.
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 program’s threshold sweeps in theory-radar.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Threshold.lean,
theorems predicted_anti, tp_anti,
fp_anti, decision_comp,
predicted_extremes, at observation-data-mining f3914f0;
what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation primer S, chapters 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
Related
classifier; threshold; Monotone Invariance Theorem; calibration; reliability weight.
See also
Sources-table rows that share a record with the entry without naming it: chapter 5 section 5.4, chapter 6 section 6.3.
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.