operating point concept
| Definition | The row at which a consumer is read, or the threshold at which a classifier is scored. A probe pays 2d evaluations for one. Chapter 0 section 0.5 and chapter 11 section 11.7. |
|---|---|
| Example | A probe at one row with 16 directions spends 32 calls at that one operating point. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id operating-point, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.8. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/FiniteDifference.lean, lean/DataMiningAsObservation/Threshold.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.8.
\[g_j\;\approx\;\frac{C(x+h\,e_j)-C(x-h\,e_j)}{2h},\qquad j=1,\dots,d.\]
Book equation 11.4.
\[\text{directions resolved}(k)=\begin{cases}1\ \text{or}\ 2,& k<d\\[2pt] \operatorname{rank}P_C,& k\ge d\end{cases}\qquad \text{cost}=2d\ \text{consumer calls per operating point}.\]
Conditions
- The row at which a consumer is read, or the threshold at which a classifier is scored. A central-difference probe pays two evaluations per coordinate for one operating point, and raising a classifier’s threshold can only shrink the set it calls positive.
- Whether many cheaper operating points can average their way back to the population operator was measured within a budget range and not proved, and the cliff at k equal to d does not soften for a probe confined to the directions it chooses.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 0 section 0.5 and chapter 11 section 11.7 of Data Mining
as Observation, with the budget law in
readscope/README.md:118-141.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/FiniteDifference.lean,
theorems central_quad, forward_quad,
forward_error, central_cost, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
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 chapters 0, 2, 5, 6, 11, 14.
Related
finite difference; budget; budget cliff; threshold; blind probe.
See also
Book equations stated beside the entry’s terms, not defining it: 0.28.
Ledger rows that cite the entry’s records without naming it: OT-3, GO-4.
Sources-table rows that share a record with the entry without naming it: 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.