output metric concept
| Definition | The rule by which a consumer's mistakes are scored, the second element of an observer. Chapter 1. |
|---|---|
| Example | Classifiers with one and three false positives against three and one false negatives tie on accuracy and split on any cost matrix. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id output-metric, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/OutputMetric.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The rule by which a consumer’s mistakes are scored, the second element of an observer. A consumer and its negation have the same read operator and reverse every comparison, so the read operator alone does not fix the observer, and two cost matrices score the same pair of classifiers in opposite orders, so naming the output metric is naming what a downstream mistake is.
- A dataset-level loss, accuracy, F1, a rank correlation, or dollars lost is not a local geometry on the score and cannot be inserted into the read-operator formula. Each interestingness measure of chapter 5 and each fairness metric of chapter 14 is an output metric, right for some consumer and wrong for others.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 1 section 1.2 of Data Mining as Observation, with
the flip’s verdict inversion in
geometric-observation/chapters/ch08_value.md:1-30.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/OutputMetric.lean,
theorems neg_reverses, readOp_of_neg,
cost_flips, 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, 1, 3, 5, 6, 8, 9, 11, 14.
Related
observer; consumer; read operator; budget.
See also
Book equations stated beside the entry’s terms, not defining it: 1.1, 0.9, 6.1.
Ledger rows that cite the entry’s records without naming it: GO-2 (neg. half: not reconstruction), GO-2 (pos. half: consumer-projected covariance controls).
Sources-table rows that share a record with the entry without naming it: chapter 3 section 3.2, chapter 4 section 4.3.
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.