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output metric concept

DefinitionThe rule by which a consumer's mistakes are scored, the second element of an observer. Chapter 1.
ExampleClassifiers with one and three false positives against three and one false negatives tie on accuracy and split on any cost matrix.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id output-metric, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • 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.
Prior artnone recorded
Evidencelean/DataMiningAsObservation/OutputMetric.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
consumerthe computationoutput metricwhat a mistake costsbudgetwhat can be spentthe read operator is what the triple induces, and its kernel is the nuisance
What a mistake costs, the second element of the observer.

Equation

none

Conditions

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.

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