reliability weight concept

Definition	Zero or twice a validated encoder's held-out AUROC minus one, whichever is larger, used as that encoder's authority. It is a discrimination weight, unchanged by increasing transforms of the score and not by decreasing ones, and the calibration evidence is the expected calibration error reported beside it. Equation 0.38.
Example	A held-out AUROC of 0.8035 gives reliability weight 0.607, and an AUROC of 0.45 gives zero.
Book	Data Mining as Observation, draft 0.2, commit `f3914f0`; entry id `reliability-weight`, kind concept.
Status	no ledger row names this entry. Corrections: none recorded.
Defining equation	Book equation 0.38.
Assumptions and scope	Zero or twice the held-out AUROC minus one, whichever is larger. It is a discrimination weight, unchanged by a strictly increasing transform of the encoder’s score and not by a decreasing one, which sends A to 1 minus A and the weight to zero whenever A was above one half. The calibration evidence is the expected calibration error reported beside it, and the weight is computed on a held-out split under the cross-corpus gate, so it is one formula from one source.
Prior art	none recorded
Evidence	`gtc-prototype/docs/CALIBRATED_AUTHORITY.md:19-63`, `gtc-prototype/docs/CALIBRATED_AUTHORITY.md:1-65`, `lean/DataMiningAsObservation/ReliabilityWeight.lean`
Reviewed	semantic review 2026-09-06; generated 2026-09-10 from records at the commits on the provenance page.

Twice the held-out AUROC minus one, or zero.

Equation

Book equation 0.38.

\[w=\max\big(0,\ 2\cdot\mathrm{AUROC}-1\big).\]

Conditions

Zero or twice the held-out AUROC minus one, whichever is larger. It is a discrimination weight, unchanged by a strictly increasing transform of the encoder’s score and not by a decreasing one, which sends A to 1 minus A and the weight to zero whenever A was above one half.
The calibration evidence is the expected calibration error reported beside it, and the weight is computed on a held-out split under the cross-corpus gate, so it is one formula from one source.

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

The moral-embedding program’s calibrated authority, gtc-prototype/docs/CALIBRATED_AUTHORITY.md:19-63 and xbse/README.md:175-195, and chapter 12 section 12.5 and chapter 14 section 14.2 of Data Mining as Observation.

Measurements

Where the book states it	Numbers, as the book’s sources table records them	Source
chapter 12 section 12.5	ECE 0.018 to 0.101 vs raw up to 0.223, reliability weight, audit binding	`xbse/README.md:175-195`; `gtc-prototype/docs/CALIBRATED_AUTHORITY.md:19-63`
chapter 14 section 14.2	reliability weights and calibration errors per axis, the collapsed family’s mean weight 0.559 against the general valence channel’s own 0.735, the three design rules, 0.048 to 0.049 and 0.089 to 0.101 at 696 pairs	`gtc-prototype/docs/CALIBRATED_AUTHORITY.md:1-65`

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/ReliabilityWeight.lean, theorems pair_le_one, aurocNum_le, auroc_le_one, weight_mem_unit, weight_eq_zero_of_le_half, weight_comp, 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, 12, 14.

Monotone Invariance Theorem; harness; posited versus measured; certificate.

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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