Manuscript Oai265-B@2 · Oai265-B-v2.tex · lemma · 94b6f42f

Lemma: Missing analyzer record allowance

Loss, heralding, drift, and reference safeguards › Declared output on loss · lines 914–929 · proof included or linked

Oai265-B@2#lem:missing

Suppose an ideal parity $Z_{j}^{ideal} \in [- 1, 1]$ is defined on every attempt and agrees with the observed parity whenever readout is available. Score missing records by zero. If their unconditional probability is at most $q_{j}$ , then

E Z_{j}^{scored} - E Z_{j}^{ideal} \leq q_{j} .

Proof. The pointwise score change is at most the missing-record indicator. Take expectations.

Displayed formulas in this passage

unlabeled · line 920
$E Z_{j}^{scored} - E Z_{j}^{ideal} \leq q_{j} .$

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section: Declared output on loss
section: Declared output on loss