ScoreQuant

Result · DWW-PURIFICATION-MOMENTS

Randomized assignments purify on atomless laws

Establishedpublication: published

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Meaning

Classical purification preserves the cell masses and first moments that determine the information objective.

Statement

For an atomless score law and finite labels, Dvoretzky-Wald-Wolfowitz purification can preserve all cell probabilities and first score moments of a randomized quantizer.

randomized-vs-deterministic population equivalence

Relationships

Enables

Local graph
Local map of Atomless purification preserves (W_b,m_b)0 prerequisites to the left, 1 results it enables or questions it raises to the right, 0 boundary cases below.Randomized and deterministic population optima coincide for moment-based criteria under atomlessnessRandomized and determ…Atomless purification preserves (W_b,m_b)Atomless purification…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

S5. Atomless purification

For an atomless score law, Dvoretzky–Wald–Wolfowitz purification preserves all (Wb,mb)(W_b,m_b) of a randomized finite-action quantizer. Hence randomized and deterministic quantizers have the same population optimum value for every criterion depending only on these moments.

This is a classical theorem applied to the present Fisher-score moment representation.

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