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Result · FI-REFINEMENT-MONOTONICITY

Refining cells cannot lose information

Derived from the literaturepublication: derived from published

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Meaning

Splitting cells increases retained information in the positive-semidefinite order.

Statement

If partition P' refines P then I_P' >= I_P in Loewner order.

Relationships

Rests on

Enables

Local graph
Local map of Refinement monotonicity1 prerequisites to the left, 2 results it enables or questions it raises to the right, 0 boundary cases below.Quantized Fisher-information identityQuantized Fisher-info…Singleton-refinement branch-and-bound upper bound for DSingleton-refinement…Refinement upper bounds for Loewner-monotone criteriaRefinement upper boun…Refinement monotonicityRefinement monotonici…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

U5. Refinement monotonicity

If P′\mathcal P' refines P\mathcal P, then

IP′⪰IP.I_{\mathcal P'}\succeq I_{\mathcal P}.

This powers branch-and-bound upper bounds for every Loewner-monotone criterion.

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