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Result · INFO-D-EFFICIENCY

D-efficiency measures determinant retention

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Meaning

D-efficiency compares binned and unbinned information through a dimension-normalized determinant ratio.

Scientific context

The geometric mean of the retention eigenvalues (INFO-RETENTION-SPECTRUM) is reported as the standard determinant efficiency number: a single figure summarizing how much of the full-data information a partition retains, in the units set by the determinant criterion.

Statement

eta_D=(det I_q/det I_full)^(1/d), the geometric mean retained Fisher information over normalized parameter directions.

required user-facing information-loss score

Closest prior work

Relationships

Rests on

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Enables

Raises

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In the library

Carried by InformationReport.geometric_mean_retention. Reference.

Every object and refusal

Local graph
Local map of D-efficiency relative to unbinned inference1 prerequisites to the left, 5 results it enables or questions it raises to the right, 0 boundary cases below.Normalized retained-information spectrumNormalized retained-i…Direction-wise guarantees from determinant efficiencyDirection-wise guaran…Sharp D-efficiency bounds versus KSharp D-efficiency bo…High-rate D quantization asymptoticsHigh-rate D quantizat…Frozen-rule vector retention: plug-in CLT for the geometric-mean D-retention with a consistent influence-function varianceFrozen-rule vector re…Reported versus true retention of a frozen label map under a score error: an exact two-term expansion in the Fisher-whitened score errorReported versus true…D-efficiency relative to unbinned inferenceD-efficiency relative…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

Proof

I1. D-efficiency
ηD=(det⁡Iq/det⁡Ifull)1/d.\eta_D=(\det I_q/\det I_{\rm full})^{1/d}.

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