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Open question · OPEN-D-DIRECTIONAL-BOUND

What does determinant efficiency guarantee by direction?

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Meaning

Seek directional retention guarantees from a determinant-based aggregate.

Scientific context

A good determinant efficiency does not by itself guarantee that every parameter direction is well measured. Only the trivial ordering between the worst direction, the geometric mean and the average is available; anything sharper is open. The direction-resolved diagnostics exist precisely because the summary efficiency number cannot be trusted to speak for the worst direction.

Statement

Bound the worst normalized retained eigenvalue from eta_D, and conversely, with useful additional assumptions.

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Local map of Direction-wise guarantees from determinant efficiency2 prerequisites to the left, 0 results it enables or questions it raises to the right, 0 boundary cases below.D-efficiency relative to unbinned inferenceD-efficiency relative…Direction-resolved retained-information diagnosticsDirection-resolved re…Direction-wise guarantees from determinant efficiencyDirection-wise guaran…
Prerequisites to the left, what it enables or raises to the right, boundary cases below. Open in the map.

The question in full

Direction-wise guarantees from determinant efficiency

Given ηD\eta_D, bound λmin⁡(R)\lambda_{\min}(R) and conversely; find assumptions under which determinant retention controls worst-direction loss tightly.

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