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Open question · OPEN-D-HIGH-RATE

What happens with many D-optimal bins?

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Meaning

Develop high-rate asymptotics for determinant-preserving quantization.

Statement

Derive K->infinity asymptotics; test the hypothesis that first order is Fisher-whitened quadratic quantization and D-specific shape effects enter at second order.

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Local map of High-rate D quantization asymptotics2 prerequisites to the left, 0 results it enables or questions it raises to the right, 0 boundary cases below.Normalized trace equals Fisher-whitened k-meansNormalized trace equa…D-efficiency relative to unbinned inferenceD-efficiency relative…High-rate D quantization asymptoticsHigh-rate D quantizat…
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The question in full

High-rate $K\to\infty$ asymptotics

With L=Ifull−IqL=I_{\rm full}-I_q, expand log⁡det⁡(Ifull−L)\log\det(I_{\rm full}-L) to second order. Working hypothesis: first order is Fisher-whitened quadratic quantization; D-specific cell-shape effects appear at second order. Connect to Zador–Gersho high-rate theory.

From OPEN_PROBLEMS.md