2 problems

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Conjecture on the statistical dimension of fixed-order monotone cones
Statistical-dimension conjecture. For every fixed $k\geq 0$ , the correct order of $\delta_{K_{\uparrow,k}}$ should be
Conjectureopenmonotone-cones shape-constrained-inference statistical-dimensionarXiv posted 2 days ago
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Approximation of statistical dimension by distance to the scaled subdifferential
Approximation conjecture. For these choices of $f$ , the statistical dimension is well approximated by the squared Euclidean distance to the scaled subdifferential:
Conjectureopencompressed-sensing convex-optimization statistical-dimensionarXiv posted 2 days ago

Conjecture on the statistical dimension of fixed-order monotone cones