Contact Geometry and Covariance Deficits in Volume-Sampled Least Squares
cs.LG, stat.ML
Submitted: 2026-08-27
Updated: 2026-10-06
Comments: 55 pages. Revised title and substantially reorganized theoretical exposition. Includes contact-space and whole-query classification, all-size leave-one-out covariance-deficit comparisons, quantitative contact geometry, and query-risk bounds, with proofs, exact constructions, and ancillary exact-arithmetic checks
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- The Schur-Horn theorem for operators and frames with prescribed norms and frame operator
- Expansions from frame coefficients with erasures
- Adaptive randomized pivoting and volume sampling
- Reduced Label Complexity For Tight $\ell_2$ Regression
- Debiasing Random Oblique Projections for Subsampled OLS and Fast CUR in High Dimensions
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