When Can We Trust the Matching Principle? Robust Deployment Geometry Under Finite-Sample and Model Uncertainty

Title:When Can We Trust the Matching Principle? Robust Deployment Geometry Under Finite-Sample and Model Uncertainty

Abstract:Match only geometry you can identify; otherwise spread the penalty. We quantify that decision by the trust ratio tau = epsilon / gamma (estimation uncertainty over spectral separation). Under the linear-quadratic Matching response, oracle-relative drift between estimated and oracle projector matching scales as tau^2 for probes in the chosen top-r deployment subspace -- O(tau^2) in the Davis-Kahan separation region tau < 1/2, with practical usefulness depending on constants. Confidence-Calibrated Matching (CCM) turns tau into a policy -- directional when tau is small, progressively isotropic when not -- with thresholds from calibration, not from the theorem (match sits in the separation region; soft is mostly heuristic). Experiments show both regimes, including UCI HAR embeddings where always-match is worse than abstain on every cell.

14 pages. Companion to arXiv:2604.21395 and arXiv:2605.22800

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.02894 [cs.LG]

(or arXiv:2610.02894v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.02894 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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