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

arXiv机器学习 2026-10-02 14:38 6 阅读 查看原文

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.