arXiv：cs.LG· Vishal Rajput·· 3 小时前AI 评分29
何时能信任匹配原则？有限样本与模型不确定性下的稳健部署几何
When Can We Trust the Matching Principle? Robust Deployment Geometry Under Finite-Sample and Model Uncertainty
AI 导读
研究提出用信任比 tau = epsilon / gamma（估计不确定性除以谱分离度）来量化"匹配"决策的可靠性。在线性二次 Matching 响应下，估计投影器与 oracle 投影器的相对漂移在所选 top-r 部署子空间内按 tau^2 缩放，在 Davis-Kahan 分离区 tau < 1/2 内为 O(tau^2)。
正文
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.
| Comments: | 14 pages. Companion to arXiv:2604.21395 and arXiv:2605.22800 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.02894 [cs.LG] |
| (or arXiv:2610.02894v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02894 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Vishal Rajput [view email]
[v1]
Fri, 2 Oct 2026 06:38:38 UTC (414 KB)
来源：arXiv：cs.LG · arxiv.org