因果修复的目标依赖极限：高斯模型中的前导对数前沿

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Abstract:Knowing how much a causal predictor could improve need not reveal the gain of the repair actually learned. We quantify this gap in a scalar Gaussian causal experiment with known intervention geometry: auxiliary data identify effect magnitude up to bounded contamination, while diagnostics identify direction. The target is the squared-loss gain of the realized trained repair relative to a fitted reference. Jointly optimizing the learner and assessor under uniform learning MSE $\eta$ avoids the trivial solution of making no repair. At the usual $1/k$ learning scale, every feasible learner incurs a $k^{-2}$ assessment floor, even when oracle potential is estimable at a faster rate. In the magnitude-rich regime, we characterize a sharp leading-log frontier: the assessment exponent is $\min{\ell_k,2k\eta_k/U}$ to first relative order, where $\ell_k=\log(1/(k^2E_k))$ and $E_k$ is auxiliary precision. A diagnostic-abstention rule attains this exponent with unknown nuisance parameters. We also bound the critical allowance window and transfer the frontier to adaptive sampling by exact Gaussian simulation. Finite-grid experiments distinguish sign-tail suppression from total MSE and expose conservative finite-budget behavior. The result isolates how the assessment target changes information requirements in this experiment; it is not a general causal identifiability claim.

Subjects:	Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
Cite as:	arXiv:2610.00424 [stat.ML]
	(or arXiv:2610.00424v1 [stat.ML] for this version)
	https://doi.org/10.48550/arXiv.2610.00424 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Qinchuan Cheng [view email]
[v1] Wed, 30 Sep 2026 15:48:39 UTC (103 KB)