Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model
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 η 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 minℓk,2kηk/U to first relative order, where ℓk=log(1/(k2Ek)) and Ek 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.
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BibTeX
@misc{cheng2026targetdependent,
title = {{Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model}},
author = {Qinchuan Cheng and Jiaqi Liu and Ruixuan Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00424},
eprint = {2610.00424},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00424},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model
AU - Qinchuan Cheng
AU - Jiaqi Liu
AU - Ruixuan Xie
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00424
UR - https://arxiv.org/abs/2610.00424
AB - 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 η 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 minℓ_k,2kη_k/U to first relative order, where ℓ_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.
ER -