# Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model

arXiv: https://arxiv.org/abs/2610.00424 · HTML: https://mlsanity.com/paper/2610.00424/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021)
- [Optimal strategies for reject option classifiers](https://mlsanity.com/paper/2101.12523/) (2021)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Bandits with Partially Observable Confounded Data](https://mlsanity.com/paper/2006.06731/) (2020)
- [Fantastic Generalization Measures are Nowhere to be Found](https://mlsanity.com/paper/2309.13658/) (2023)
- [The Value of Information When Deciding What to Learn](https://mlsanity.com/paper/2110.13973/) (2021)
- [Copula-based Sensitivity Analysis for Multi-Treatment Causal Inference with Unobserved Confounding](https://mlsanity.com/paper/2102.09412/) (2021)
- [CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Design](https://mlsanity.com/paper/2302.14015/) (2023)
- [On the Statistical Complexity of Sample Amplification](https://mlsanity.com/paper/2201.04315/) (2022)

## Abstract (arXiv)

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.