aiqbench analysis
This paper establishes a theoretical limit on the gap between potential causal improvement and the gain achieved by learned repairs in Gaussian models, revealing a $k^{-2}$ assessment floor that persists even when oracle potentials are estimable faster. By characterizing a sharp leading-log frontier for the assessment exponent, the work clarifies how specific experimental targets alter information requirements rather than addressing general causal identifiability. These findings provide rigorous bounds on performance limits for learners and assessors operating under uniform mean squared error constraints in causal inference settings.
Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model
arXiv:2610.00424v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2610.00424 [stat.ML]
(or arXiv:2610.00424v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.00424 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 292 words
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