aiqbench analysis
This paper establishes theoretical minimax rates for estimating conditional average treatment effects, demonstrating how the smoothness of covariate designs directly impacts convergence speed in causal inference. The findings are significant for machine learning practitioners developing robust algorithms for heterogeneous treatment effect estimation, particularly when dealing with non-uniform data distributions.
Minimax rates for pointwise CATE estimation: the role of design smoothness
arXiv:2610.18623v1 Announce Type: cross Abstract: We study the role of design smoothness in the minimax estimation of conditional average treatment effects at a fixed covariate point. For design densities bounded above and away from zero, without further regularity, we derive upper and lower risk bounds with an arbitrarily small gap in the convergence-rate exponent. Under uniform design, we obtain matching upper and lower bounds at interior points in the regime of low nuisance smoothness. These results show that rough covariate designs can lead to slower rates than uniform designs, even under the same smoothness assumptions on the treatment effect and nuisance functions, highlighting the role of the covariate distribution in pointwise causal estimation.
Abstract:We study the role of design smoothness in the minimax estimation of conditional average treatment effects at a fixed covariate point. For design densities bounded above and away from zero, without further regularity, we derive upper and lower risk bounds with an arbitrarily small gap in the convergence-rate exponent. Under uniform design, we obtain matching upper and lower bounds at interior points in the regime of low nuisance smoothness. These results show that rough covariate designs can lead to slower rates than uniform designs, even under the same smoothness assumptions on the treatment effect and nuisance functions, highlighting the role of the covariate distribution in pointwise causal estimation.
Statistics Theory (math.ST); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2610.18623 [math.ST]
(or arXiv:2610.18623v1 [math.ST] for this version)
https://doi.org/10.48550/arXiv.2610.18623 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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