Minimax rates for pointwise CATE estimation: the role of design smoothness
We study the role of design smoothness in the minimax estimation of conditional average treatment effects at a fixed covariate point.
ProofPaper ↗
Key points
- 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.
Sources (1)
- [1]Minimax rates for pointwise CATE estimation: the role of design smoothnessarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 04:02 PM
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.
Extractive summary: sentences quoted from the sources.
Before this
- Oct 13, 2026Recalibrating Many Questions with Few Labels: Minimax Rates and Identification Limits
- Oct 13, 2026Rarity Determines Minimax Rates of Semantic Entropy From Weak Pairwise Judgments With a Known Channel
- Oct 12, 2026Should we be worried about MiniMax potentially being censored in the future?
- Oct 12, 2026Minimax Optimality of Shampoo for Nonstationary Stochastic Optimization
- Oct 12, 2026Online Individualized Treatment Selection under Partial Feedback: False Discovery Control and Minimax Optimality
- Oct 11, 2026Instance-Adaptive Online Multiclass Multicalibration