Minimax rates for pointwise CATE estimation: the role of design smoothness

We study partial identification of conditional treatment effects with a continuous treatment under unobserved confounding. We target the conditional average potential outcome (CAPO) E[Y_x|z] and the conditional average treatment effect (CATE) between two treatment levels. We assume a bounded outcome and Lipschitz continuity of the response functions and of the propensity scores given the latent confounder, and show that these conditions imply the smooth treatment response and smooth treatment selection conditions of Kim et al. (2018). The combined bound of Kim et al. uses only two reference points on the identified diagonal and is generally loose. Bounding through every diagonal reference point instead gives explicit bounds whose average is the sharp identified set of the CAPO at every treatment, inside or outside the observational support. Capping the difference between the upper and lower bounds gives sharp causal bounds on the CATE. These bounds are informative without monotonicity or overlap assumptions.

Estimating conditional average treatment effects (CATE) enables efficient targeting of interventions, but many applications have limited experimental samples, making it difficult to estimate heterogeneous effects from high-dimensional covariates. In such settings, policymakers and medical practitioners often succumb to the curse of dimensionality or apply off-the-shelf dimension reduction methods that may not preserve treatment heterogeneity. Yet these domains often come with large historical datasets measuring a wide range of outcomes -- a source of supervision that is rarely exploited in practice. Following causal representation learning, we hypothesize that such domains with high-dimensional covariates have lower-dimensional underlying dynamics. We can thus leverage the diverse outcomes measured in historical data to learn a lower-dimensional representation of the covariates. Theoretically, we prove that when the auxiliary outcomes satisfy a set of surrogacy conditions and the representation retains relevant covariate information, the original CATE is identified when the high-dimensional covariates are replaced by the learned representation. Combined with existing dimension-dependent rates for CATE estimation, the result implies greater sample-efficiency on the same experimental sample. Additionally, we characterize the bias-variance tradeoff when the assumptions do not hold perfectly, and show that the representation-based estimator can still achieve lower error when the reduction in estimator variance outweighs the bias due to compression. Empirically, we evaluate the method on synthetic data and semi-synthetic medical data.

We study the problem of selecting covariates for unbiased estimation of the total causal effect.Existing approaches typically rely on global causal structure learning over all variables, or on strong assumptions such as causal sufficiency - where observed variables share no latent confounders - or the pretreatment assumption, which limits covariates to those unaffected by the treatment or outcome. These requirements are often unrealistic in practice, and global learning becomes computationally prohibitive in high-dimensional settings.To address these challenges, we propose a novel local learning method for covariate selection in nonparametric causal effect estimation that avoids both the pretreatment and causal sufficiency assumptions. We first characterize a local boundary that contains at least one valid adjustment set whenever one exists for identifying the causal effect, and then develop local identification procedures to efficiently search within this boundary.We prove that the proposed method is sound and complete. Experiments on multiple synthetic datasets and two real-world datasets show that our approach achieves accurate causal effect estimation while substantially improving computational efficiency.