treatment effect extrapolation

This paper addresses causal inference under continuous treatment, focusing on nonparametric estimation of the derivative function of the dose–response curve—i.e., the marginal treatment effect—to overcome the limitation of conventional methods that only target the mean response and neglect critical slope information. We propose the first doubly robust framework for causal derivative estimation: under the positivity assumption, we construct a kernel-smoothed doubly robust estimator; when positivity fails, we develop bias-corrected inverse-probability-weighted (IPW) and doubly robust estimators, and establish the nonparametric efficiency bound. Our estimators achieve the standard nonparametric convergence rate and are asymptotically normal. Simulation studies and empirical analysis of a job training program demonstrate both statistical efficiency and model robustness.

This study addresses the problem of extrapolating causal effects from multi-site randomized controlled trials (RCTs) to a new target site with baseline survey data only. To handle site-level population heterogeneity and unobserved confounding, we propose modeling baseline covariates as functional data—thereby capturing site-specific confounding structures—for the first time. We then develop a design-oriented, nonparametric method to construct an optimal finite-dimensional feature space, ensuring optimal convergence rates for conditional average treatment effect (CATE) estimation. Our approach integrates functional data analysis, nonparametric regression, and causal transfer learning theory. Evaluated across five integrated multi-site RCTs on cash transfer programs, the method significantly improves prediction accuracy of treatment effects at target sites and quantifies the estimation gain attributable to adaptive transfer.

This paper addresses the causal inference problem of extrapolating long-term dose–response curves under continuous interventions from short-term experimental data—particularly for evaluating long-horizon consequences of continuous actions in AI. We propose a nonparametric estimator based on kernel embeddings and kernel ridge regression, capable of modeling continuous actions/rewards in arbitrary domains, nonlinear responses, and individual heterogeneity. To our knowledge, this is the first method to establish a finite-sample, dimension-dependent uniform convergence bound for such extrapolation. The theoretical analysis integrates weak convergence theory with out-of-distribution extrapolation to ensure statistical reliability of counterfactual distribution estimation. Empirically, we successfully replicate and extend the long-term class-size effect curve using data from the Project STAR randomized education experiment, demonstrating both effectiveness and robustness of the proposed approach.

This paper addresses complex causal problems—such as interference—that resist conventional experimental design, by proposing a unified functional-space framework for causal inference. Methodologically, it systematically introduces the Riesz representation theorem for the first time in this context, modeling causal effects as linear functionals on potential outcome functions and encoding prior assumptions via the structure of function spaces. This enables principled, unified modeling across diverse causal settings. Theoretically, the paper establishes necessary and sufficient conditions for unbiasedness, consistency, and asymptotic normality of the proposed estimators. Computationally, it constructs a new class of estimators with rigorous statistical guarantees and provides a computable conservative variance estimator, enabling reliable confidence interval construction. Overall, the framework furnishes a rigorous functional-analytic foundation for design-driven causal inference.

This paper addresses the challenge of estimating heterogeneous dose–response curves (HDRCs) under long-term continuous treatment, where existing methods rely on strong assumptions—such as no unmeasured confounding and binary treatment—that hinder personalized decision-making. We propose an optimal transport-based weighting framework for data alignment, the first to incorporate optimal transport into long-term causal inference; it mitigates bias from unmeasured confounding via reweighting. We derive a generalization bound for counterfactual prediction under the reweighted distribution and jointly model continuous dosing and individual-level heterogeneous treatment effects. On synthetic and semi-synthetic benchmarks, our HDRC estimator reduces estimation error by over 30% compared to state-of-the-art methods, demonstrating both the tightness of our theoretical bound and the robustness of the estimator.

This study addresses causal dose–response function estimation under continuous treatment in the presence of unobserved confounding, assuming only a proxy variable for the latent confounder is observed. It proposes the first proximal doubly robust estimator by constructing a novel proximal doubly robust pseudo-outcome, which, combined with local linear regression, quadratic bias correction, and cross-fitting, yields debiased estimates at the mean squared error–optimal bandwidth—without requiring undersmoothing or entropy conditions on function classes. Theoretically, the estimator achieves pointwise and finite-dimensional asymptotic normality as well as uniform Gaussian approximation. Empirical results demonstrate its strong performance in settings with latent confounding.

This study addresses the challenge of identifying causal treatment effects in the presence of unobserved spatially varying confounders. The authors develop a linear causal model that parameterizes the spatial covariance structure between the exposure and the unobserved confounder, establishing a general identifiability framework applicable to both discrete and continuous spatial data. Under mild conditions on the spatial configuration of observed locations and the association between exposure and confounding, the work provides the first systematic proof of identifiability for treatment effects across several commonly used spatial models. It also delineates precise boundary cases where identifiability fails, thereby offering a rigorous theoretical foundation for robust causal inference in spatial settings.