Kernel-based estimators for functional causal effects
We propose causal effect estimators based on empirical Fr\'{e}chet means and operator-valued kernels, tailored to functional data spaces. These methods address the challenges of high-dimensionality, sequential ordering, and model complexity while preserving robustness to treatment misspecification. Using structural assumptions, we obtain compact representations of potential outcomes, enabling scalable estimation of causal effects over time and across covariates. We provide both theoretical, regarding the consistency of functional causal effects, as well as empirical comparison of a range of proposed causal effect estimators. Applications to binary treatment settings with functional outcomes illustrate the framework's utility in biomedical monitoring, where outcomes exhibit complex temporal dynamics. Our estimators accommodate scenarios with registered covariates and outcomes, aligning them to the Fr\'{e}chet means, as well as cases requiring higher-order representations to capture intricate covariate-outcome interactions. These advancements extend causal inference to dynamic and non-linear domains, offering new tools for understanding complex treatment effects in functional data settings.
Code (1)
Tasks
Causal InferenceMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Doubly Robust Kernel Statistics for Testing Distributional Treatment Effects
With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem …
Causal InferencecounterfactualOff-policy evaluationIdentification and Estimation of Conditional Average Partial Causal Effects via Instrumental Variable
There has been considerable recent interest in estimating heterogeneous causal effects. In this paper, we study conditional average partial causal effects (CAPCE) to reveal the heterogeneity of causal effects with contin…
Learning Causal Effects via Weighted Empirical Risk Minimization
Learning causal effects from data is a fundamental problem across the sciences. Determining the identifiability of a target effect from a combination of the observational distribution and the causal graph underlying a ph…
Causal IdentificationCausal InferenceAdversarial Estimation of Riesz Representers
Many causal parameters are linear functionals of an underlying regression. The Riesz representer is a key component in the asymptotic variance of a semiparametrically estimated linear functional. We propose an adversaria…
Average Causal Effect Estimation in DAGs with Hidden Variables: Extensions of Back-Door and Front-Door Criteria
The identification theory for causal effects in directed acyclic graphs (DAGs) with hidden variables is well-developed, but methods for estimating and inferring functionals beyond the g-formula remain limited. Previous s…
Density EstimationNumerical Integration