mlsanityData to 7 Oct 2026

Kernel-based estimators for functional causal effects

arXiv 2503.05024 ↗First posted 6 Mar 2025stat.ME cs.LG math.STcited by 3

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Abstract (arXiv)

We propose causal effect estimators based on empirical Fr'echet 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'echet 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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 15 of its 53 references that are in the map. First posted on arXiv 6 Mar 2025.

Builds on

15 of 53 references.

References · 15

  1. 2015Operator-valued Kernels for Learning from Functional Response Datacited by 59
  2. 2021Semiparametric counterfactual density estimationcited by 42
  3. 2020Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curvescited by 36
  4. 2013Program Evaluation and Causal Inference with High-Dimensional Datacited by 29
  5. 2013Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variablescited by 23
  6. 2021BayesIMP: Uncertainty Quantification for Causal Data Fusioncited by 21
  7. 2021Causal inference with misspecified exposure mappings: separating definitions and assumptionscited by 14
  8. 2021Causal Inference on Distribution Functionscited by 11
  9. 2023Causal inference with a functional outcomecited by 8
  10. 2023The Signature Kernelcited by 8
  11. 2023A Unifying Perspective on Non-Stationary Kernels for Deeper Gaussian Processescited by 8
  12. 2024Geodesic Causal Inferencecited by 7
3 more
  1. 2025Doubly-Robust Functional Average Treatment Effect Estimationcited by 4
  2. 2024Interventional Processes for Causal Uncertainty Quantificationcited by 2
  3. 2020Probabilistic modelling of gait for robust passive monitoring in daily lifecited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026A Doubly Robust Machine Learning Approach for Disentangling Treatment Effect Heterogeneity with Functional Outcomescited by 1
  2. 2026Wasserstein Policy Learning for Distributional Outcomescited by 0
  3. 2026Causal inference for group-contaminated structured outcomes: observable quotients, lossless reduction and exact randomization inferencecited by 0