mlsanityData to 7 Oct 2026

Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression

arXiv 2102.08208 ↗First posted 16 Feb 2021stat.ML cs.LGcited by 40

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Abstract (arXiv)

We propose to analyse the conditional distributional treatment effect (CoDiTE), which, in contrast to the more common conditional average treatment effect (CATE), is designed to encode a treatment's distributional aspects beyond the mean. We first introduce a formal definition of the CoDiTE associated with a distance function between probability measures. Then we discuss the CoDiTE associated with the maximum mean discrepancy via kernel conditional mean embeddings, which, coupled with a hypothesis test, tells us whether there is any conditional distributional effect of the treatment. Finally, we investigate what kind of conditional distributional effect the treatment has, both in an exploratory manner via the conditional witness function, and in a quantitative manner via U-statistic regression, generalising the CATE to higher-order moments. Experiments on synthetic, semi-synthetic and real datasets demonstrate the merits of our approach.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). Builds on 20 of its 83 references that are in the map. First posted on arXiv 16 Feb 2021.

Builds on

20 of 83 references.

References · 20

  1. 2015Estimation and Inference of Heterogeneous Treatment Effects using Random Forestscited by 597
  2. 2017Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learningcited by 475
  3. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  4. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  5. 2016Learning Representations for Counterfactual Inferencecited by 327
  6. 2019Adapting Neural Networks for the Estimation of Treatment Effectscited by 285
  7. 2017Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processescited by 156
  8. 2020Kernel methods through the roof: handling billions of points efficientlycited by 88
  9. 2020A Measure-Theoretic Approach to Kernel Conditional Mean Embeddingscited by 86
  10. 2017FALKON: An Optimal Large Scale Kernel Methodcited by 82
  11. 2015Operator-valued Kernels for Learning from Functional Response Datacited by 59
  12. 2020Identifying Causal-Effect Inference Failure with Uncertainty-Aware Modelscited by 57
8 more
  1. 2017Some methods for heterogeneous treatment effect estimation in high-dimensionscited by 48
  2. 2016Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributionscited by 39
  3. 2019Globally Convergent Newton Methods for Ill-conditioned Generalized Self-concordant Lossescited by 17
  4. 2017Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithmscited by 16
  5. 2018Causal effects based on distributional distancescited by 15
  6. 2020Robust Recursive Partitioning for Heterogeneous Treatment Effects with Uncertainty Quantificationcited by 12
  7. 2020Regularised Least-Squares Regression with Infinite-Dimensional Output Spacecited by 4
  8. 2018Network and Panel Quantile Effects Via Distribution Regressioncited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 8; 2023: 8; 2024: 6; 2025: 10; 2026: 7.

40 papers.

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  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  2. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 54
  3. 2022Robust and Agnostic Learning of Conditional Distributional Treatment Effectscited by 18
  4. 2022On the Relationship Between Explanation and Prediction: A Causal Viewcited by 14
  5. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  6. 2023An Efficient Doubly-Robust Test for the Kernel Treatment Effectcited by 10
  7. 2024Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learnercited by 10
  8. 2022Context-Aware Drift Detectioncited by 9
  9. 2021Estimating Potential Outcome Distributions with Collaborating Causal Networkscited by 8
  10. 2024Early Concept Drift Detection via Prediction Uncertaintycited by 8
  11. 2022Feature Selection for Discovering Distributional Treatment Effect Modifierscited by 7
  12. 2024Neural-Kernel Conditional Mean Embeddingscited by 7
28 more
  1. 2025On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomizationcited by 6
  2. 2023Confidence and Uncertainty Assessment for Distributional Random Forestscited by 5
  3. 2023iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Modelscited by 5
  4. 2024Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reductioncited by 5
  5. 2022Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regressioncited by 4
  6. 2024Optimizing Estimators of Squared Calibration Errors in Classificationcited by 3
  7. 2025Doubly-Robust Estimation of Counterfactual Policy Mean Embeddingscited by 3
  8. 2022Doubly Robust Kernel Statistics for Testing Distributional Treatment Effectscited by 2
  9. 2023Asymptotically Unbiased Synthetic Control Methods by Moment Matchingcited by 2
  10. 2025Frugal, Flexible, Faithful: Causal Data Simulation via Frengressioncited by 2
  11. 2025Beyond the Average: Distributional Causal Inference under Imperfect Compliancecited by 2
  12. 2022BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effectcited by 1
  13. 2025I-trustworthy Models. A framework for trustworthiness evaluation of probabilistic classifierscited by 1
  14. 2025GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomescited by 1
  15. 2025ActiveCQ: Active Estimation of Causal Quantitiescited by 1
  16. 2025Kernel Treatment Effects with Adaptively Collected Datacited by 1
  17. 2025Inference on Variable Importance for Treatment Effect Heterogeneity: Shapley Values and Beyondcited by 1
  18. 2026Conservative Continuous-Time Treatment Optimizationcited by 1
  19. 2026Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testingcited by 1
  20. 2023Learning sources of variability from high-dimensional observational studiescited by 0
  21. 2023Towards Practicable Sequential Shift Detectorscited by 0
  22. 2023Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumptioncited by 0
  23. 2025A fine-grained look at causal effects in causal spacescited by 0
  24. 2026Preference-based Conditional Treatment Effects and Policy Learningcited by 0
  25. 2026Data Fusion with Distributional Equivalence Test-then-poolcited by 0
  26. 2026Distributional Causal Mediation via Conditional Generative Modelingcited by 0
  27. 2026Attention-Based Estimation of the Individual Treatment Benefit Probability under Dose Variationcited by 0
  28. 2026Wasserstein Causal Forests for Distribution-Valued Outcomescited by 0