mlsanityData to 7 Oct 2026

VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments

arXiv 2103.07861 ↗First posted 14 Mar 2021cs.LG stat.MLcited by 59

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Abstract (arXiv)

Motivated by the rising abundance of observational data with continuous treatments, we investigate the problem of estimating the average dose-response curve (ADRF). Available parametric methods are limited in their model space, and previous attempts in leveraging neural network to enhance model expressiveness relied on partitioning continuous treatment into blocks and using separate heads for each block; this however produces in practice discontinuous ADRFs. Therefore, the question of how to adapt the structure and training of neural network to estimate ADRFs remains open. This paper makes two important contributions. First, we propose a novel varying coefficient neural network (VCNet) that improves model expressiveness while preserving continuity of the estimated ADRF. Second, to improve finite sample performance, we generalize targeted regularization to obtain a doubly robust estimator of the whole ADRF curve.

Key facts. Cited by 59 papers in the map (data through 7 Oct 2026). Builds on 16 of its 53 references that are in the map. First posted on arXiv 14 Mar 2021.

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16 of 53 references.

References · 16

  1. 2015Variational Inference with Normalizing Flowscited by 2,161
  2. 2016Density estimation using Real NVPcited by 2,029
  3. 2016HyperNetworkscited by 1,003
  4. 2015Estimation and Inference of Heterogeneous Treatment Effects using Random Forestscited by 597
  5. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  6. 2016Learning Representations for Counterfactual Inferencecited by 327
  7. 2019Adapting Neural Networks for the Estimation of Treatment Effectscited by 285
  8. 2017Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processescited by 156
  9. 2019Learning Counterfactual Representations for Estimating Individual Dose-Response Curvescited by 90
  10. 2020Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networkscited by 78
  11. 2017Double/Debiased/Neyman Machine Learning of Treatment Effectscited by 76
  12. 2015Nonparametric methods for doubly robust estimation of continuous treatment effectscited by 62
4 more
  1. 2018Deep Neural Networks for Estimation and Inferencecited by 62
  2. 2018Conditional Density Estimation with Bayesian Normalising Flowscited by 54
  3. 2019Conditional Density Estimation with Neural Networks: Best Practices and Benchmarkscited by 37
  4. 2017The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variablescited by 14

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 13; 2023: 11; 2024: 18; 2025: 8; 2026: 7.

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  1. 2024Causal machine learning for predicting treatment outcomescited by 73
  2. 2021Causal Effect Inference for Structured Treatmentscited by 38
  3. 2022Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimationcited by 25
  4. 2022Normalizing Flows for Interventional Density Estimationcited by 21
  5. 2022Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventionscited by 20
  6. 2024Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learningcited by 19
  7. 2024Conformal Prediction for Causal Effects of Continuous Treatmentscited by 19
  8. 2022Domain-Specific Risk Minimization for Out-of-Distribution Generalizationcited by 15
  9. 2023Reliable Off-Policy Learning for Dosage Combinationscited by 15
  10. 2023Causal Effect Estimation: Recent Advances, Challenges, and Opportunitiescited by 14
  11. 2022Deep Causal Learning: Representation, Discovery and Inferencecited by 11
  12. 2022Comparison of meta-learners for estimating multi-valued treatment heterogeneous effectscited by 10
38 more
  1. 2022A Survey of Deep Causal Models and Their Industrial Applicationscited by 10
  2. 2023Counterfactual Prediction Under Outcome Measurement Errorcited by 10
  3. 2023Adversarially Balanced Representation for Continuous Treatment Effect Estimationcited by 10
  4. 2021End-to-End Balancing for Causal Continuous Treatment-Effect Estimationcited by 9
  5. 2022Generalization bounds and algorithms for estimating conditional average treatment effect of dosagecited by 9
  6. 2023Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confoundingcited by 7
  7. 2024Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothingcited by 7
  8. 2024Causal Machine Learning for Cost-Effective Allocation of Development Aidcited by 6
  9. 2024Contrastive Balancing Representation Learning for Heterogeneous Dose-Response Curves Estimationcited by 6
  10. 2024Deep Autoregressive Models as Causal Inference Enginescited by 6
  11. 2022Learning Instrumental Variable from Data Fusion for Treatment Effect Estimationcited by 5
  12. 2022Time Series Causal Link Estimation under Hidden Confounding using Knockoff Interventionscited by 5
  13. 2025Differentially Private Learners for Heterogeneous Treatment Effectscited by 5
  14. 2025Projection Pursuit Density Ratio Estimationcited by 5
  15. 2022Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regressioncited by 4
  16. 2024Uplift modeling with continuous treatments: A predict-then-optimize approachcited by 4
  17. 2026Causal Foundation Models with Continuous Treatmentscited by 4
  18. 2022GCF: Generalized Causal Forest for Heterogeneous Treatment Effect Estimation in Online Marketplacecited by 3
  19. 2023SpaCE: The Spatial Confounding Environmentcited by 3
  20. 2024PairNet: Training with Observed Pairs to Estimate Individual Treatment Effectcited by 3
  21. 2024Causal Inference with Complex Treatments: A Surveycited by 3
  22. 2024DISCRET: Synthesizing Faithful Explanations For Treatment Effect Estimationcited by 2
  23. 2024Sources of Gain: Decomposing Performance in Conditional Average Dose Response Estimationcited by 2
  24. 2022BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effectcited by 1
  25. 2023A Causal Perspective on Loan Pricing: Investigating the Impacts of Selection Bias on Identifying Bid-Response Functionscited by 1
  26. 2024SubgroupTE: Advancing Treatment Effect Estimation with Subgroup Identificationcited by 1
  27. 2024Heterogeneous treatment effect estimation with subpopulation identification for personalized medicine in opioid use disordercited by 1
  28. 2024New User Event Prediction Through the Lens of Causal Inferencecited by 1
  29. 2025MMCE: A Framework for Deep Monotonic Modeling of Multiple Causal Effectscited by 1
  30. 2025Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Timecited by 1
  31. 2023Causal Estimation of Exposure Shifts with Neural Networkscited by 0
  32. 2023Identification of Causal Relationship between Amyloid-beta Accumulation and Alzheimer's Disease Progression via Counterfactual Inferencecited by 0
  33. 2023De-confounding Representation Learning for Counterfactual Inference on Continuous Treatment via Generative Adversarial Networkcited by 0
  34. 2023Using representation balancing to learn conditional-average dose responses from clustered datacited by 0
  35. 2024Pareto-Optimal Estimation and Policy Learning on Short-term and Long-term Treatment Effectscited by 0
  36. 2024Disentangled Representation via Variational AutoEncoder for Continuous Treatment Effect Estimationcited by 0
  37. 2024Generalized Encouragement-Based Instrumental Variables for Counterfactual Regressioncited by 0
  38. 2025Leveraging a Simulator for Learning Causal Representations from Post-Treatment Covariates for CATEcited by 0

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