mlsanityData to 7 Oct 2026

Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation

arXiv 2310.17463 ↗First posted 26 Oct 2023cs.LGcited by 26

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Abstract (arXiv)

Treatment effect estimation in continuous time is crucial for personalized medicine. However, existing methods for this task are limited to point estimates of the potential outcomes, whereas uncertainty estimates have been ignored. Needless to say, uncertainty quantification is crucial for reliable decision-making in medical applications. To fill this gap, we propose a novel Bayesian neural controlled differential equation (BNCDE) for treatment effect estimation in continuous time. In our BNCDE, the time dimension is modeled through a coupled system of neural controlled differential equations and neural stochastic differential equations, where the neural stochastic differential equations allow for tractable variational Bayesian inference. Thereby, for an assigned sequence of treatments, our BNCDE provides meaningful posterior predictive distributions of the potential outcomes. To the best of our knowledge, ours is the first tailored neural method to provide uncertainty estimates of treatment effects in continuous time. As such, our method is of direct practical value for promoting reliable decision-making in medicine.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 33 of its 74 references that are in the map. First posted on arXiv 26 Oct 2023.

Builds on

33 of 74 references.

References · 33

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2014On the Properties of Neural Machine Translation: Encoder-Decoder Approachescited by 1,303
  4. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  5. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  6. 2017Stable Architectures for Deep Neural Networkscited by 340
  7. 2016Learning Representations for Counterfactual Inferencecited by 327
  8. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  9. 2017Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equationscited by 203
  10. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  11. 2017Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processescited by 156
  12. 2020Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representationscited by 154
21 more
  1. 2021Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithmscited by 144
  2. 2019MIMIC-Extract: A Data Extraction, Preprocessing, and Representation Pipeline for MIMIC-IIIcited by 121
  3. 2022Causal Transformer for Estimating Counterfactual Outcomescited by 121
  4. 2022Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equationscited by 59
  5. 2020Identifying Causal-Effect Inference Failure with Uncertainty-Aware Modelscited by 57
  6. 2021Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confoundingcited by 50
  7. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  8. 2020Bayesian Neural Ordinary Differential Equationscited by 44
  9. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  10. 2019ODE2VAE: Deep generative second order ODEs with Bayesian neural networkscited by 36
  11. 2022Estimating average causal effects from patient trajectoriescited by 29
  12. 2023B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confoundingcited by 28
  13. 2022Predicting the impact of treatments over time with uncertainty aware neural differential equationscited by 23
  14. 2022Normalizing Flows for Interventional Density Estimationcited by 21
  15. 2017Learning from Clinical Judgments: Semi-Markov-Modulated Marked Hawkes Processes for Risk Prognosiscited by 18
  16. 2021Deconfounding Temporal Autoencoder: Estimating Treatment Effects over Time Using Noisy Proxiescited by 16
  17. 2023Reliable Off-Policy Learning for Dosage Combinationscited by 15
  18. 2021AttDMM: An Attentive Deep Markov Model for Risk Scoring in Intensive Care Unitscited by 14
  19. 2023Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Timecited by 14
  20. 2021Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomescited by 9
  21. 2023Uncertainty and Structure in Neural Ordinary Differential Equationscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 10; 2025: 9; 2026: 6.

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  1. 2024Causal machine learning for predicting treatment outcomescited by 73
  2. 2023Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimationcited by 20
  3. 2024Conformal Prediction for Causal Effects of Continuous Treatmentscited by 19
  4. 2024Model-agnostic meta-learners for estimating heterogeneous treatment effects over timecited by 18
  5. 2024DiffPO: A causal diffusion model for learning distributions of potential outcomescited by 17
  6. 2025Uncertainty Quantification for Machine Learning in Healthcare: A Surveycited by 11
  7. 2024IGC-Net for conditional average potential outcome estimation over timecited by 10
  8. 2024Stabilized Neural Prediction of Potential Outcomes in Continuous Timecited by 7
  9. 2024Semi-Supervised Learning for Deep Causal Generative Modelscited by 6
  10. 2024Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasetscited by 6
  11. 2025Efficient and Sharp Off-Policy Learning under Unobserved Confoundingcited by 5
  12. 2025Orthogonal Representation Learning for Estimating Causal Quantitiescited by 4
14 more
  1. 2024Uncertainty-Aware Optimal Treatment Selection for Clinical Time Seriescited by 3
  2. 2024Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximationscited by 3
  3. 2025Overlap-weighted orthogonal meta-learner for treatment effect estimation over timecited by 3
  4. 2025PrivATE: Differentially Private Confidence Intervals for Average Treatment Effectscited by 2
  5. 2025Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Timecited by 1
  6. 2025GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomescited by 1
  7. 2025DeepBlip: Estimating Conditional Average Treatment Effects Over Timecited by 1
  8. 2026Conservative Continuous-Time Treatment Optimizationcited by 1
  9. 2026Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equationscited by 1
  10. 2026Debiased neural operators for estimating functionalscited by 1
  11. 2025Generative Modeling of Clinical Time Series via Latent Stochastic Differential Equationscited by 0
  12. 2026Targeted Synthetic Control Methodcited by 0
  13. 2026From Static Risk to Dynamic Trajectories: Toward World-Model-Inspired Clinical Predictioncited by 0
  14. 2026OrthoReg: Orthogonal Regularization for Hybrid Symbolic-Neural Dynamical Systemscited by 0