mlsanityData to 14 Oct 2026

Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations

arXiv 2206.08311 ↗First posted 16 Jun 2022cs.LG stat.MLcited by 59

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Abstract (arXiv)

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer ''what-iF'' questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time-series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all simulated scenarios with irregular sampling.

Key facts. Cited by 59 papers in the map (data through 14 Oct 2026). Builds on 23 of its 56 references that are in the map. First posted on arXiv 16 Jun 2022.

Builds on

23 of 56 references.

References · 23

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2015Domain-Adversarial Training of Neural Networkscited by 3,044
  4. 2015Estimation and Inference of Heterogeneous Treatment Effects using Random Forestscited by 600
  5. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
  6. 2016Learning Representations for Counterfactual Inferencecited by 329
  7. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 231
  8. 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 183
  9. 2017Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processescited by 158
  10. 2020Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representationscited by 155
  11. 2018Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flowcited by 135
  12. 2018The Blessings of Multiple Causescited by 104
11 more
  1. 2019Support and Invertibility in Domain-Invariant Representationscited by 87
  2. 2019Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounderscited by 75
  3. 2020Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effectscited by 72
  4. 2020Identifying Causal-Effect Inference Failure with Uncertainty-Aware Modelscited by 57
  5. 2019Approximation Capabilities of Neural ODEs and Invertible Residual Networkscited by 56
  6. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  7. 2020Neural Ordinary Differential Equations for Intervention Modelingcited by 19
  8. 2017Learning from Clinical Judgments: Semi-Markov-Modulated Marked Hawkes Processes for Risk Prognosiscited by 18
  9. 2021Policy Analysis using Synthetic Controls in Continuous-Timecited by 18
  10. 2016Hawkes Processes with Stochastic Excitationscited by 4
  11. 2018The additive hazard estimator is consistent for continuous-time marginal structural modelscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 16; 2024: 16; 2025: 12; 2026: 12.

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  1. 2024Causal machine learning for predicting treatment outcomescited by 74
  2. 2023Bayesian Neural Controlled Differential Equations for Treatment Effect Estimationcited by 26
  3. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 24
  4. 2023Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimationcited by 20
  5. 2024Model-agnostic meta-learners for estimating heterogeneous treatment effects over timecited by 19
  6. 2023Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounderscited by 17
  7. 2023Counterfactual Generative Models for Time-Varying Treatmentscited by 17
  8. 2023CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systemscited by 16
  9. 2024Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patchingcited by 16
  10. 2023Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Timecited by 15
  11. 2024Automatically Learning Hybrid Digital Twins of Dynamical Systemscited by 14
  12. 2024ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inferencecited by 12
38 more
  1. 2022A Survey of Deep Causal Models and Their Industrial Applicationscited by 10
  2. 2023Neural Laplace Control for Continuous-time Delayed Systemscited by 10
  3. 2024IGC-Net for conditional average potential outcome estimation over timecited by 10
  4. 2022Adversarial De-confounding in Individualised Treatment Effects Estimationcited by 9
  5. 2025medDreamer: Model-Based Reinforcement Learning with Latent Imagination on Complex EHRs for Clinical Decision Supportcited by 9
  6. 2024Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systemscited by 8
  7. 2024G-Transformer: Counterfactual Outcome Prediction under Dynamic and Time-varying Treatment Regimescited by 8
  8. 2026ChronoMedicalWorld: A Medical World Model for Learning Patient Trajectories from Longitudinal Care Datacited by 8
  9. 2024Causal Contrastive Learning for Counterfactual Regression Over Timecited by 7
  10. 2024Stabilized Neural Prediction of Potential Outcomes in Continuous Timecited by 7
  11. 2024Rough Transformers for Continuous and Efficient Time-Series Modellingcited by 6
  12. 2024Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equationscited by 6
  13. 2025GST-UNet: A Neural Framework for Spatiotemporal Causal Inference with Time-Varying Confoundingcited by 5
  14. 2024Balanced Neural ODEs: nonlinear model order reduction and Koopman operator approximationscited by 4
  15. 2025Transformer-Based Spatial-Temporal Counterfactual Outcomes Estimationcited by 4
  16. 2025TrajSurv: Learning Continuous Latent Trajectories from Electronic Health Records for Trustworthy Survival Predictioncited by 4
  17. 2025Counterfactual Probabilistic Diffusion with Expert Modelscited by 4
  18. 2023On the Generalization and Approximation Capacities of Neural Controlled Differential Equationscited by 3
  19. 2024Uncertainty-Aware Optimal Treatment Selection for Clinical Time Seriescited by 3
  20. 2025Overlap-weighted orthogonal meta-learner for treatment effect estimation over timecited by 3
  21. 2022Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomescited by 2
  22. 2023Benchmarking Continuous Time Models for Predicting Multiple Sclerosis Progressioncited by 2
  23. 2023CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Predictioncited by 2
  24. 2023COSTAR: Improved Temporal Counterfactual Estimation with Self-Supervised Learningcited by 2
  25. 2025DeepBlip: Estimating Conditional Average Treatment Effects Over Timecited by 2
  26. 2026EHR-MPC: Inference-Time Control for Sepsis Treatment with Generative Patient Digital Twinscited by 2
  27. 2023Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventionscited by 1
  28. 2023A Counterfactual Fair Model for Longitudinal Electronic Health Records via Deconfoundercited by 1
  29. 2023A Foundational Framework and Methodology for Personalized Early and Timely Diagnosiscited by 1
  30. 2025Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Timecited by 1
  31. 2026Are LLMs Ready for Neural-integrated Mechanistic Modeling? A Benchmark and Agentic Frameworkcited by 1
  32. 2026Conservative Continuous-Time Treatment Optimizationcited by 1
  33. 2023Counterfactual Outcome Prediction using Structured State Space Modelcited by 0
  34. 2023Explainable History Distillation by Marked Temporal Point Processcited by 0
  35. 2024Spatio-Temporal Graphical Counterfactuals: An Overviewcited by 0
  36. 2025Time After Time: Deep-Q Effect Estimation for Interventions on When and What to docited by 0
  37. 2025An Orthogonal Learner for Individualized Outcomes in Markov Decision Processescited by 0
  38. 2025Counterfactual Forecasting for Panel Datacited by 0

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