mlsanityData to 7 Oct 2026

Predicting the impact of treatments over time with uncertainty aware neural differential equations

arXiv 2202.11987 ↗First posted 24 Feb 2022cs.LGcited by 23

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Abstract (arXiv)

Predicting the impact of treatments from observational data only still represents a majorchallenge despite recent significant advances in time series modeling. Treatment assignments are usually correlated with the predictors of the response, resulting in a lack of data support for counterfactual predictions and therefore in poor quality estimates. Developments in causal inference have lead to methods addressing this confounding by requiring a minimum level of overlap. However,overlap is difficult to assess and usually notsatisfied in practice. In this work, we propose Counterfactual ODE (CF-ODE), a novel method to predict the impact of treatments continuously over time using Neural Ordinary Differential Equations equipped with uncertainty estimates. This allows to specifically assess which treatment outcomes can be reliably predicted. We demonstrate over several longitudinal data sets that CF-ODE provides more accurate predictions and more reliable uncertainty estimates than previously available methods.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 21 of its 52 references that are in the map. First posted on arXiv 24 Feb 2022.

Builds on

21 of 52 references.

References · 21

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
  4. 2017Causal Effect Inference with Deep Latent-Variable Modelscited by 408
  5. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  6. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  7. 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 182
  8. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  9. 2020Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representationscited by 154
  10. 2020Identifying Causal-Effect Inference Failure with Uncertainty-Aware Modelscited by 57
  11. 2021Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confoundingcited by 50
  12. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
9 more
  1. 2020Bayesian Neural Ordinary Differential Equationscited by 44
  2. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  3. 2020Generative ODE Modeling with Known Unknownscited by 24
  4. 2020Neural Ordinary Differential Equations for Intervention Modelingcited by 19
  5. 2019Characterization of Overlap in Observational Studiescited by 15
  6. 2020Learning Partially Known Stochastic Dynamics with Empirical PAC Bayescited by 15
  7. 2021Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Seriescited by 14
  8. 2018Adaptive Path-Integral Autoencoder: Representation Learning and Planning for Dynamical Systemscited by 7
  9. 2018Deep Ensemble Tensor Factorization for Longitudinal Patient Trajectories Classificationcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 8; 2024: 6; 2025: 4; 2026: 3.

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  1. 2023Bayesian Neural Controlled Differential Equations for Treatment Effect Estimationcited by 26
  2. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 21
  3. 2023Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounderscited by 17
  4. 2023CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systemscited by 16
  5. 2023Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Timecited by 14
  6. 2025Uncertainty Quantification for Machine Learning in Healthcare: A Surveycited by 11
  7. 2024Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systemscited by 8
  8. 2025medDreamer: Model-Based Reinforcement Learning with Latent Imagination on Complex EHRs for Clinical Decision Supportcited by 8
  9. 2024Dynamical Survival Analysis with Controlled Latent Statescited by 7
  10. 2024Causal Contrastive Learning for Counterfactual Regression Over Timecited by 7
  11. 2022Deep Counterfactual Estimation with Categorical Background Variablescited by 5
  12. 2024Uncertainty-Aware Optimal Treatment Selection for Clinical Time Seriescited by 3
11 more
  1. 2023Anamnesic Neural Differential Equations with Orthogonal Polynomial Projectionscited by 2
  2. 2023CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Predictioncited by 2
  3. 2022Learning predictive checklists from continuous medical datacited by 1
  4. 2025multivariateGPT: a decoder-only transformer for multivariate categorical and numeric datacited by 1
  5. 2026Conservative Continuous-Time Treatment Optimizationcited by 1
  6. 2023GDBN: a Graph Neural Network Approach to Dynamic Bayesian Networkcited by 0
  7. 2023Continuous Time Evidential Distributions for Irregular Time Seriescited by 0
  8. 2024Learning Predictive Checklists with Probabilistic Logic Programmingcited by 0
  9. 2025Generative Modeling of Clinical Time Series via Latent Stochastic Differential Equationscited by 0
  10. 2026Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Timecited by 0
  11. 2026From Static Risk to Dynamic Trajectories: Toward World-Model-Inspired Clinical Predictioncited by 0