mlsanityData to 7 Oct 2026

Policy Analysis using Synthetic Controls in Continuous-Time

arXiv 2102.01577 ↗First posted 2 Feb 2021stat.ML cs.LGcited by 18

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Abstract (arXiv)

Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic controls expressed as linear combinations of observed control units. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations. This model is directly applicable to the general setting of irregularly-aligned multivariate time series and may be optimized in rich function spaces -- thereby improving on some limitations of existing approaches.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 14 of its 41 references that are in the map. First posted on arXiv 2 Feb 2021.

Builds on

14 of 41 references.

References · 14

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2015Continuous control with deep reinforcement learningcited by 3,279
  3. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  4. 2019Augmented Neural ODEscited by 396
  5. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  6. 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 182
  7. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  8. 2020Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representationscited by 154
  9. 2019Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noisecited by 98
  10. 2020SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimatescited by 75
  11. 2019Approximation Capabilities of Neural ODEs and Invertible Residual Networkscited by 56
  12. 2017An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controlscited by 36
2 more
  1. 2017Robust Synthetic Controlcited by 25
  2. 2018Dynamical systems theory for causal inference with application to synthetic control methodscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 4; 2023: 6; 2024: 2; 2025: 1; 2026: 1.

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  1. 2022Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equationscited by 59
  2. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  3. 2021Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamicscited by 46
  4. 2021Neural graphical modelling in continuous-time: consistency guarantees and algorithmscited by 42
  5. 2023Neural signature kernels as infinite-width-depth-limits of controlled ResNetscited by 25
  6. 2022Normalizing Flows for Interventional Density Estimationcited by 21
  7. 2024Trajectory Flow Matching with Applications to Clinical Time Series Modelingcited by 21
  8. 2022Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Mediacited by 20
  9. 2023Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounderscited by 17
  10. 2023CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systemscited by 16
  11. 2023Accounting For Informative Sampling When Learning to Forecast Treatment Outcomes Over Timecited by 14
  12. 2023New directions in the applications of rough path theorycited by 12
6 more
  1. 2024Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systemscited by 8
  2. 2022Towards Better Long-range Time Series Forecasting using Generative Forecastingcited by 3
  3. 2021Towards Better Long-range Time Series Forecasting using Generative Adversarial Networkscited by 0
  4. 2023Continuous time recurrent neural networks: overview and application to forecasting blood glucose in the intensive care unitcited by 0
  5. 2025FAME: Adaptive Functional Attention with Expert Routing for Function-on-Function Regressioncited by 0
  6. 2026Targeted Synthetic Control Methodcited by 0