# Observable Neural ODEs for Identifiable Causal Forecasting in Continuous Time

arXiv: https://arxiv.org/abs/2604.26070 · HTML: https://mlsanity.com/paper/2604.26070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 14 of 14)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Causal Modeling of Dynamical Systems](https://mlsanity.com/paper/1803.08784/) (2018)
- [Predicting the impact of treatments over time with uncertainty aware neural differential equations](https://mlsanity.com/paper/2202.11987/) (2022)
- [Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder](https://mlsanity.com/paper/2310.01937/) (2023)
- [G-Net: A Deep Learning Approach to G-computation for Counterfactual Outcome Prediction Under Dynamic Treatment Regimes](https://mlsanity.com/paper/2003.10551/) (2020)
- [IGC-Net for conditional average potential outcome estimation over time](https://mlsanity.com/paper/2405.21012/) (2024)
- [Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes](https://mlsanity.com/paper/2105.02088/) (2021)
- [Stabilized Neural Prediction of Potential Outcomes in Continuous Time](https://mlsanity.com/paper/2410.03514/) (2024)

## Abstract (arXiv)

Causal inference in continuous-time sequential decision problems is challenged by hidden confounding and partially observed states. We show that, under explicit structural assumptions, observability of the latent state enables identification of dynamic treatment effects through a continuous-time conditional front-door adjustment, even in the presence of hidden confounding. We derive a general adjustment formula and show that it reduces to a tractable state-space formula when unobserved contemporaneous disturbances are temporally uncorrelated. This formula expresses potential-outcome distributions under alternative treatment trajectories through the measurement model, latent dynamics, and the filtering distribution over latent states. We propose Observable Neural ODEs (ObsNODEs), Neural ODE models in observable normal form that implement this tractable adjustment for causal forecasting. ObsNODEs learn continuous-time dynamics with states reconstructible from observations, enabling outcome prediction under alternative treatment paths. Experiments on synthetic, semi-synthetic, and real-world clinical data demonstrate strong performance over recent sequence models, including external validation.