# ODE Discovery for Longitudinal Heterogeneous Treatment Effects Inference

arXiv: https://arxiv.org/abs/2403.10766 · HTML: https://mlsanity.com/paper/2403.10766/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 93 references that are in the map.
- First posted on arXiv 16 Mar 2024.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (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)
- [Learning Long-Term Dependencies in Irregularly-Sampled Time Series](https://mlsanity.com/paper/2006.04418/) (2020)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach](https://mlsanity.com/paper/2105.04869/) (2021)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [Causal models for dynamical systems](https://mlsanity.com/paper/2001.06208/) (2020)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [Neural Laplace: Learning diverse classes of differential equations in the Laplace domain](https://mlsanity.com/paper/2206.04843/) (2022)
- [Counterfactual Temporal Point Processes](https://mlsanity.com/paper/2111.07603/) (2021)
- [Causal Deep Learning](https://mlsanity.com/paper/2303.02186/) (2023)
- [Neural Ordinary Differential Equations for Intervention Modeling](https://mlsanity.com/paper/2010.08304/) (2020)
- [Learning outside the Black-Box: The pursuit of interpretable models](https://mlsanity.com/paper/2011.08596/) (2020)
- [A Bayesian Nonparametric Approach for Estimating Individualized Treatment-Response Curves](https://mlsanity.com/paper/1608.05182/) (2016)
- [When and How to Lift the Lockdown? Global COVID-19 Scenario Analysis and Policy Assessment using Compartmental Gaussian Processes](https://mlsanity.com/paper/2005.08837/) (2020)
- [Neural Laplace Control for Continuous-time Delayed Systems](https://mlsanity.com/paper/2302.12604/) (2023)
- [Disentangled Counterfactual Recurrent Networks for Treatment Effect Inference over Time](https://mlsanity.com/paper/2112.03811/) (2021)
- [Estimating Conditional Average Treatment Effects with Missing Treatment Information](https://mlsanity.com/paper/2203.01422/) (2022)
- [MetaPhysiCa: OOD Robustness in Physics-informed Machine Learning](https://mlsanity.com/paper/2303.03181/) (2023)
- [Parametric Estimation of Ordinary Differential Equations with Orthogonality Conditions](https://mlsanity.com/paper/1410.7566/) (2014)
- [The additive hazard estimator is consistent for continuous-time marginal structural models](https://mlsanity.com/paper/1802.01946/) (2018)
- [Transfer Learning via ℓ1 Regularization](https://mlsanity.com/paper/2006.14845/) (2020)

## Built on by (most cited first, 12 of 12)

- [Discovering Preference Optimization Algorithms with and for Large Language Models](https://mlsanity.com/paper/2406.08414/) (2024)
- [Automatically Learning Hybrid Digital Twins of Dynamical Systems](https://mlsanity.com/paper/2410.23691/) (2024)
- [G-Transformer: Counterfactual Outcome Prediction under Dynamic and Time-varying Treatment Regimes](https://mlsanity.com/paper/2406.05504/) (2024)
- [G-Sim: Generative Simulations with Large Language Models and Gradient-Free Calibration](https://mlsanity.com/paper/2506.09272/) (2025)
- [No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs](https://mlsanity.com/paper/2501.18563/) (2025)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
- [Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time](https://mlsanity.com/paper/2507.07271/) (2025)
- [CAETC: Causal Autoencoding and Treatment Conditioning for Counterfactual Estimation over Time](https://mlsanity.com/paper/2603.11565/) (2026)
- [Conservative Continuous-Time Treatment Optimization](https://mlsanity.com/paper/2603.16789/) (2026)
- [Revolutionizing Clinical Trials: A Manifesto for AI-Driven Transformation](https://mlsanity.com/paper/2506.09102/) (2025)
- [Generative Modeling of Clinical Time Series via Latent Stochastic Differential Equations](https://mlsanity.com/paper/2511.16427/) (2025)
- [Robust SDE Parameter Estimation Under Missing Time Information Setting](https://mlsanity.com/paper/2601.20268/) (2026)

## Abstract (arXiv)

Inferring unbiased treatment effects has received widespread attention in the machine learning community. In recent years, our community has proposed numerous solutions in standard settings, high-dimensional treatment settings, and even longitudinal settings. While very diverse, the solution has mostly relied on neural networks for inference and simultaneous correction of assignment bias. New approaches typically build on top of previous approaches by proposing new (or refined) architectures and learning algorithms. However, the end result -- a neural-network-based inference machine -- remains unchallenged. In this paper, we introduce a different type of solution in the longitudinal setting: a closed-form ordinary differential equation (ODE). While we still rely on continuous optimization to learn an ODE, the resulting inference machine is no longer a neural network. Doing so yields several advantages such as interpretability, irregular sampling, and a different set of identification assumptions. Above all, we consider the introduction of a completely new type of solution to be our most important contribution as it may spark entirely new innovations in treatment effects in general. We facilitate this by formulating our contribution as a framework that can transform any ODE discovery method into a treatment effects method.