# Estimating Treatment Effects in Continuous Time with Hidden Confounders

arXiv: https://arxiv.org/abs/2302.09446 · HTML: https://mlsanity.com/paper/2302.09446/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 49 references that are in the map.
- First posted on arXiv 19 Feb 2023.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [Lipschitz Recurrent Neural Networks](https://mlsanity.com/paper/2006.12070/) (2020)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Learning Individual Causal Effects from Networked Observational Data](https://mlsanity.com/paper/1906.03485/) (2019)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Debiasing Concept-based Explanations with Causal Analysis](https://mlsanity.com/paper/2007.11500/) (2020)
- [Causal Inference with Noisy and Missing Covariates via Matrix Factorization](https://mlsanity.com/paper/1806.00811/) (2018)
- [Sequential Deconfounding for Causal Inference with Unobserved Confounders](https://mlsanity.com/paper/2104.09323/) (2021)
- [Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Media](https://mlsanity.com/paper/2210.07518/) (2022)
- [Invertible DenseNets with Concatenated LipSwish](https://mlsanity.com/paper/2102.02694/) (2021)
- [Deconfounding Temporal Autoencoder: Estimating Treatment Effects over Time Using Noisy Proxies](https://mlsanity.com/paper/2112.03013/) (2021)
- [AttDMM: An Attentive Deep Markov Model for Risk Scoring in Intensive Care Units](https://mlsanity.com/paper/2102.04702/) (2021)

## Built on by (most cited first, 3 of 3)

- [Causal Contrastive Learning for Counterfactual Regression Over Time](https://mlsanity.com/paper/2406.00535/) (2024)
- [An Empirical Examination of Balancing Strategy for Counterfactual Estimation on Time Series](https://mlsanity.com/paper/2408.08815/) (2024)
- [From Static Risk to Dynamic Trajectories: Toward World-Model-Inspired Clinical Prediction](https://mlsanity.com/paper/2605.16927/) (2026)

## Abstract (arXiv)

Estimating treatment effects plays a crucial role in causal inference, having many real-world applications like policy analysis and decision making. Nevertheless, estimating treatment effects in the longitudinal setting in the presence of hidden confounders remains an extremely challenging problem. Recently, there is a growing body of work attempting to obtain unbiased ITE estimates from time-dynamic observational data by ignoring the possible existence of hidden confounders. Additionally, many existing works handling hidden confounders are not applicable for continuous-time settings. In this paper, we extend the line of work focusing on deconfounding in the dynamic time setting in the presence of hidden confounders. We leverage recent advancements in neural differential equations to build a latent factor model using a stochastic controlled differential equation and Lipschitz constrained convolutional operation in order to continuously incorporate information about ongoing interventions and irregularly sampled observations. Experiments on both synthetic and real-world datasets highlight the promise of continuous time methods for estimating treatment effects in the presence of hidden confounders.