# Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders

arXiv: https://arxiv.org/abs/2303.02320 · HTML: https://mlsanity.com/paper/2303.02320/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 80 references that are in the map.
- First posted on arXiv 4 Mar 2023.

## Builds on (most cited first, 30 of 43)

- [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)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [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)
- [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)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Understanding and Improving Information Transfer in Multi-Task Learning](https://mlsanity.com/paper/2005.00944/) (2020)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [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)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (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)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [Spectral Temporal Graph Neural Network for Trajectory Prediction](https://mlsanity.com/paper/2106.02930/) (2021)
- [From Deterministic ODEs to Dynamic Structural Causal Models](https://mlsanity.com/paper/1608.08028/) (2016)
- [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)
- [DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting](https://mlsanity.com/paper/2203.07681/) (2022)
- [Sequential Deconfounding for Causal Inference with Unobserved Confounders](https://mlsanity.com/paper/2104.09323/) (2021)
- [Predicting the impact of treatments over time with uncertainty aware neural differential equations](https://mlsanity.com/paper/2202.11987/) (2022)

## Built on by (most cited first, 17 of 17)

- [TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Model](https://mlsanity.com/paper/2409.02322/) (2024)
- [MIRA: Medical Time Series Foundation Model for Real-World Health Data](https://mlsanity.com/paper/2506.07584/) (2025)
- [A Survey of Reasoning and Agentic Systems in Time Series with Large Language Models](https://mlsanity.com/paper/2509.11575/) (2025)
- [Improving Transferability for Cross-domain Trajectory Prediction via Neural Stochastic Differential Equation](https://mlsanity.com/paper/2312.15906/) (2023)
- [Instrumental Variable Estimation for Causal Inference in Longitudinal Data with Time-Dependent Latent Confounders](https://mlsanity.com/paper/2312.07175/) (2023)
- [TimeGraph: Synthetic Benchmark Datasets for Robust Time-Series Causal Discovery](https://mlsanity.com/paper/2506.01361/) (2025)
- [Right on Time: Revising Time Series Models by Constraining their Explanations](https://mlsanity.com/paper/2402.12921/) (2024)
- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Prediction](https://mlsanity.com/paper/2308.09735/) (2023)
- [COSTAR: Improved Temporal Counterfactual Estimation with Self-Supervised Learning](https://mlsanity.com/paper/2311.00886/) (2023)
- [An Empirical Examination of Balancing Strategy for Counterfactual Estimation on Time Series](https://mlsanity.com/paper/2408.08815/) (2024)
- [CSRA: Controlled Spectral Residual Augmentation for Robust Sepsis Prediction](https://mlsanity.com/paper/2604.14532/) (2026)
- [Leaning Time-Varying Instruments for Identifying Causal Effects in Time-Series Data](https://mlsanity.com/paper/2411.17774/) (2024)
- [Balanced Twins: Causal Inference on Time Series with Hidden Confounding](https://mlsanity.com/paper/2606.18969/) (2026)
- [Speaking Numbers to LLMs: Multi-Wavelet Number Embeddings for Time Series Forecasting](https://mlsanity.com/paper/2606.26487/) (2026)
- [Trustworthy Protein-Ligand Binding Affinity Prediction via Reliability-Aware Multi-Engine Fusion](https://mlsanity.com/paper/2607.17601/) (2026)

## Abstract (arXiv)

Causal analysis for time series data, in particular estimating individualized treatment effect (ITE), is a key task in many real-world applications, such as finance, retail, healthcare, etc. Real-world time series can include large-scale, irregular, and intermittent time series observations, raising significant challenges to existing work attempting to estimate treatment effects. Specifically, the existence of hidden confounders can lead to biased treatment estimates and complicate the causal inference process. In particular, anomaly hidden confounders which exceed the typical range can lead to high variance estimates. Moreover, in continuous time settings with irregular samples, it is challenging to directly handle the dynamics of causality. In this paper, we leverage recent advances in Lipschitz regularization and neural controlled differential equations (CDE) to develop an effective and scalable solution, namely LipCDE, to address the above challenges. LipCDE can directly model the dynamic causal relationships between historical data and outcomes with irregular samples by considering the boundary of hidden confounders given by Lipschitz-constrained neural networks. Furthermore, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate the effectiveness and scalability of LipCDE.