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Causal analysis for time series data, in particular estimating individualizedtreatment effect (ITE), is a key task in many real-world applications, such asfinance, retail, healthcare, etc. Real-world time series can includelarge-scale, irregular, and intermittent time series observations, raisingsignificant challenges to existing work attempting to estimate treatmenteffects. Specifically, the existence of hidden confounders can lead to biasedtreatment estimates and complicate the causal inference process. In particular,anomaly hidden confounders which exceed the typical range can lead to highvariance estimates. Moreover, in continuous time settings with irregularsamples, it is challenging to directly handle the dynamics of causality. Inthis paper, we leverage recent advances in Lipschitz regularization and neuralcontrolled differential equations (CDE) to develop an effective and scalablesolution, namely LipCDE, to address the above challenges. LipCDE can directlymodel the dynamic causal relationships between historical data and outcomeswith irregular samples by considering the boundary of hidden confounders givenby Lipschitz-constrained neural networks. Furthermore, we conduct extensiveexperiments on both synthetic and real-world datasets to demonstrate theeffectiveness and scalability of LipCDE.

Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders