  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.
