Correct and Optimal: The Regular Expression Inference Challenge

Abstract

In the medical field, treatment sequences significantly influence future outcomes through complex temporal interactions. Therefore, highlighting the role of temporal treatments within the model is crucial for accurate counterfactual estimation, which is often overlooked in current methods. To address this, we employ Koopman theory, known for its capability to model complex dynamic systems, and introduce a novel model named the Counterfactual Temporal Dynamics Network via Neural Koopman Operators (CTD-NKO). This model utilizes Koopman operators to encapsulate sequential treatment data, aiming to capture the causal dynamics within the system induced by temporal interactions between treatments. Moreover, CTD-NKO implements a weighting strategy that aligns joint and marginal distributions of the system state and the current treatment to mitigate time-varying confounding bias. This deviates from the balanced representation strategy employed by existing methods, as we demonstrate that such a strategy may suffer from the potential information loss of historical treatments. These designs allow CTD-NKO to exploit treatment information more thoroughly and effectively, resulting in superior performance on both synthetic and real-world datasets.