High-dimensional counterfactual analysis with latent neural differential equations

Counterfactual estimation is important in longitudinal data analysis, particularly in healthcare, where the goal is to infer how an observed patient trajectory would have evolved under an alternative intervention. This problem is especially challenging in real-world settings with longitudinal data, where measurements are typically high-dimensional and exhibit complex temporal structure. Although causal inference has been studied extensively, existing approaches are often tailored to low-dimensional data and do not naturally accommodate continuous-time dynamics. We address these limitations by proposing CLL-NODE, a Counterfactual analysis of high-dimensional Longitudinal data using Latent Neural ODE model. Our model parameterizes latent continuous-time dynamics as a function of treatment assignment and instance-level auxiliary covariates, enabling treatment and covariate dependent evolution while supporting flexible interpolation and extrapolation in time. To facilitate reliable counterfactual estimation, we introduce an adversarial regularization term that encourages treatment-invariant representations of the initial latent state. We evaluate CLL-NODE on multiple datasets and demonstrate competitive performance relative to strong deep-learning baselines for high-dimensional counterfactual modeling.