Jacobian-Regularized Causal Neural ODE for Counterfactual Time-Series Forecasting

Forecasting systems deployed in decision-making loops must answer counter factual questions—what would happen under an alternative treatment path— rather than purely associative ones, and must do so from observational data with time-varying confounding and irregular sampling. We propose CT-DCODE, a continuous-time deconfounded causal ODE that couples (i) treatment-driven Neural ODE latent dynamics, (ii) an explicit propensity/intensity model, (iii) dynamic representation balancing, and (iv) a sequential doubly robust risk, together with a Jacobian sparsity prior ∥∂fθ/∂z∥1 on the drift that biases the learned dynamics toward sparse instantaneous influences. We complement the method with a theoretical analysis of long-horizon counterfactual rollouts: error grows exponentially with horizon under merely Lipschitz (expansive) dynamics—and this is unavoidable in a minimax sense—but becomes horizon-uniform under contractive dynamics characterized by a negative Jacobian log-norm, motivating Jacobian based regularization. Empirically, on a unified benchmark of three counterfactual forecasting datasets (a TE-CDE-style tumor-growth simulator, semi-synthetic MIMIC-III, and IncomeSCM) with matched hyperparameter-search budgets, CT-DCODE attains strong factual accuracy and competitive counterfactual error against six published baselines (RMSN, CRN, Time Series Deconfounder, TE-CDE, Causal Transformer, G-Transformer), and remains markedly more stable than sequence baselines under multi-step counterfactual rollouts. Ablations under a fixed-hyperparameter, multi-seed protocol show that the contribution of individual deconfounding terms is dataset-dependent, which we report and discuss candidly.