Amortized Interventional Forecasting for Multivariate CIR Processes

Most benchmarks for causal inference over time series are observational, small, or domain-specific, leaving interventional and counterfactual estimation under-served exactly where it matters most, such as in healthcare, policy evaluation, and climate science. We introduce \textbf{DoTime}, an open, scalable, and theoretically grounded generator of multivariate temporal structural causal models (TSCMs) with interventions, released as the \code{dotime} PyPI package together with four frozen evaluation suites. Beyond existing work, it adds capabilities absent from prior generators: continuous-time intervention \emph{windows}, counterfactual sampling modes with a positivity guard, regime-switching SCMs as a strict generalization of interrupted time series, non-stationary dynamics by construction with switching SCM parameters, and deterministic ramp and sinusoidal intervention profiles that place trends and structural breaks \emph{inside} the evaluation window. Moreover, it demonstrates the suitability of the generator as a prior for a causal foundation model reference implementation. The released suites span a training-scale snapshot of $100{,}000$ trajectories and eight named identification structures, each with exact ground truth: paired interventional trajectories from the same SCM throughout, and shared-noise counterfactuals in the continuous-time suite. We ship reference baseline implementations with an evaluation harness, and pose a falsifiable claim: interventional training buys a measurable direction-accuracy advantage over an observational model of identical capacity. It is tested across three training seeds per arm. Under structure-matched evaluation on held-out episodes, the interventional prior-fitted network's (PFN) gap is positive in every structure, trajectory length, and seed tested.

Generative models for counterfactual outcomes have great potential to support decision-making under complex interventions, but existing approaches are limited by unstable estimation, poor generalization across environments, and bias from nuisance model misspecification. We introduce ADIGen, a framework for automatic, debiased, and invariant counterfactual generation under general interventions, including high-dimensional interventions and outcomes. ADIGen combines Riesz regression to avoid unstable density-ratio estimation, causal invariance to improve generalization under distribution shift, and orthogonal statistical learning to obtain doubly robust guarantees against nuisance model misspecification. We provide excess-risk bounds showing that ADIGen controls counterfactual risk under general interventions, with a product-bias nuisance remainder and an invariant risk bound across environments.

Estimating counterfactual outcomes over time from longitudinal observational data is central to clinical decision support. Existing methods rely on domain confusion -- adversarial training that renders representations invariant to treatment assignment -- yet this invariance creates a mutual information conflict: it suppresses treatment-correlated covariate signals necessary for accurate outcome prediction. We formalise this tension via a Jensen-Shannon divergence bound on counterfactual prediction error and develop two complementary models. CSSD (Causal State-Space model with Direct decoder) adapts selective State Space Models with a parallel multi-step decoder that eliminates accumulated rollout error by producing all prediction horizons simultaneously in a single forward pass. CSSPD (Causal State-Space model with Predictive regularisation and Direct decoder) augments CSSD with Contrastive Predictive Coding and Local Information Maximisation to reinforce temporal predictability in the balancing representation and recover local covariate information destroyed by domain confusion. On MIMIC-III, CSSPD achieves lower counterfactual RMSE than the Causal Transformer at every horizon tau >= 2 at O(T) encoder cost, with gains from 0.02 (2-step) to 0.07 (6-step). On Cancer Simulation across confounding strengths gamma in {0,1,2,3,4}, CSSPD outperforms CT at gamma <= 3 (margins 25.9%--37.0%), and CSSD achieves the lowest overall average RMSE (12.7% reduction over CT), confirming the MI conflict analysis. To our knowledge, this is the first work to formalise the balancing-prediction MI conflict and propose a structured resolution through complementary predictive and information-theoretic training objectives.