Identification and uncertainty propagation in continuous-time causal interventions

Establish explicit identification conditions for continuous-time causal intervention models, including formal overlap requirements and treatments of unmeasured confounding and partial observability; and develop a rigorous inferential framework that propagates uncertainty from counterfactual distribution generators through to policy evaluation for dynamic treatment regimes, with particular attention to local robustness and sensitivity analysis.

Background

In the book’s causal inference chapter, dynamic treatment regimes are framed as policies inducing counterfactual distributions, and generative flow models are proposed as flexible nuisance components for counterfactual generation while double/debiased machine learning provides inference for target parameters. The text then extends this perspective to continuous time, where interventions are described via controlled differential equations, and emphasizes that counterfactuals become trajectories under alternative controls.

While this unifies identification, transport, and inference conceptually, the authors explicitly note unresolved issues in continuous-time settings: the need to formalize identification assumptions—such as explicit overlap, handling of unmeasured confounding, and partial observability—and the need for a theory that carries counterfactual uncertainty through to policy evaluation with robustness guarantees. Addressing these would solidify the theoretical foundation for inference-aware continuous-time counterfactual generation and policy learning.

References

Open problems include making identification assumptions explicit in continuous-time settings (overlap, unmeasured confounding, partial observability) and developing theory that propagates counterfactual uncertainty into policy evaluation (local robustness, sensitivity analysis).

— Statistical Inference via Generative Models: Flow Matching and Causal Inference  (2603.09009 - Eguchi, 9 Mar 2026) in Section "From ATE/CATE to Dynamic Treatment Regimes" (Chapter "Causal Inference: Counterfactual Distributions and Double Robustness")

Developing CBO methods that explicitly model sensitivity to hidden confounding, for example, by propagating bounds on the causal effect under varying degrees of unmeasured confounding \citep{pearl2009causality}, is an important open direction.

— Causal Bayesian Optimization: Foundations, Methods, and Applications  (2609.24112 - Huang et al., 21 Sep 2026) in Section 6.1, paragraph “Hidden confounding”