Causal Models and Interventions › Summary

• Causal models add intervention semantics to distributions. A structural causal model assigns variables generating rules. Under an explicit autonomy assumption, non-target rules remain fixed for the contemplated intervention; useful transfer requires that assumption to hold and the changed mechanism to be identifiable.
• Seeing is not doing. $P(Y \mid X)$ and $P(Y \mid \mathrm{do}(X))$ can differ because interventions replace the assignment mechanism. Logged models are confounded when omitted causes influence both policy assignment and outcomes; policy-generated data are not automatically confounded when sufficient history, exchangeability, and support hold.
• Counterfactuals need structure, not just statistics. Abduction–action–prediction supports per-episode "what if" reasoning, but only under strong assumptions about mechanisms and noise that distributions alone cannot certify. Two models can agree on everything observable, including all interventions, and still disagree on counterfactuals, so counterfactual outputs from learned models should be treated as diagnostics, not ground truth.
• Insufficient recorded state can create hidden confounding, but the concepts are not identical. Adjustment, experiments, instruments, proxies, sensitivity analysis, and partial-identification bounds address different failure modes. Conventional uncertainty estimates that omit confounding may fail, while sensitivity-aware or robust planners can sometimes act from bounded effects.
• Invariance and transportability support conditional transfer claims. An invariant relation is a causal candidate only relative to informative environments and target-mechanism assumptions. Localized sim-to-real repair further requires correct localization, autonomy, identifiability, and sufficient target data.
• Causal representation learning needs extra structure. Temporal processes, controlled interventions, multiple environments, auxiliary variables, and scientific experiments can all supply it. Action-conditioned latent dynamics may support planning over realizable actions without coordinate-wise causal latents; direct latent editing requires stronger intervention semantics.

The next chapter develops structured simulators, where some interventions can be implemented as edits to an explicit computational graph, alongside neural operators, which learn mappings between function spaces and are not intrinsically causal.