Causal Models and Interventions › Confounding: The Shadow of Unmodeled Common Causes

Because $C$ points into both $X$ and $Y$, variation in $C$ can create association along a backdoor path unrelated to the effect of $X$ on $Y$. The observational distribution alone need not reveal how much association comes from each path. In the linear additive worked example, covariance admits a direct closed-form decomposition; that two-term arithmetic is a property of the example, not of arbitrary nonlinear systems.

Confounding is one important way learned world models can be wrong in a systematic and exploitable way. In our opening example, the hidden heat load causes both the operators' cooling decisions and the temperature, so the learned association mixes the load's effect with cooling's effect. Unlike zero-mean sampling noise, this bias persists in the population regression and can give a planner a wrong gradient. Ensembles or pessimistic objectives may help when their uncertainty model spans the misspecification, but they do not automatically detect a shared confounding bias. Its size also depends on the behavior policy and action-noise distribution rather than being uniformly largest in the densest region.

Three facts about confounding are worth internalizing:

• It is not generally identifiable from one observational distribution alone. Distinct causal models can induce the same distribution of $(X,Y)$ while disagreeing about the effect of $X$ on $Y$. Distinguishing them requires assumptions, additional measured variables, multiple environments, temporal information, or interventional probes. In special model classes, observational constraints can still orient some edges, so the limitation should be read as non-identifiability in general rather than impossibility in every case.
• It can arise from insufficient recorded state. If a representation omits a common cause of action and outcome, adding a valid measured adjustment variable can close that backdoor. State insufficiency is broader: it can harm prediction or control without creating confounding, and causal identification may also fail through positivity, selection, or measurement error. Instruments, proxies, experiments, partial-identification bounds, and sensitivity analysis provide alternatives when the common cause cannot simply be measured.
• Interaction can remove or introduce selection dependence. Randomizing an action independently of relevant common causes breaks the behavior-policy backdoor for that randomized component. Merely adding stochasticity, including epsilon-greedy exploration, does not guarantee this if randomization probabilities still depend on hidden state or if support remains poor. A deterministic policy based on hidden state can create severe confounding, but its magnitude depends on the structural equations and noise. Designing safe, informative action randomization is therefore an experimental-design problem, not a universal dial with a guaranteed monotonic benefit.