Observational SHAP

Unlike interventional methods that break correlations by sampling from marginal distributions, Observational SHAP estimates missing features using the conditional expectation E[f(x) | x_S]. This means when a feature is 'absent' from a coalition, its value is inferred from the features that are present, preserving the joint distribution. This is critical for avoiding evaluations on impossible data points—like a 6-foot-tall individual weighing 50 pounds—that would never occur in reality.

By conditioning on observed values, this formulation explains the model's behavior on the natural data manifold. This answers the question: 'How does the model behave on real, correlated data?' rather than 'How would the model behave if we artificially randomized features?' This distinction is vital for auditing deployed models where features are inherently correlated—such as credit risk models where income, debt-to-income ratio, and loan amount move together.

Observational SHAP distributes credit among correlated features based on their statistical associations. If two features are highly correlated, the model may rely on either one, and SHAP values will reflect this shared importance. This is distinct from Interventional SHAP, which measures causal effects by forcing features to be independent. Choose Observational SHAP when you need to understand model behavior in the observational world; choose interventional methods when you need to estimate causal impacts.

Estimating E[f(x) | x_S] is computationally intensive because it requires modeling the conditional distribution of the held-out features given the in-coalition features. Exact computation is often intractable for high-dimensional data. Practical implementations use approximations such as:

• Gaussian copula models for continuous features
• K-nearest neighbors to estimate conditional expectations
• Variational autoencoders to learn the conditional density These trade-offs between accuracy and speed are a central design consideration.

A key advantage of Observational SHAP is avoiding model extrapolation. Interventional methods force the model to predict on feature combinations never seen during training—like a loan applicant with a credit score of 800 but zero income. The model's predictions on these synthetic points may be nonsensical, contaminating the SHAP values. Observational SHAP only evaluates the model on plausible, in-distribution data points, yielding more reliable and trustworthy attributions.

Observational SHAP satisfies the efficiency axiom (attributions sum to the prediction minus the baseline) but subtly reinterprets missingness. In the observational formulation, a 'missing' feature is not truly absent—it is imputed from observed features. This means the explanation is faithful to the model's behavior under the joint data distribution, but it may violate the interventional missingness property. Understanding this trade-off is essential for selecting the right SHAP variant for your use case.