Causal Attribution

The formal framework underlying causal attribution. An SCM defines a set of endogenous variables and exogenous noise variables connected by structural equations that represent causal mechanisms.

• Nodes: Represent variables in the system.
• Edges: Represent direct causal relationships, not just statistical dependence.
• Equations: Define how a variable's value is generated from its direct causes.

This allows the model to answer interventional queries (e.g., 'What happens to the prediction if we force this feature to a specific value?'), which purely statistical models cannot.

A key mathematical tool for causal attribution. The do-operator do(X=x) represents an intervention that sets a variable X to a value x, severing its incoming causal links.

• Observational: P(Y|X=x) — the probability of Y given we observe X=x.
• Interventional: P(Y|do(X=x)) — the probability of Y given we force X=x.

Causal attribution uses this distinction to compute the causal effect of a feature, isolating its direct influence on the prediction from confounding factors.

The ability to answer 'what if' questions about a specific instance. A counterfactual explanation identifies the minimal change to input features that would have changed the model's prediction.

• Example: 'If this patient's biomarker level had been 15% lower, the model would have predicted a negative diagnosis.'
• Mechanism: Uses the SCM to trace the outcome back through causal pathways, updating only the necessary variables while respecting causal constraints.

This is distinct from adversarial examples, as counterfactuals must respect the causal structure of the data-generating process.

Standard feature attribution methods like SHAP or LIME measure associational importance, which can be misleading when features are correlated.

• Associational: Identifies features that are predictive, including spurious correlates.
• Causal: Identifies features that are direct causes of the outcome.

Example: In a diagnostic model, 'yellow fingers' might be highly predictive of lung cancer (associational), but 'smoking' is the true cause. Causal attribution correctly assigns importance to smoking, not the spurious correlate.

A primary metric for quantifying causal attribution. The ACE measures the expected change in a model's output when a feature is intervened upon.

• Computation: ACE = E[Y|do(X=x_high)] - E[Y|do(X=x_low)]
• Purpose: Provides a single, interpretable number representing a feature's causal influence.

This metric is crucial for FDA submission teams needing to demonstrate that a diagnostic model relies on clinically valid, causal biomarkers rather than confounding variables.

Methods to learn the causal graph directly from observational data when a pre-defined SCM is unavailable.

• Constraint-based (e.g., PC algorithm): Uses conditional independence tests to infer causal structure.
• Score-based (e.g., GES): Searches for the graph that optimizes a goodness-of-fit score.
• Functional causal models (e.g., LiNGAM): Exploits non-Gaussianity or non-linearity to identify causal direction.

These algorithms are essential for biomarker identification where the true causal relationships between genes, proteins, and disease are unknown.

Quantitative measures that assess whether an explanation accurately reflects the model's true reasoning, rather than being a plausible but misleading narrative.

• Comprehensiveness: Does removing top-attributed features degrade prediction confidence?
• Sufficiency: Can the top-attributed features alone sustain the original prediction?
• Monotonicity: Does adding features with higher attribution monotonically increase confidence?
• Essential for FDA submission packages where explanation reliability must be demonstrated empirically

Estimates the confidence bounds around both predictions and their explanations. In causal attribution, this answers: How stable is this causal claim across model retraining or data perturbations?

• Aleatoric uncertainty: Irreducible noise in the biomarker measurements themselves
• Epistemic uncertainty: Model ignorance reducible with more training data
• Conformal prediction provides distribution-free prediction sets with coverage guarantees
• Critical for high-stakes diagnostics where overconfident causal claims can misdirect treatment