CAS: A Causal Attribution Score for Local and Global Explainable Artificial Intelligence

CAS: A Causal Attribution Score for Local and Global Explainable Artificial Intelligence

Summary

This paper introduces the Causal Attribution Score (CAS), a compact score architecture for causal explanation in explainable artificial intelligence (XAI). The authors argue that predictive explanation methods like LIME and SHAP attribute a model output, but they do not attribute an intervention effect on the real-world outcome. CAS addresses this by starting from an identified interventional coalition game, allocating the joint intervention contrast with causal Shapley contributions, and converting those raw outcome-scale effects into Local CAS, Signed Local CAS, and two complementary Global CAS summaries.

The paper states: "Predictive explanation methods attribute a model output; they do not, by themselves, attribute an intervention effect on the real-world outcome. We introduce the Causal Attribution Score (CAS), a compact score architecture for causal explanation. CAS starts from an identified interventional coalition game, allocates the joint intervention contrast with causal Shapley contributions and converts those raw outcome-scale effects into Local CAS, Signed Local CAS and two complementary Global CAS summaries. The innovation is not a new Shapley formula, but a local-to-global causal reporting layer with an explicit intervention target."

The core novelty is not a new Shapley value but the score layer built around a declared intervention game, which involves: (1) defining the causal quantity being explained; (2) allocating its joint intervention contrast in outcome units; (3) converting the allocation into comparable local scores; and (4) aggregating local scores into distinct global summaries. The paper emphasizes: "This separation is the central contribution. The score is meaningful only under a declared intervention set and standard causal identification assumptions: well-defined interventions, consistency, conditional exchangeability, positivity/joint support and an interference specification."

CAS Definitions

For a set of declared actionable concepts Q = 1,..., q, each action j has a baseline level a0j and a target level a1j. For coalition S ⊆ Q, the interventional game is defined as vx(S) = E[Y(a(S)) X = x], and the joint intervention contrast is ∆Q(x) = vx(Q) − vx(∅). The raw causal contribution uses the classical Shapley value applied to the interventional game: ϕC j(x) = Σ S⊆Qj [S!(q − S − 1)!/q!] [vx(S ∪ j) − vx(S)], with the property that Σ j ϕC j(x) = ∆Q(x).

Local CAS is defined as CASL(j)(x) = ϕC j(x) / Σ k ϕC k(x), which is the fraction of absolute causal mass assigned to action j, non-negative and summing to one. Signed Local CAS is CAS̃L(j)(x) = ϕC j(x) / Σ k ϕC k(x), with the property that Σ j CAS̃L(j)(x) = ∆Q(x) / A+(x) ∈ [−1, 1], exposing reinforcement or cancellation.

Two Global CAS summaries are provided: (1) CASG,inst(j) = E X[CASL(j)(X)], which gives every profile equal weight and answers which action is typically prominent across individuals; and (2) CASG,mass(j) = E X[ϕC j(X)] / Σ k E X[ϕC k(X)], which weights by causal-effect mass and answers which action accounts for the greatest absolute causal effect in the population. The paper notes: This distinction is necessary because an action may be modest but frequently important, or rare but very large.

The paper explains that under additivity, vx(S) = vx(∅) + Σ j∈S τj(x), CAS reduces to normalised conditional treatment effects: ϕC j(x) = τj(x) and CASL(j)(x) = τj(x) / Σ k τk(x). Its coalition-aware added value appears when the effect of one intervention depends on which other interventions are active.

Estimation and Feature-CAS

For empirical illustrations, the paper uses two datasets from the Python DoubleML package: the 401(k) sample (n = 9,915 observations, treatment = eligibility e401, outcome = net financial assets net tfa) and the Pennsylvania sample (n = 5,099 observations, treatment = treatment-group indicator tg, outcome = log unemployment duration inuidur1). Treatment effects are estimated with cross-fitting and an orthogonal augmented inverse-probability weighting (AIPW) score following double/debiased machine learning (DML).

For feature-level comparison with predictive XAI, the paper uses Feature-CAS, which explains the estimated treatment-effect surface, not the outcome prediction: τbi = bi + Σ j γij, where bi is the fold-specific TreeSHAP base value and γij is computed with TreeSHAP on the exact fold-specific CATE learner. The corresponding local and global feature scores are FCASL,j(xi) = γij / Σ k γik and FCASG,j = Eγj(X) / Σ k Eγk(X). These are effect-modifier attributions identifying which pre-treatment covariates explain heterogeneity in the estimated causal effect.

The paper emphasizes that Feature-CAS is deliberately not a direct instance of the interventional game: pre-treatment covariates are effect modifiers, not declared actions with baseline/target levels a0j, a1j. The comparison is intentionally between different explanation targets.

Results

In the known-truth benchmark with eight repeated primary-interaction simulations (n = 2,200 each, three actions), the mean Local CAS mean absolute error (MAE) was 0.107 for coalition-aware CAS, compared with 0.173 for one-at-a-time normalisation and 0.213 for a global normalised absolute average treatment effect (ATE) vector. The paired advantage over one-at-a-time normalisation increased from −0.003 under additivity to 0.091 under strong interactions. The paper states: "The paired Local CAS MAE reduction (one-at-a-time minus coalition-aware CAS) was 0.066 [0.057, 0.075] in the primary-interaction scenario and 0.091 [0.080, 0.103] under strong interactions. With interactions removed it was −0.003 [−0.010, 0.003], statistically indistinguishable from zero at this Monte Carlo resolution."

On both empirical DoubleML datasets, predictive SHAP/TreeSHAP rankings differed materially from Feature-CAS rankings of treatment-effect modifiers. In the 401(k) dataset, SHAP and TreeSHAP emphasised inc, pira and age, whereas Feature-CAS shifted mass toward inc, age and educ, with pira moving from predictive global rank 2 to Feature-CAS rank 7. In Pennsylvania, predictive explanations emphasised agelt35, black and agegt54, whereas Feature-CAS placed female, dep1 and lusd at the top, with dep1 moving from predictive global rank 13 to Feature-CAS rank 2 and being the leading local Feature-CAS modifier.

The paper concludes: These results isolate the added value of separating what predicts the outcome from what explains heterogeneity in an estimated causal effect.

What CAS Adds

The paper supports three narrow claims: (1) CAS changes the explained object—predictive SHAP/LIME answer what contributed to this prediction? while CAS answers how is an identified intervention effect allocated?; (2) Local and global causal importance are not interchangeable—Local CAS is a compositional explanation for one profile, Instance-Balanced Global CAS describes typical local prominence, and Effect-Mass Global CAS describes population causal mass; (3) Coalition awareness matters exactly when interactions matter—under additivity, CAS reduces to normalised CATEs, but under interaction, one-at-a-time effects omit coalition context.

The paper concludes: "CAS provides a minimal local-to-global language for causal attribution. It begins with a declared interventional target, preserves a raw outcome-scale causal allocation, then separates magnitude, sign, individual prominence and population effect mass. The framework deliberately collapses to normalised conditional treatment effects in additive settings and departs from them only when coalition context changes marginal effects."

Improvements to AI Systems Based on CAS:

1. Intervention-Aware Explanation Engine: Build an AI explanation module that, instead of explaining predictions, explains the causal effect of a user-specified intervention set (e.g., changing treatment from baseline to target level). The system would require the user to declare actionable concepts, their baseline/target levels, and causal identification assumptions (consistency, exchangeability, positivity). It then outputs Local CAS, Signed Local CAS, and Global CAS summaries, enabling stakeholders to ask how does intervening on these factors change the outcome for this specific profile? rather than why was this prediction made?

2. Coalition-Aware Effect Attribution for Decision Support: Enhance AI systems that recommend multi-action policies (e.g., medical treatment bundles, marketing campaigns) by using CAS's coalition game formulation. The system would compute Shapley contributions over the joint intervention contrast, capturing interaction effects where the impact of one action depends on others being active. This prevents the common error of summing one-at-a-time effects, which over- or under-estimates combined impact. The improved system can answer: If I apply actions A and B together, how much of the total effect is due to A given B is active?

3. Dual-Mode Explainability with Target Separation: Implement an AI system with two distinct explanation modes: (a) predictive mode (SHAP/LIME) for what drove this prediction? and (b) causal mode (CAS) for how does this intervention affect the outcome? The system would automatically flag when these two modes diverge, alerting users that features predicting outcomes are not necessarily the same as those driving treatment-effect heterogeneity. This prevents misleading reliance on predictive importance for causal decision-making.

4. Local-to-Global Causal Importance Dashboard: Create an AI monitoring system that tracks both Instance-Balanced Global CAS (typical local prominence across individuals) and Effect-Mass Global CAS (population-level absolute causal effect). The system would display both metrics side-by-side, enabling users to distinguish between this action is frequently important for many individuals versus this action has large effects for a few individuals. This is critical for resource allocation—e.g., targeting interventions where they matter most versus where they are most commonly relevant.

5. Effect-Modifier Attribution for Personalized Treatment: Improve AI systems that personalize treatments by using Feature-CAS to identify which pre-treatment covariates explain heterogeneity in estimated causal effects. The system would output a ranked list of effect modifiers (e.g., age, income) with local and global scores, allowing clinicians or policymakers to see which patient characteristics drive variation in treatment response—not just which features predict outcomes. This enables more precise subgroup targeting and adaptive treatment strategies.

6. Benchmark-Aware Causal Explanation Validator: Build an AI validation tool that, given a known ground-truth simulation (with interactions), automatically tests whether the explanation method (CAS vs. one-at-a-time vs. global ATE) recovers true causal contributions. The system would report mean absolute error and confidence intervals, flagging when coalition-aware CAS significantly outperforms simpler methods. This allows developers to verify that their explanation layer is correctly capturing interaction structure before deployment.

7. Causal Explanation API with Assumption Checks: Develop an AI service that, before computing CAS, automatically checks and reports whether the declared intervention set satisfies positivity, consistency, and no-interference assumptions. If assumptions are violated, the system refuses to output CAS and instead provides a diagnostic report. This prevents misuse of causal attributions in settings where identification fails, improving trustworthiness and scientific rigor in automated decision systems.