do-SHAP: Causal Attribution Framework

• do-SHAP is a causal attribution framework that computes average interventional effects using Shapley values within a Structural Causal Model.
• It utilizes exact computation via irreducible sets and frontier-reduction methods to efficiently collapse redundant coalition evaluations.
• Practical implementations leverage estimand-agnostic causal inference by training learned SCMs to estimate intervention queries without bespoke derivations.

do-SHAP, also called do-Shapley or causal Shapley values, is a causal attribution framework that explains the contribution of features to an outcome by averaging interventional effects across coalitions rather than relying on correlation, conditional dependence, or purely observational masking rules. In a Structural Causal Model (SCM), it assigns to each variable an average contribution to a target under interventions of the form $\mathrm{do}(S=\mathbf{x}_S)$, thereby interpreting feature relevance as a causal effect on the outcome for a specific instance (Witter et al., 6 Feb 2026). Recent work has developed both an exact computational theory based on irreducible sets and a practical estimation pipeline based on learned SCMs and estimand-agnostic causal inference, making do-SHAP substantially more usable on complex graphs than earlier estimand-specific workflows (Witter et al., 6 Feb 2026, Parafita et al., 24 Sep 2025).

1. Causal value function and Shapley construction

The defining object in do-SHAP is an interventional value function. In the SCM-based formulation, for a coalition $S \subseteq [d]$ one uses

$$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$

where the variables in $S$ are externally set to their observed values in the instance being explained (Witter et al., 6 Feb 2026). In the practical formulation for a sample $x$ and coalition $S \subseteq X$, the same idea is written as

$\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$

This replaces the masking semantics of standard SHAP with an explicitly causal query (Parafita et al., 24 Sep 2025).

The do-Shapley value for feature $i$ is then obtained by the usual Shapley averaging over marginal contributions: $$\phi_i = \sum_{S \subseteq [d] \setminus \{i\}} \big[\nu(S \cup \{i\}) - \nu(S)\big]\, p_{|S|}, \qquad p_\ell = \frac{1}{d}\binom{d-1}{\ell}^{-1}.$$ Equivalently, in the practical notation with $K$ variables,

$S \subseteq [d]$0

or

$S \subseteq [d]$1

Thus do-SHAP answers the question: on average over all coalitions, how much does intervening on a feature change the expected outcome causally (Witter et al., 6 Feb 2026, Parafita et al., 24 Sep 2025).

This causal semantics distinguishes do-SHAP from standard SHAP variants. The practical do-SHAP literature explicitly contrasts it with Marginal SHAP, which replaces missing features by draws from the marginal distribution and can generate unrealistic, out-of-support feature combinations, and with Conditional SHAP, which respects correlations but can introduce anti-causal effects (Parafita et al., 24 Sep 2025). A concrete illustration given in that literature is that conditioning on education can induce changes in age, which is physically impossible (Parafita et al., 24 Sep 2025).

2. Structural causal model setting and identifiability

The formal setting is an SCM with a causal graph, structural equations, and exogenous noise. One formulation assumes a DAG $S \subseteq [d]$2 over observed variables and latent confounders, with each observed node generated by

$S \subseteq [d]$3

Another writes the SCM as

$S \subseteq [d]$4

where $S \subseteq [d]$5 are measured variables, $S \subseteq [d]$6 includes exogenous noise and latent confounders, and

$S \subseteq [d]$7

Interventions are standard Pearl interventions: $S \subseteq [d]$8 replaces the structural assignment for $S \subseteq [d]$9 by the constant $$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$0 and removes incoming edges to $$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$1 (Witter et al., 6 Feb 2026, Parafita et al., 24 Sep 2025).

A central issue is identifiability. The exact-computation literature proves a strong reduction: $$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$2 Equivalently, non-parametric identifiability of do-Shapley values requires only the identification of interventional effects for the $$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$3 singleton coalitions, rather than all classes (Witter et al., 6 Feb 2026). The practical consequence is that one can screen identifiability by checking only singleton interventions instead of all coalitions.

This result is conceptually important because naive do-SHAP appears to require causal identification for exponentially many coalition queries. The singleton reduction shows that the identifiability burden is much smaller than the combinatorial form of the Shapley sum initially suggests (Witter et al., 6 Feb 2026).

3. Exact computation via irreducible sets

The principal algorithmic advance in exact do-SHAP computation is a reformulation in terms of irreducible sets or causal equivalence classes. For a coalition $$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$4, the basis is

$$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$5

and the closure is

$$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$6

A set is irreducible if it is equal to its basis (Witter et al., 6 Feb 2026).

These objects induce equivalence classes of coalitions. If $$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$7, then

$$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$8

Hence the powerset $$\nu(S) = \mathbb{E}[Y \mid \mathrm{do}(S=\mathbf{x}_S)],$$9 is partitioned into classes $S$0, where $S$1 is the number of irreducible sets. The do-Shapley value can then be rewritten as

$S$2

with class weights computed from the basis and closure of each class (Witter et al., 6 Feb 2026).

The computational gain is that exact computation depends on $S$3, not on $S$4. The number of irreducible sets is graph-dependent and can vary from $S$5 to $S$6. The exact algorithm is proved to run in

$S$7

where $S$8 is the number of edges in the causal graph and $S$9 is the time to query $x$0 once (Witter et al., 6 Feb 2026). This is linear in the number of classes rather than exponential in the number of features.

The same work also introduces a fixed-budget estimator based on a boundary sampler. It explores the lattice of classes rather than sampling coalitions blindly, discovers $x$1 distinct classes with a budget of $x$2 queries, runs in

$x$3

and returns the Shapley values up to machine precision when the budget reaches $x$4 (Witter et al., 6 Feb 2026). The sharp distinction between the number of coalitions and the number of causal classes is one of the defining computational insights of modern do-SHAP.

4. Practical do-SHAP with estimand-agnostic causal inference

A separate line of work addresses a different bottleneck: the original estimand-based workflow. In that setting, each query $x$5 requires deriving an estimand and fitting models for the terms in that estimand, which becomes cumbersome when repeated for up to $x$6 coalitions (Parafita et al., 24 Sep 2025).

The proposed alternative is estimand-agnostic causal inference. Instead of deriving a bespoke observational formula for each coalition, one trains a proxy SCM $x$7 with the same graph $x$8 to fit the observational distribution $x$9. Then, for any identifiable query, one estimates it directly by sampling from the learned SCM, applying the intervention inside the SCM, and averaging the resulting outcomes (Parafita et al., 24 Sep 2025). In this formulation, one learned causal model answers all identifiable coalition queries without requiring a separate estimand derivation for each of them.

To reduce the number of coalition evaluations, this work introduces the Frontier-Reducibility Algorithm (FRA). FRA exploits two causal facts. First, if a feature $S \subseteq X$0 is not an ancestor of the target $S \subseteq X$1, then

$S \subseteq X$2

Second, if a set $S \subseteq X$3 is a frontier between $S \subseteq X$4 and $S \subseteq X$5—that is, $S \subseteq X$6 and every directed path from $S \subseteq X$7 to $S \subseteq X$8 is blocked by some node in $S \subseteq X$9—then

$\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$0

Thus the presence of $\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$1 is causally redundant once the frontier is fixed (Parafita et al., 24 Sep 2025).

The key theorem used by FRA states that for a coalition $\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$2, if

$\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$3

then

$\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$4

and $\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$5 is irreducible (Parafita et al., 24 Sep 2025). In effect, multiple superfluous variables can be removed at once, and many coalitions collapse to the same reduced representative. FRA does not change the exponential worst-case complexity of exact do-SHAP, but it substantially reduces redundant evaluations in practice and is reported to add negligible overhead (Parafita et al., 24 Sep 2025).

The same practical framework also addresses inaccessible data-generating processes. Under an additive noise model with no latent confounders into $\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$6,

$\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$7

the noise variable can be treated as an extra player, with

$\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$8

Practically, one approximates $\nu_x(S) := \mathbb{E}[Y \mid do(S=s)].$9 with a fitted model $i$0 and defines

$i$1

This yields a decomposition that attributes the unexplained part of the realized outcome to the noise term (Parafita et al., 24 Sep 2025).

5. Relation to neighboring SHAP formalisms

The term “do-SHAP” is frequently conflated with several adjacent but distinct lines of SHAP research.

Conditional SHAP is not do-SHAP. A conditional expectation network has been proposed to compute the conditional value function

$i$2

efficiently via a masked surrogate neural network, precisely to preserve feature dependence (Richman et al., 2023). This is a conditional-expectation construction, not an intervention-based one.

Trustable SHAP is also not do-SHAP. One line of work argues that failures of standard SHAP arise from the characteristic function

$i$3

and proposes alternative Shapley-compatible characteristic functions $i$4, $i$5, $i$6, and $i$7 based on prediction similarity and AXp/CXp logic (Letoffe et al., 2024). It does not define do-SHAP and is described as orthogonal to the causal/interventional literature.

Marginal SHAP with a causal reading is not, by itself, formal do-SHAP. Statistical inference work on SHAP power summaries explicitly states that it uses the model-agnostic marginal SHAP definition and that the only place where “do” appears is a conceptual remark about marginal SHAP having a causal interpretation as a do-operation in Pearl’s sense; it does not define a do-SHAP functional or estimator (Whitehouse et al., 11 Feb 2026).

Interventional SHAP on extended support is adjacent but distinct. A theoretical safe-feature-removal result shows that if SHAP vanishes on the product-of-marginals extended support, then a feature can be safely discarded on that support, and the paper describes this as a core “do-SHAP” style result (Bhattacharjee et al., 29 Mar 2025). This suggests a close connection to intervention-like semantics, but the construction is framed as a soundness result for aggregate SHAP rather than as the SCM-based do-Shapley formalism.

Tensor-network SHAP and interaction tensor SHAP operate on interventional or marginal value functions, and one tensor-network paper explicitly introduces a tensorized “do operator” in the construction of the value tensor (Marzouk et al., 24 Oct 2025). Yet these works concern exact SHAP and higher-order interaction computation under Tensor Train structure, not the SCM-based do-Shapley framework itself (Marzouk et al., 24 Oct 2025, Hasegawa et al., 5 Dec 2025).

Privacy-preserving SHAP regularization is conceptually related only in the sense that it targets the explanation output itself. A privacy paper explicitly notes that its method is “not a do-SHAP algorithm in the causal/interventional sense”; it regularizes SHAP attribution entropy to reduce leakage while retaining interpretability (Sharma et al., 12 Nov 2025).

These distinctions matter because “do-SHAP” is not a generic label for any SHAP variant with interventional language. In the strict sense developed in recent causal-XAI work, it denotes Shapley values of a genuinely interventional SCM value function (Witter et al., 6 Feb 2026, Parafita et al., 24 Sep 2025).

6. Limitations, caveats, and current research directions

Current do-SHAP methods retain several limitations. Exact do-Shapley computation is still exponential in the worst case because the number of irreducible sets can be $i$8 (Witter et al., 6 Feb 2026). FRA reduces redundancy but does not alter that worst-case complexity (Parafita et al., 24 Sep 2025). Practical deployment also requires a known causal graph and identifiable intervention queries (Parafita et al., 24 Sep 2025).

The quality of practical do-SHAP depends on the quality of the learned SCM. In the estimand-agnostic framework, better fit to the observational distribution correlates with better do-SHAP estimation, and model class matters: linear SCMs perform worst on the reported synthetic experiments, while more expressive causal generative models perform better (Parafita et al., 24 Sep 2025). This suggests that do-SHAP inherits not only the conceptual strengths of causal modeling but also its model-misspecification risks.

A further caveat is that do-SHAP is population-interventional rather than a full counterfactual explanation. The practical literature addresses this partly by introducing an explicit noise-player attribution under additive noise models, but that construction relies on specific structural assumptions (Parafita et al., 24 Sep 2025).

At the same time, the recent literature indicates a convergence of themes around causal semantics, tractable computation, and explanation reliability. Exact computation via irreducible classes reduces the combinatorial burden (Witter et al., 6 Feb 2026). Estimand-agnostic SCM inference removes the need for per-query symbolic derivations (Parafita et al., 24 Sep 2025). Adjacent work on extended support, tensorized interventional operators, and trustability criteria suggests a broader shift toward explanations whose semantics are explicit rather than implicit (Bhattacharjee et al., 29 Mar 2025, Marzouk et al., 24 Oct 2025, Letoffe et al., 2024).

In that sense, do-SHAP is best understood not as a minor variant of SHAP, but as a distinct causal attribution program: it replaces observational masking rules with SCM interventions, interprets feature relevance as an average causal effect across coalitions, and exploits graph structure to make that program computationally and statistically feasible in nontrivial settings (Witter et al., 6 Feb 2026, Parafita et al., 24 Sep 2025).