Causal SHAP: Feature Attribution with Dependency Awareness through Causal Discovery

Li Rong Wang; Siyuan Liu; Woon Yee Ng; Xiuyi Fan

REVIEW 5 major objections 6 minor 32 references

Causal SHAP: Feature Attribution with Dependency Awareness through Causal Discovery

T0 review · 5 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Causal SHAP reweights feature attributions by total causal effect, so merely correlated features fall to zero while SHAP's properties hold.

desk verdict Causal SHAP is a plausible pipeline idea but the theoretical claims are overstated, the real-world gains are within noise, and the IDA path-product step double-counts mediated effects. read the letter →

arxiv 2509.00846 v1 pith:OPPL3SKX submitted 2025-08-31 cs.LG cs.AIstat.ME

Woon Yee Ng , Li Rong Wang , Siyuan Liu , Xiuyi Fan This is my paper

classification cs.LGcs.AIstat.ME

keywords SHAPfeatureattributioncausaldiscoveryPCalgorithmIDAexplainableAIvaluefunctionintervention

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes Causal SHAP, an attribution method that grafts causal discovery and causal-strength estimation onto SHAP. Its central claim is that weighting each feature's Shapley sum by the total causal effect of that feature on the target—rather than by raw correlation—reduces the attribution of features that are only correlated with the prediction, and can zero them out entirely. The paper defines a causal value function that samples out-of-coalition features from parent-conditioned distributions, and a normalization step that keeps attributions additive. It proves that local accuracy, missingness, and consistency survive the modification, and supports the claim with synthetic graphs and biomedical insertion tests. If the claim is right, model explanations can track true causes without requiring a human-supplied causal graph.

What carries the argument

The workhorse is the causal weight factor γ_i = |W_i| / Σ_j |W_j|, a normalized total causal effect that multiplies each feature's Shapley term in Eq. 10. W_i is built by summing, over all simple directed paths from feature i to the target, the products of IDA edge weights along each path (Eqs. 7–8); IDA supplies those edge weights from the CPDAG learned by the PC algorithm. The companion mechanism is the causal value function v_c(S) in Eq. 4, which samples non-intervened features according to their parent-conditioned distributions (Eqs. 5–6) rather than marginal distributions, preventing the generation of impossible data points. Together these two pieces zero out features with no causal pat

What would settle it

Simulate a known chain X→Z→Y and add an unobserved confounder H that also affects both X and Y. Run Causal SHAP with H excluded from the features; if X's attribution does not shrink relative to the confounder-free version of the same data, the method has credited a non-causal correlation.

Watch

Extended reading notes

Core claim

Causal SHAP claims a two-step modification of SHAP that makes attribution depend on causal structure rather than correlation. First, it replaces SHAP's interventional value function with a causal value function v_c(S) (Eq. 4) that samples out-of-coalition features from distributions conditioned on their parents in a causal graph, so impossible feature combinations are not generated. Second, it rescales the Shapley summation weight for feature i by a causal weight γ_i = |W_i| / Σ_j |W_j|, where W_i is the total causal effect of feature i on the target, computed as the sum over directed paths of products of IDA edge weights (Eqs. 7–9). A final normalization (Eq. 11) forces the attributions to

Load-bearing premise

The load-bearing premise is that the causal graph learned from the same observational data used to train the model is the true causal graph, with no hidden common causes; the paper states this assumption explicitly in Section VII.

Editorial extensions

If this is right

A feature with no directed causal path to the target receives an attribution of exactly zero, no matter how strongly it correlates with the prediction.
Attribution magnitudes are proportional to causal path strength, so a mediator is credited only for the causal influence it actually transmits.
Explanations stay additive after normalization: attributions always sum to f(x) − E[f(X)], preserving SHAP's local accuracy.
The whole pipeline runs from observational data without a domain-expert graph, using PC for structure and IDA for edge weights.
On the real-world insertion-test evaluations reported, the causal reweighting matches or improves over prior SHAP variants that assume a known graph.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Inference: the same γ_i reweighting could be applied to any additive explanation method, not just SHAP; the paper does not explore this.
Inference: because W_i is a sum of products of linear-regression edge weights, on strongly nonlinear data the total-effect estimate may miss interactions; a testable extension is to compare against nonparametric effect estimation.
Inference: the paper's stated future direction of replacing PC with FCI would also make Causal SHAP testable under hidden confounding, and would directly address the assumption flagged in Section VII.
Inference: a practical diagnostic for deployment would be to bootstrap PC and IDA stability and report attribution variance across resampled graphs, something the paper does not do.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's my take. The paper's central idea—use PC to get a graph, IDA to get causal strengths, and a gamma-weighted Shapley sum with a graph-conditional value function—does appear to be new relative to the cited work. Existing causal SHAP variants assume an expert graph; this one tries to automate it. The synthetic experiments are clean and show the intended behavior: non-causal features get zero attribution. That construction works, because Eq. 9 forces gamma_i=0 for isolated features.

The soft spots are not minor. First, the missingness theorem (V.2) is mislabeled: it proves that features without a causal path get zero attribution, which is a causal prior, not the SHAP missingness axiom. And the 'zero for drink coffee' result is wired in by gamma, not learned.

Second, the path-product step in Eqs. 7-8 has a genuine flaw. IDA returns total causal effects, not path-specific direct effects. For a linear model with X->Y and X->M->Y, IDA gives total effect a+bc on edge X->Y, and then the path X->M->Y adds bc again, so the sum is a+2bc. This biases gamma_i for any feature with both direct and mediated paths. The stress-test note is right; I checked the math. This is internal to the method, not a causal discovery limitation.

Third, the consistency claim doesn't survive normalization: Eq. 11 scales by the sum of phi^c, which can change between models, so monotonicity in the unnormalized values doesn't carry over. The paper's assertion that it's 'easy to see' is hand-wavy.

Fourth, the real-world insertion scores in Table III are all within one standard deviation of baseline. The claimed best AUROC on IBS is 0.8594 versus On Manifold's 0.8589; that's noise. So the empirical case for 'superior' isn't there.

Also, the RMSE numbers in Table II don't match the attributions shown, and there's no code or data to check.

What the paper does well: it identifies a real gap, is upfront about the causal sufficiency assumption, and the synthetic setup is easy to follow. The idea is worth someone's time to fix.

Bottom line: not citable as is, but the combination is a legitimate contribution to the causal XAI discussion. If a referee reviews it, they should require: fix the path-product definition (use direct effects, or change the aggregation), restate the theorems honestly, drop the real-world claims, and release code/data. Recommendation: send to peer review with major revision.

Referee Report

5 major / 6 minor

Summary. The paper proposes Causal SHAP, a feature-attribution method that combines the PC algorithm for causal discovery, IDA for causal effect estimation, and Shapley values. It defines a causal value function that samples non-coalition features from the post-intervention distribution implied by the discovered graph, computes per-feature causal weights gamma_i from path-summed IDA effects, multiplies the Shapley sum by these weights, and then normalizes to restore local accuracy. The authors claim the resulting attributions reduce scores of merely correlated features while preserving local accuracy, missingness, and consistency, and report experiments on two synthetic and two biomedical datasets.

Significance. If the method worked as claimed, it would offer a practical way to add causal awareness to SHAP without requiring a hand-specified graph, and the synthetic designs (linear mechanisms with known ground truth) are well suited to exposing failures of correlation-based SHAP. The paper is clearly organized and contains a concrete algorithm. However, the current theoretical foundations have serious gaps: the path-product computation of W_i is not a valid total causal effect, the missingness and consistency claims are not established for the normalized values actually used, and the experimental 'validation' of zero attribution for non-causal correlates is largely built into the construction. These issues are fixable but affect the paper's main claims.

major comments (5)

[§IV.B, Eqs. (7)-(8)] The definition of W_i as the sum over simple paths of products of IDA edge weights is not a correct total causal effect. In standard IDA/pcalg usage, each w_jk is the total causal effect of j on k, which already includes mediated paths. Multiplying along paths and summing re-adds the same indirect contributions. For example, in the linear SEM X->Y (effect a), X->M (effect b), M->Y (effect c), IDA returns w_XY = a+bc, w_XM = b, and w_MY = c; Eq. (8) gives W_X = (a+bc) + bc = a+2bc instead of the true total effect a+bc. The normalization in Eq. (11) then propagates this bias to all features. This failure occurs even with a perfectly recovered DAG and no hidden variables, so it is not merely a causal-discovery limitation. Please either define w_jk as direct path coefficients from a fitted structural equation model, or set W_i directly to IDA's estimate of the total effect of feature i on th
[§V, Theorem V.2] Theorem V.2 does not prove the SHAP missingness axiom. It proves only that if W_i = 0 then gamma_i = 0, and since Eq. (10) multiplies every term by gamma_i, phi^c_i = 0. This is true by construction and is independent of the model f. A feature with no causal path but strong predictive correlation is precisely the case the method is designed to zero out, so presenting this as empirical or axiomatic support is circular. The standard missingness property (a feature missing from the instance receives zero attribution) is never addressed. Please state exactly which property is proved and either prove the actual missingness axiom or remove the claim that it is preserved.
[§V, Theorem V.3] The consistency proof covers only the unnormalized phi^c_i, and the final note claiming the result 'is easy to see' for phi^n_i is false. The normalization factor in Eq. (11) depends on f(x)-E[f(X)] and on the sum of phi^c_j, so it is different for two models f and f'. A larger phi^c_i before normalization can be scaled down below a smaller value from another model. Concretely, with n=2, gamma=(1,0), phi^c(f)=(1,0), phi^c(f')=(2,0), and f(x)-E[f(X)]=1 for both models, normalization gives phi^n(f)=phi^n(f')=(1,0), violating the strict inequality required by consistency. Thus consistency cannot be claimed for the normalized values used in the experiments. The statement and proof need to be revised, or the consistency claim restricted to the unnormalized variant.
[§IV.B and footnote 1] The method requires a topological order for the causal-value-function sampler (Eq. (6), Algorithm 1) and directed paths for Eq. (8), but PC outputs a CPDAG with undirected edges. The paper never specifies how a single DAG is chosen from the equivalence class, how the topological order is produced, or whether the path set P_i is taken from one DAG or averaged over all DAGs in the IDA output. This ambiguity affects the sampled distribution and every W_i, and it makes the method irreproducible. Please specify the resolution rule and implementation details.
[§VI.A, Table II] The synthetic results are presented as evidence that Causal SHAP 'correctly attributes zero' to drink coffee and mental health, but this outcome is forced by gamma_i = 0 in Eqs. (9)-(10) and does not depend on the model or the data. The RMSE comparison is also hard to interpret because the 'Ground Truth' column is never defined. For the lung-cancer data the generating coefficients are (2,1.2), yet the reported ground truth is (5.2171,0.2507), and the description of a 'reduced feature set' does not explain how these values were computed. Please define the ground-truth attribution explicitly and separate validation of the causal-discovery step from validation of the attribution formula. As reported, the experiments cannot distinguish the proposed method from a trivial rule that zeros out every feature without a causal path to the target.

minor comments (6)

[§IV.B, Eq. (4)] The notation X_barS ~ Pr(X_barS | do(X_S = x_S)) is informal; the do-operator should be applied to the distribution, e.g., P(X_barS | do(X_S = x_S)). Please clarify.
[§IV.B, Eq. (11)] The normalization is undefined if sum_j phi^c_j = 0. Please state how this case is handled or add a small epsilon/fallback.
[Algorithm 1] Uniform subset sampling with updates for all i not in S estimates (1/2^n) times the exact sum in Eq. (10), not the exact sum itself. Because the factor is common to all features, the normalized values are unaffected, but the text should state this to avoid confusion about the estimator.
[§V, Theorem V.3] The theorem uses both n and M for the number of features. Use one symbol consistently.
[§VI.B, Table III] The improvement over baselines is small (e.g., IBS AUROC 0.8594 vs 0.8589 for On Manifold) and no significance tests or confidence intervals are reported. The claim of 'superior performance' should be tempered.
[General] Minor typographical errors: 'cof f ee' in Eq. (17), 'ASV ,' in Section II, and inconsistent spacing in the references. These do not affect the substance.

Circularity Check

2 steps flagged · score 6.0 of 10

The headline qualitative result — zero attribution for correlated non-causal features — is built into Eq. 9–10; Theorem V.2 restates the construction, and the synthetic 'validation' is a self-consistency check.

self definitional [Section V, Theorem V.2 (with Eq. 9 and Eq. 10)]
"If i has no path to the target variable in G, then ϕc_i = 0. Proof. This follows from two cases. Firstly, if i /∈ V , then by definition Wi = 0 and thus γi = |Wi|/Σ |Wj| = 0. Secondly, if i has no path to the target, then |Wi| = 0 as there is no causal effect, again leading to γi = 0. In both cases, ϕc_i = 0."

The 'missingness' theorem is not derived from SHAP properties; it is a direct restatement of the definition of γi. In Eq. 10, every Shapley kernel is multiplied by γi, so setting Wi=0 forces ϕc_i=0 for any model f. Thus the property is an input of the construction, not an output of the derivation.
fitted input called prediction [Section VI.A.1, Figure 6 caption and Table II]
"In Figure 5, we observe that Causal SHAP attributes a zero SHAP score to drink coffee in accordance with the causal graph. ... drink coffee in Causal SHAP is correctly attributed zero score as it is not affecting Lung Cancer Risk"

The zero attribution for 'drink coffee' is forced by the method: the synthetic data-generating equation (17) gives drink coffee no causal path to lung cancer, PC is expected to recover that structure, IDA then returns W_drink=0, and Eq. 9–10 set the attribution to zero regardless of the model f or the value function. Presenting this as an experimental 'validation' of the central claim is a self-consistency check of the construction, not an empirical discovery.

full rationale

The paper contains no load-bearing self-citations; PC and IDA are external algorithms. The real-world insertion-test comparisons are self-contained against external benchmarks. However, the core qualitative claim — that Causal SHAP 'reduces attribution scores for features that are merely correlated with the target' — is definitional: Eq. 9 defines γi from IDA total effects, and Eq. 10 multiplies every Shapley contribution by γi. Any feature with zero estimated causal effect automatically receives zero attribution, and any feature with small causal effect is automatically down-weighted. Theorem V.2 (Missingness) is therefore a tautology, and the synthetic 'drink coffee' result is a direct consequence of the weighting scheme. The double-counting concern about Eq. 7–8 (using IDA total effects as edge weights) is a correctness flaw, not an additional circularity, so it is not counted here. Overall, the partial circularity is in the presentation of a built-in design property as a validated finding, giving a score of 6.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the causal discovery being correct (causal sufficiency, faithfulness), on linear-Gaussian mechanisms in the value-function sampler, on the linear path-product formula for total effects, and on a DAG that PC does not actually output. Free parameters include the IDA-derived causal weights γi, the normalization scalar, the OLS sampler parameters, and unreported PC/IDA settings. No invented entities.

free parameters (5)

causal weight factor γi (Eq. 9) = derived from IDA total effects Wi on the training data (e.g., zero for drink coffee and mental health in the synthetic s
γi = |Wi| / Σj |Wj| is estimated from data and directly forces zero attribution for features with no estimated causal path; it is the main vehicle of the claimed causal behavior.
normalization factor in Eq. 11 = per-instance scalar (f(x) - E[f(X)]) / Σj φc_j
Chosen to enforce local accuracy; it is not bounded, can be negative or undefined when the denominator approaches zero, and no constraints on it are analyzed.
conditional sampler parameters µi, σi (Eq. 6) = OLS estimates from parent regressions on the same data
The causal value function samples out-of-coalition features as N(µi, σi); for non-Gaussian or nonlinear mechanisms this is a misspecified approximation whose effect on attributions is unexamined.
PC significance level α = not reported
Controls edge removals in PC; with no reported value, the discovered graph for IBS (31 features, 294 samples) is not reproducible and sensitivity of the results to α is untested.
IDA edge weights wjk (Eq. 7) = not reported
The paper describes IDA as estimating effects of an intervention on a target, but Eq. 7 consumes per-edge weights; the mapping from IDA's output to wjk is not specified, and no fitted weights are reported.

assumptions (6)

domain assumption Causal sufficiency: no hidden/common causes among the features
Stated in Section VII: PC is used 'under the assumption that no hidden variables influence the dataset'. If violated, PC's skeleton and orientations can be wrong and every downstream attribution inherits the error.
standard math Faithfulness and causal Markov condition of the joint distribution
PC's correctness relies on these; invoked implicitly when the paper treats the PC output in Fig. 5 as the causal graph (Sections IV-B and VI-B-1).
domain assumption Linear Gaussian conditional mechanisms for out-of-coalition sampling (Eq. 6)
vc(S) samples non-intervened features as N(µi, σi) from linear regressions on parents; exact for linear Gaussian SEMs, but the synthetic cardiovascular data includes a uniform feature and the real data are not validated to be linear Gaussian.
domain assumption Linear path-product decomposition of total causal effects (Eq. 7)
The total effect of feature i on the target is taken as the sum over simple paths of products of edge weights; exact for linear SEMs, approximate for the random-forest models used in the real-world experiments.
domain assumption The explained model f respects the same feature causal structure used to build γ and the sampler
The consistency proof (Theorem V.3) requires f and f' to share the causal structure; the framework also assumes the black box does not introduce feature dependencies that contradict the discovered graph.
ad hoc to paper The PC output can be resolved into a single DAG for the topological-order sampling
Algorithm 1 and Eq. 6 need a DAG, PC returns a CPDAG, and no resolution procedure is given; footnote 1 only acknowledges the issue.

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Cite this review

Pith. "Pith review of Causal SHAP: Feature Attribution with Dependency Awareness through Causal Discovery." pith.science (2026). https://pith.science/paper/OPPL3SKX

@misc{pith2026250900846,
  author       = {Pith},
  title        = {Pith review of: Causal SHAP: Feature Attribution with Dependency Awareness through Causal Discovery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OPPL3SKX}},
  note         = {Machine review of arXiv:2509.00846}
}

read the original abstract

Explaining machine learning (ML) predictions has become crucial as ML models are increasingly deployed in high-stakes domains such as healthcare. While SHapley Additive exPlanations (SHAP) is widely used for model interpretability, it fails to differentiate between causality and correlation, often misattributing feature importance when features are highly correlated. We propose Causal SHAP, a novel framework that integrates causal relationships into feature attribution while preserving many desirable properties of SHAP. By combining the Peter-Clark (PC) algorithm for causal discovery and the Intervention Calculus when the DAG is Absent (IDA) algorithm for causal strength quantification, our approach addresses the weakness of SHAP. Specifically, Causal SHAP reduces attribution scores for features that are merely correlated with the target, as validated through experiments on both synthetic and real-world datasets. This study contributes to the field of Explainable AI (XAI) by providing a practical framework for causal-aware model explanations. Our approach is particularly valuable in domains such as healthcare, where understanding true causal relationships is critical for informed decision-making.

Figures

Figures reproduced from arXiv: 2509.00846 by the authors.

**Figure 2.** An example of two phases in PC algorithm Starting with a fully connected undirected graph (assuming full interactions between all features), phase 1 systematically removes edges between conditionally independent pairs based on statistical tests, i.e., for each pair of variables found to be conditionally independent given a set of other variables (called the separating set), the edge between the pair is removed. Thes… view at source ↗

**Figure 3.** An illustration of IDA (adapted from [7]). [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Causal SHAP Framework: A pipeline for integrating causality into SHAP feature attribution. The framework consists of three main components: (1) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 6.** Figure 6: Kernel SHAP (top) versus Causal SHAP (bottom) for features in Lung [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 5.** Figure 5: Diagram shows the causal graph of Lung Cancer Data set (Left), [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: Kernel SHAP (top) versus Causal SHAP (bottom) for features in Car [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

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