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Practical do-Shapley Explanations with Estimand-Agnostic Causal Inference
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Makes do-SHAP practical by estimating interventional value functions from a single learned SCM (estimand-agnostic), accelerates coalition evaluation with the Frontier-Reducibility Algorithm, and extends do-SHAP to inaccessible DGPs via noise attribution.
Problem
do-SHAP requires a separate estimand and ML models for each of up to 2^|X| interventional coalition queries, making it impractical on complex causal graphs.
Approach
Use the estimand-agnostic approach: train one SCM (proxy) to fit the observational distribution, then compute any identifiable interventional coalition value by sampling the intervened SCM. Add the Frontier-Reducibility Algorithm to map each coalition to an irreducible subset with identical value, caching evaluations; and attribute the outcome gap for inaccessible DGPs to the noise variable of an
Key results
- On a synthetic Markovian graph (30 replications, N=1000), proxy SCMs with better log-likelihood gave better do-SV estimates; DCGs and CNFs performed similarly, with DCG chosen for handling latent confounders.
- FRA computes only (1 - 1/2^K)-type reductions; for p=0.1 the computed-coalition ratio approaches 0.1 (90% reduction) at large K, and FRA runs about an order of magnitude faster than the baseline and twice as fast as a plain cache.
- For K=100 with 1000 permutations, do-SHAP took 26m01s (no cache), 25m20s (cache) and 21m14s (FRA cache), with DCG training of 16s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FRA with coalition caching instead of caching alone (ablation) | do-SHAP with a linear DCG · Synthetic graphs with K=100 | execution time: 25m20s -> 21m14s; 4m | Helped |
| Use FRA-cache instead of evaluating coalitions without a cache (ablation) | do-SHAP with a linear DCG · Synthetic graphs with K=100 | execution time: 26m01s -> 21m14s | Helped |
| Use an FRA-cache instead of the baseline (ablation) | do-SHAP · Synthetic random graphs, K >= 8 and p = 0.25 | execution time: an order of magnitude faster | Helped |
| Use an FRA-cache instead of a cache alone (ablation) | do-SHAP · Synthetic random graphs, K >= 8 and p = 0.25 | execution time: twice faster | Helped |
| Use a linear SCM rather than a better-fitting SCM architecture | do-SHAP estimation · Synthetic Markovian graph | SHAP estimation loss | Hurt |
| Use DCGs rather than the other tested SCM architectures | do-SHAP estimation · Synthetic semi-Markovian graph | SHAP estimation loss | Helped |
| Use a CNF rather than a DCG | do-SHAP estimation · Synthetic Markovian graph | SHAP estimation loss | No clear effect |
| Use a CNF rather than a DCG | do-SHAP estimation · Synthetic Markovian graph | estimation variance | Mixed |
| Model the observational distribution more accurately | proxy SCM do-SHAP estimation · Synthetic Markovian graph | SHAP estimation loss | Helped |
| Use marginal-SHAP instead of do-SHAP | SHAP attribution · Synthetic Markovian graph | SHAP estimation loss | Hurt |
| Apply FRA coalition reduction (ablation) | do-SHAP · Random graphs G_{K,p}, K in {5, ..., 20} | number of coalition evaluations: for p=0.1, a reduction in nu-computations of 90% | Helped |
Surprising findings
- Marginal-SHAP values differ substantially from do-SHAP ground truth, showing the two measure different attributions.
Limitations
- Requires a known causal graph; results are sensitive to graph misspecification and EA methods lack doubly-robust guarantees.
- do-SHAP remains exponential in the number of features; FRA gives no reduction when all features are parents of Y.
- Interventional value functions are population-level, so they do not explain individual outcomes without counterfactual value functions.
Experimental setup
Datasets: synthetic SCM data
Benchmarks: synthetic SCM ground-truth do-SVs two real-world datasets (appendix)
Metrics: SHAP estimation loss L2 average test log-likelihood feature importance execution time fraction of coalitions computed
Baselines: marginal SHAP linear SCM
Builds on: do-SHAP Neural Causal Models Causal Normalizing Flows Deep Causal Graphs Luther et al. conditional SHAP pruning
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