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Towards Learning and Explaining Indirect Causal Effects in Neural Networks
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Proposes AHCE, an ante-hoc method that adds learnable lateral feedforward edges among input neurons (following a known causal graph) so an NN can learn and quantify direct, indirect, and total causal effects, with binning/Taylor approximations for scalability.
Problem
Existing causal explanation methods for neural networks treat input features as independent, so they capture only direct and total causal effects and cannot quantify indirect effects propagated through other inputs.
Approach
Treat the NN as an SCM and add feedforward (lateral) connections among input neurons according to domain causal knowledge, train with a two-phase ante-hoc procedure with a regularizer tying derived child values to observed values, and estimate interventional means/covariances via a second-order Taylor approximation with binning for efficiency.
Key results
- On the synthetic dataset, AHCE reaches average total-effect RMSE 0.06 vs 0.08 for the best baseline (CA and CREDO), and Frechet 0.17 vs 0.22 for CREDO.
- On Sachs, AHCE achieves average RMSE 0.22 vs 0.32 for the best baseline (CSHAP), and Frechet 0.31 vs 0.34 for CSHAP.
- Binning with KD Tree/DBSCAN gives 3 to 10-fold runtime improvements with only slight precision loss in the flight simulation experiments.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use AHCE instead of the strongest listed baseline | causal-effect estimation · Synthetic | RMSE: 0.08$\pm$0.00 -> 0.06$\pm$0.01 | Helped |
| use AHCE instead of the strongest listed baseline | causal-effect estimation · Auto-MPG | RMSE: 0.09$\pm$0.00 -> 0.07$\pm$0.00 | Helped |
| use AHCE instead of the strongest listed baseline | causal-effect estimation · Lung Cancer | RMSE: 0.56$\pm$0.00 -> 0.54$\pm$0.33 | Helped |
| use AHCE instead of the strongest listed baseline | causal-effect estimation · Sachs | RMSE: 0.32$\pm$0.00 -> 0.22$\pm$0.09 | Helped |
| use AHCE instead of the strongest listed baseline | causal-effect estimation · Synthetic | Frechet: 0.19$\pm$0.03 -> 0.17$\pm$0.04 | Helped |
| use AHCE instead of the strongest listed baseline | causal-effect estimation · Auto-MPG | Frechet: 0.16$\pm$0.01 -> 0.12$\pm$0.02 | Helped |
| use AHCE instead of the strongest listed baseline | causal-effect estimation · Sachs | Frechet: 0.34$\pm$0.00 -> 0.31$\pm$0.12 | Helped |
| add outgoing edges among input features (ablation) | AHCE · Synthetic | RMSE: 0.08$\pm$0.01 -> 0.06$\pm$0.01 | Helped |
| add outgoing edges among input features (ablation) | AHCE · Synthetic | Frechet: 0.20$\pm$0.02 -> 0.17$\pm$0.04 | Helped |
| use AHCE rather than CSHAP for indirect effects | indirect causal-effect estimation · Synthetic | RMSE: 1.72$\pm$0.00 -> 1.67$\pm$0.01 | Helped |
| use AHCE rather than CSHAP for indirect effects | indirect causal-effect estimation · Synthetic | Frechet: 2.80$\pm$0.00 -> 2.86$\pm$0.03 | Hurt |
| add the binning implementation | causal-effect computation · PBD, FD, and MAD | Time (minutes) | Helped |
Surprising findings
- On the Lung Cancer dataset, AHCE's average RMSE of 0.54 has large variance (±0.33), and per-feature errors are sometimes worse than baselines (e.g., Bronchitis 1.11 vs 0.93 for CSHAP).
Limitations
- Indirect effects are identifiable only where feedforward edges among inputs are supplied from domain knowledge; the causal graph may be partial or incorrect.
- Auto-MPG causal graph was constructed from domain knowledge and checked with GPT-3.5, so no ground truth indirect effects can be evaluated there.
- Results on real-world data show high variance and mixed per-feature performance.
Experimental setup
Datasets: Synthetic (3 features, 1000 points) Auto-MPG Lung Cancer Sachs Parking Brake Dataset Flap Dataset Multiple Anomaly Dataset
Benchmarks: Synthetic Auto-MPG Lung Cancer Sachs Flight simulation datasets (PBD, FD, MAD)
Metrics: RMSE Frechet distance Accuracy computation time (minutes)
Baselines: Integrated Gradients Causal Attributions Causal Shapley values CREDO
Builds on: Causal Attributions (CA) Causal regularization using domain priors (CREDO) Integrated Gradients Causal Shapley values
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