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Explain Temporal Black-Box Models via Functional Decomposition
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Proposes FDTempExplainer, a model-agnostic functional-decomposition explainer that splits a black-box time series model into per-time-step main effects and consecutive-step pure interactions, estimated with a CVAE-based conditional sampler.
Problem
Explaining black-box time series models is hard because time steps interact through strong temporal dependencies, and existing attribution methods treat time steps as isolated or rely on out-of-distribution perturbations.
Approach
Decompose the model into main effects plus interactions between consecutive time steps, define "pure" interactions relative to the observed sample so they can be estimated in closed form via conditional expectations, and distribute interaction effects equally among involved time steps for attribution.
Key results
- On the synthetic interaction-based anomaly detector f(2), FDTempExplainer reaches 0.9967 top-3 accuracy versus 0.782 for the next best (DeepLIFT) and 0.183-0.535 for occlusion/FIT/WinIT/DynamicMask.
- On Large Kitchen Appliances, FDTempExplainer gets consistency 0.2293 at k=40 (lower is better) versus 0.3333 for IG, and ACC drop 0.6453 versus 0.576 for IG.
- On MIMIC-III, FDTempExplainer achieves AUPRC-drop (k=50) of 0.043 versus 0.039 for DynamicMask and 0.038 for WinIT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use functional decomposition to separate temporal interactions from main effects | LSTM anomaly detector f(2) · Anomaly detection f(2) | Top-3 accuracy: 0.872 -> 0.9967 | Helped |
| Use functional decomposition to separate temporal interactions from main effects | LSTM anomaly detector f(2) · Anomaly detection f(2) | AUPRC: 0.936 -> 0.9968 | Helped |
| Use FDTempExplainer instead of WinIT | LSTM classifier · MIMIC-III | AUPRC-drop (95-pc): 0.029 -> 0.030 | Helped |
| Use FDTempExplainer instead of DynamicMask | LSTM classifier · MIMIC-III | AUPRC-drop (k=50): 0.039 -> 0.043 | Helped |
| Use FDTempExplainer instead of FO | LSTM classifier · Large Kitchen Appliances | ACC drop (k=40): 0.2 -> 0.6453 | Helped |
| Use FDTempExplainer instead of GRADSHAP | LSTM forecaster · Synthetic forecasting | Top-2 accuracy: 0.6125 -> 0.6438 | Helped |
| Use FDTempExplainer instead of GRADSHAP | LSTM forecaster · Synthetic forecasting | AUPRC: 0.7194 -> 0.7306 | Helped |
| Ignore interactions above fifth order (ablation) | FDTempExplainer · Large Kitchen Appliances | ACC drop (k=40): 0.6427 -> 0.5973 | Hurt |
| Ignore interactions above tenth order (ablation) | FDTempExplainer · Large Kitchen Appliances | ACC drop (k=40): 0.6427 -> 0.6533 | Helped |
| Use patches of 5 time steps (ablation) | FDTempExplainer · Large Kitchen Appliances | Runtime (s): 285 | Mixed |
| Use patches of 10 time steps (ablation) | FDTempExplainer · Large Kitchen Appliances | Runtime (s): 71 | Mixed |
| Use patches of 20 time steps (ablation) | FDTempExplainer · Large Kitchen Appliances | Runtime (s): 17 | Mixed |
Surprising findings
- Occlusion-based methods designed around marginal gains (FO, AFO, FIT) perform poorly on the interaction-driven detector, with top-3 accuracy of 0.183-0.313.
Limitations
- Computational cost grows quadratically with the number of time steps, which is heavy for long inputs such as anomaly detection.
- Interactions are restricted to consecutive time steps, so non-consecutive interactions are absorbed into broader terms.
- Evaluation relies largely on synthetic datasets because ground-truth explanations are unavailable for real data.
Experimental setup
Datasets: synthetic anomaly detection dataset (1000 series) MIMIC-III Large Kitchen Appliances (UCR) synthetic forecasting dataset (1000 series)
Benchmarks: synthetic anomaly detection (top-3 accuracy, AUPRC) MIMIC-III (AUPRC drop) Large Kitchen Appliances (consistency, ACC drop) synthetic forecasting (top-2 accuracy)
Metrics: top-k accuracy AUPRC AUPRC drop consistency ACC drop
Baselines: IG GradSHAP DeepLIFT FO AFO FIT WinIT DynamicMask
Builds on: PureGAM WinIT Feature Importance in Time (FIT) CVAE integrated gradients
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