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RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomalies
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Proposes RobustTSF, a trend-filter-based sample selection plus MAE loss that makes LSTM time series forecasters robust to constant, missing, and Gaussian point-wise anomalies in inputs and targets, with theory linking the setting to learning with noisy labels.
Problem
Time series forecasting trained on contaminated data with anomalies in both covariates (inputs) and targets, where standard training and detection-imputation-retraining pipelines degrade and small-loss LNL methods are inconsistent.
Approach
Select training windows whose trend-filter deviation (computed with an L1 fidelity term, without a pretrained detector) is small near the label, then train with MAE; theory shows MAE is robust to constant/missing target anomalies and both MAE and MSE to Gaussian target anomalies, and anomaly position in inputs matters most near the forecast target.
Key results
- On Electricity single-step forecasting, RobustTSF achieves best MAE/MSE of 0.177/0.066 on clean data and 0.183/0.070 under constant anomalies at eta=0.3, versus 0.225/0.092 for vanilla MAE with missing anomalies at eta=0.3.
- RobustTSF attains the lowest stability gap Delta of 0.003 on Traffic and 0.004 on Electricity, matching or beating loss selection.
- On multi-step Electricity forecasting with 20% anomalies, RobustTSF improves over vanilla MAE across constant, missing, and Gaussian types (e.g., 0.280/0.158 vs 0.292/0.165 clean at O=4).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RobustTSF instead of vanilla MAE training | LSTM forecasting · Electricity, Constant anomaly η=0.3 | MAE/MSE: 0.206/0.086 -> 0.183/0.070 | Helped |
| Use RobustTSF instead of offline imputation | LSTM forecasting · Traffic, Missing anomaly η=0.3 | MAE/MSE: 0.280/0.186 -> 0.243/0.140 | Hurt |
| Use RobustTSF instead of vanilla MAE training | LSTM forecasting · Electricity, clean single-step | MAE/MSE: 0.182/0.070 -> 0.177/0.065 | Helped |
| Use RobustTSF instead of vanilla MAE training | LSTM forecasting · Electricity, multi-step clean O=4 | MAE/MSE: 0.292/0.165 -> 0.280/0.158 | Helped |
| Use RobustTSF instead of vanilla MAE training | LSTM forecasting · Traffic, Missing anomaly η=0.3 | MAE/MSE: 0.295/0.208 -> 0.243/0.140 | Hurt |
| Use MAE instead of MSE loss (ablation) | RobustTSF · Electricity, Missing anomaly η=0.3 | MAE: 0.249 -> 0.194 | Helped |
| Use MAE instead of MSE loss (ablation) | RobustTSF · Electricity, Constant anomaly η=0.1 | MAE: 0.180 -> 0.177 | Helped |
| Use Dirac weighting instead of exponential weighting (ablation) | RobustTSF with MAE and trend-filter detection · Electricity, Missing anomaly η=0.3 | MAE: 0.199 -> 0.194 | Helped |
| Use trend-filter detection instead of prediction-based detection (ablation) | RobustTSF with MAE and Dirac weighting · Electricity, Missing anomaly η=0.3 | MAE: 0.206 -> 0.194 | Helped |
| Select samples based on the trend-filter anomaly score rather than randomly (ablation) | RobustTSF · Electricity, Constant anomaly η=0.3 | MAE/MSE: 0.222/0.089 -> 0.183/0.070 | Helped |
| Use offline imputation instead of RobustTSF | LSTM forecasting · Traffic, Missing anomaly η=0.3 | MAE/MSE: 0.243/0.140 -> 0.280/0.186 | Hurt |
Surprising findings
- Missing anomalies have the most negative impact on forecasting performance among the three anomaly types.
- Offline imputation, online imputation, and loss-based sample selection do not consistently improve over vanilla training across anomaly types.
Limitations
- Theoretical guarantees hold statistically and mainly for large sample sizes; performance may drop with small training sets or high anomaly rates.
- Robustness guarantees do not extend to more complex anomaly types that violate the conditional independence assumption.
- Experiments use small LSTMs and anomaly scales fixed in the main text.
Experimental setup
Datasets: Electricity Traffic ETT-h1 Exchange
Benchmarks: Electricity Traffic
Metrics: MAE MSE best-epoch test error last-epoch test error stability Delta
Baselines: Vanilla MSE Vanilla MAE Offline imputation Online imputation Loss-based sample selection
Builds on: learning with noisy labels trend filtering small loss criterion detection-imputation-retraining
Closest papers by meaning
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