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Task-oriented Time Series Imputation Evaluation via Generalized Representers
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Proposes a retraining-free, downstream-task-oriented evaluation of time series imputation that estimates per-timestep gains via a generalized-representer/NTK approximation, and uses these gains to ensemble imputations for forecasting.
Problem
Standard imputation evaluation uses reconstruction error, ignoring how imputed values affect downstream forecasting; evaluating per-timestep impact by retraining is prohibitively expensive.
Approach
Estimates the effect of swapping an imputed label at each time step on downstream test loss without retraining, using a kernel/generalized-representer (NTK-based) first-order approximation with a low-dimensional smooth-basis compression of model outputs; the gains then drive a per-timestep combination of imputation methods.
Key results
- Mean+SAITS ensemble reduces GEF forecasting MSE from 0.1750 (mean) to 0.1653 with the full estimator on univariate DLinear forecasting.
- Gain estimation with the MLP shows the segmented acceleration (Seg-N) achieves competitive correlation/accuracy while Seq-sim takes 46s vs. >48h for retraining on the MLP.
- Mean+ImputeFormer reaches 0.1657 MSE on GEF and 0.0977 on ELECTRICITY with gain estimation, versus 0.1076 for ImputeFormer alone.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Combine mean imputation with SAITS using estimated gains to replace the top 10% of time steps | DLinear forecasting · GEF | MSE: 0.1750 -> 0.1653(0.0008) | Helped |
| Combine mean imputation with SAITS using estimated gains to replace the top 10% of time steps | DLinear forecasting · ETTH1 | MSE: 0.0523 -> 0.0522(0.0000) | Helped |
| Combine mean imputation with SPIN using estimated gains to replace the top 10% of time steps | DLinear forecasting · ETTH2 | MSE: 0.1797 -> 0.1784(0.0000) | No clear effect |
| Combine mean imputation with SAITS using estimated gains to replace the top 10% of time steps | DLinear forecasting · ELECTRICITY | MSE: 0.1123 -> 0.0957(0.0006) | Helped |
| Combine mean imputation with SAITS using estimated gains to replace the top 10% of time steps | DLinear forecasting · TRAFFIC | MSE: 0.4359 -> 0.4147(0.0023) | Helped |
| Combine mean imputation with SAITS using estimated gains to replace the top 10% of time steps | DLinear forecasting · AIR | MSE: 0.1508 -> 0.1491(0.0001) | Helped |
| Use gain estimation to combine mean and ImputeFormer imputations | DLinear forecasting · GEF, multivariate input | MSE: 0.1845 -> 0.1747(0.0011) | Helped |
| Replace full gain estimation with Seg-4 accelerated gain estimation (ablation) | Mean+SAITS on DLinear · GEF | MSE: 0.1653(0.0008) -> 0.1666(0.0007) | Hurt |
| Replace full gain estimation with Seg-2 accelerated gain estimation (ablation) | Mean+SAITS on DLinear · GEF | MSE: 0.1653(0.0008) -> 0.1686(0.0005) | Hurt |
| Replace full gain estimation with Seg-1 accelerated gain estimation (ablation) | Mean+SAITS on DLinear · GEF | MSE: 0.1653(0.0008) -> 0.1696(0.0000) | Hurt |
Surprising findings
- Better imputation accuracy does not always yield better forecasting performance; a toy example shows a method with lower imputation MSE (0.0576) gives higher forecasting MSE (0.1395).
- Mean imputation outperforms most deep imputation methods on downstream forecasting in several datasets.
Limitations
- Estimation is first-order and per-timestep gains ignore interactions among samples and timesteps, so the ensemble only substitutes top c% timesteps.
- Gain estimates may not be 100% accurate and could bias imputation selection; correlation with true gains is imperfect for some settings.
- Experiments are limited to univariate forecasting with small models (MLP, DLinear) and mostly mean-imputation baseline.
Experimental setup
Datasets: GEF ETTH1 ETTH2 ELECTRICITY TRAFFIC AIR
Benchmarks: GEF ETTH1 ETTH2 ELECTRICITY TRAFFIC AIR
Metrics: MSE correlation between estimated and actual gain sign accuracy
Baselines: Mean imputation SAITS BRITS MRNN GPVAE USGAN SPIN ImputeFormer Influence Function
Builds on: generalized representer neural tangent kernel influence functions SAITS DLinear
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