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Feature-aligned N-BEATS with Sinkhorn divergence
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Proposes Feature-aligned N-BEATS, which aligns stack-wise feature measures with a Sinkhorn divergence for domain-generalized time series forecasting on FRED and NCEI data.
Problem
Time series forecasting under domain shift when the target domain is unseen during training (domain generalization), where N-BEATS lacks invariant feature learning.
Approach
Extends N-BEATS' doubly residual stacking with a stack-wise alignment loss: normalized (softmax) pushforward feature measures of each stack are aligned across source domains using the Sinkhorn divergence, combined with the forecasting loss.
Key results
- On ODG FRED, N-HiTS + FA reduces sMAPE from 0.148 to 0.134 and N-BEATS-I + FA from 0.232 to 0.214.
- On ODG NCEI, N-HiTS + FA achieves sMAPE 0.713 vs 0.723 for N-HiTS, the best among compared models.
- Ablation on N-BEATS-G (exchange rate target): Sinkhorn divergence (eps=2.5e-3) gives sMAPE 0.032 vs 0.031 for Wasserstein-2, with WD runtime 314.30 s vs 0.68 s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add stack-wise feature alignment to N-HiTS | N-HiTS · FRED ODG | sMAPE: 0.148 -> 0.134 | Helped |
| Add stack-wise feature alignment to N-HiTS | N-HiTS · NCEI ODG | MASE: 0.561 -> 0.512 | Helped |
| Add stack-wise feature alignment to N-HiTS | N-HiTS · FRED CDG | sMAPE: 0.124 -> 0.123 | Helped |
| Add stack-wise feature alignment to N-HiTS | N-HiTS · NCEI CDG | MASE: 0.581 -> 0.482 | Helped |
| Add stack-wise feature alignment to N-HiTS | N-HiTS · NCEI IDG | sMAPE: 0.718 -> 0.715 | Helped |
| Use Sinkhorn divergence with ε=2.5e-3 instead of classic Wasserstein-2 distance (ablation) | N-BEATS-G with feature alignment · ODG | sMAPE: 0.031 -> 0.032 | No clear effect |
| Set Sinkhorn ε to 1e-5 (ablation) | N-BEATS-G with feature alignment · ODG | sMAPE: 0.032 -> 0.040 | Hurt |
| Replace Sinkhorn divergence with MMD (ablation) | N-BEATS-G with feature alignment · ODG | sMAPE: 0.032 -> 0.035 | Hurt |
| Replace Sinkhorn divergence with KL divergence (ablation) | N-BEATS-G with feature alignment · ODG | sMAPE: 0.032 -> 0.045 | Hurt |
| Set Sinkhorn ε to 1e-5 (ablation) | N-BEATS-G with feature alignment · CDG | sMAPE: 0.028 -> 0.026 | Helped |
| Replace Sinkhorn divergence with MMD (ablation) | N-BEATS-G with feature alignment · CDG | sMAPE: 0.028 -> 0.029 | Hurt |
| Set Sinkhorn ε to 1e-1 (ablation) | N-BEATS-G with feature alignment · IDG | sMAPE: 0.024 -> 0.025 | Hurt |
Surprising findings
- Exact Wasserstein-2 distance gives slightly better ODG results than Sinkhorn divergence but its runtime is roughly 460 times higher.
- Sinkhorn divergence with very small epsilon (1e-5) shows instability and worse MASE.
Limitations
- Convergence analysis of the combined training loss is left unresolved.
- Gap between Sinkhorn divergence and the H-divergence used in the theory is not closed.
- Small entropic regularization epsilon causes instability.
Experimental setup
Datasets: FRED financial data (commodity, income, interest rate, exchange rate) NCEI weather data (pressure, rain, temperature, wind) Tourism M3 M4
Benchmarks: FRED NCEI
Metrics: sMAPE MASE runtime
Baselines: N-BEATS-I N-BEATS-G N-HiTS NLinear DLinear Autoformer Informer WD MMD KL
Builds on: N-BEATS domain generalization error bound (H-divergence) GeomLoss
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