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Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting
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Proposes LSTD, a variational sequential autoencoder that disentangles long-term and short-term latent states for online time series forecasting, using identification theory under unknown interventions plus smooth and interrupted-dependency constraints.
Problem
Online time series forecasting under nonstationarity: preserving long-term dependencies while adapting to short-term changes caused by unknown interventions, without entangled long/short-term states.
Approach
Formalizes a data generation process where short-term latent states are intervened on by unknown interventions, proves block-wise identifiability of long/short-term latents from this independence, and implements it with separate long/short-term priors, a smooth attention-consistency constraint for long-term states, and an L1 interrupted-dependency constraint for short-term states.
Key results
- LSTD achieves the lowest MSE on Exchange at all horizons (e.g., 0.013 at horizon 1 vs 0.017 for OneNet), a margin the authors describe as about 44% over the strongest baselines.
- LSTD reports best MSE on ECL (e.g., 1.422 vs 2.074 for OneNet at horizon 24) and WTH.
- On ETT datasets LSTD is only second-best to OneNet, which the authors attribute to fewer unknown interventions.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LSTD instead of OneNet | Online forecasting · Exchange | MSE: 44% | Helped |
| Remove the interrupted dependency constraint (LSTD-L1) (ablation) | LSTD · Exchange | forecasting performance | Hurt |
| Add the interrupted dependency constraint for short-term disentanglement (ablation) | LSTD · Exchange | forecasting performance | Helped |
| Remove the smooth constraint (LSTD-L2) (ablation) | LSTD · Exchange | forecasting performance | Hurt |
| Add the smooth constraint for long-term disentanglement (ablation) | LSTD · Exchange | forecasting performance | Helped |
| Remove the long-term and short-term priors and their KL divergence term (LSTD-KL) (ablation) | LSTD · Exchange | forecasting performance | Hurt |
Surprising findings
- On ETT datasets the proposed method is comparable to but not better than OneNet, attributed to few unknown interventions in those data.
Limitations
- Identifiability relies on strong assumptions (smooth positive density, conditional independence, linear independence) that are hard to verify in practice.
- Gains are limited on ETT datasets where unknown interventions are rare, per the authors.
Experimental setup
Datasets: ETTh2 ETTm1 Exchange Weather ECL Traffic
Benchmarks: ETTh2 ETTm1 Exchange Weather ECL Traffic
Metrics: MSE MAE
Baselines: OneNet FSNet OneNet-TCN Online-TCN ER DER++ MIR TFCL Informer
Builds on: FSNet OneNet nonlinear ICA variational autoencoder
Closest papers by meaning
- Online Time Series Forecasting with Theoretical Guarantees (NeurIPS 2025 · similarity 0.89)
- TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting (NeurIPS 2025 · similarity 0.88)
- TimeBase: The Power of Minimalism in Efficient Long-term Time Series Forecasting (ICML 2025 · similarity 0.86)
- TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting (ICML 2025 · similarity 0.85)
- A Closer Look at Transformers for Time Series Forecasting: Understanding Why They Work and Where They Struggle (ICML 2025 · similarity 0.85)
- Conditional Diffusion Model with Nonlinear Data Transformation for Time Series Forecasting (ICML 2025 · similarity 0.85)
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