Research map / Time series / Causal and generative time series

Time-Series Forecasting for Out-of-Distribution Generalization Using Invariant Learning

ICML 2024 · Time series › Causal and generative time series · approach: Probabilistic and conformal forecasting · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes FOIL, a model-agnostic invariant learning framework for time-series forecasting that uses a surrogate residual-normalization loss to handle unobserved core variables and an EM-style environment inference module with temporal label propagation.

Problem

Out-of-distribution generalization in time-series forecasting, where future test distributions differ from historical training data; standard invariant learning assumptions break because target variables depend on unobserved core variables and time-series lack environment labels.

Approach

Targets the sufficiently predictable part of the target via an Instance Residual Normalization surrogate loss that removes the effect of unobserved variables, and jointly infers temporal environments with a multi-head EM clustering that preserves temporal adjacency, then learns invariant representations across those environments.

Key results

• FOIL improves Informer, Crossformer and PatchTST across datasets and horizons, with average MSE improvements up to 80.58% on Exchange for Informer and up to 85.38% on ETTh1 at the best setting.
• On Informer with 96-step horizon, FOIL achieves MSE 0.136 on Exchange versus 0.151 for the best baseline NST and 0.169 for RevIN, and improves over the best baseline by about 10% MSE on average.
• For PatchTST, FOIL gives smaller gains (roughly 6-30% on average), indicating smaller improvements on the stronger backbone.

Measured effects reported in the paper

Surprising findings

• General OOD methods such as IRM, VREx, and GroupDRO perform poorly on TSF, often no better than ERM.
• Standard instance normalization methods (RevIN, NST) are strong baselines but are outperformed by FOIL's residual-based surrogate loss.

Limitations

• Gains shrink for long-horizon forecasting because higher uncertainty hinders learning invariant features.
• Environments are predefined by splitting the training set into k equal time segments (k tuned 2-10) since environment labels are unavailable, which is a heuristic in the experiments.
• Evaluated only on four datasets and three backbones, all univariate forecasting with covariates.

Experimental setup

Datasets: Exchange ILI ETTh1 ETTh2

Benchmarks: Exchange ILI ETTh1 ETTh2

Metrics: MSE MAE

Baselines: ERM GroupDRO IRM VREx SD IB-ERM EIIL NST RevIN IRM+RevIN EIIL+RevIN

Builds on: invariant risk minimization EIIL RevIN PatchTST Informer

Closest papers by meaning

• Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.87)
• Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation (AAAI 2025 · similarity 0.86)
• TimeEmb: A Lightweight Static-Dynamic Disentanglement Framework for Time Series Forecasting (NeurIPS 2025 · similarity 0.86)
• TimePFN: Effective Multivariate Time Series Forecasting with Synthetic Data (AAAI 2025 · similarity 0.86)
• OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain (NeurIPS 2025 · similarity 0.86)
• TimePerceiver: An Encoder-Decoder Framework for Generalized Time-Series Forecasting (NeurIPS 2025 · similarity 0.86)