Unlocking the Potential of Linear Networks for Irregular Multivariate Time Series Forecasting

TL;DR

This work tackles irregular multivariate time series forecasting (IMTS) by introducing AiT, a model that extends linear networks with an Adaptive Linear (ALinear) module to adjust weights based on observed time points and a Transformer-based Spatial Encoder to capture cross-variable correlations under asynchrony. AiT comprises a Temporal Encoder, Spatial Encoder, and per-variable Predictor, all leveraging ALinear to address intra-series inconsistency and missing data. Across four public IMTS benchmarks, AiT achieves superior forecasting accuracy (lower MSE/MAE) and substantial runtime efficiency gains versus state-of-the-art methods, validated by thorough ablations. The approach offers a simple, scalable bridge between RMTS and IMTS, with practical implications for healthcare, climate, and related domains.

Abstract

Time series forecasting holds significant importance across various industries, including finance, transportation, energy, healthcare, and climate. Despite the widespread use of linear networks due to their low computational cost and effectiveness in modeling temporal dependencies, most existing research has concentrated on regularly sampled and fully observed multivariate time series. However, in practice, we frequently encounter irregular multivariate time series characterized by variable sampling intervals and missing values. The inherent intra-series inconsistency and inter-series asynchrony in such data hinder effective modeling and forecasting with traditional linear networks relying on static weights. To tackle these challenges, this paper introduces a novel model named AiT. AiT utilizes an adaptive linear network capable of dynamically adjusting weights according to observation time points to address intra-series inconsistency, thereby enhancing the accuracy of temporal dependencies modeling. Furthermore, by incorporating the Transformer module on variable semantics embeddings, AiT efficiently captures variable correlations, avoiding the challenge of inter-series asynchrony. Comprehensive experiments across four benchmark datasets demonstrate the superiority of AiT, improving prediction accuracy by 11% and decreasing runtime by 52% compared to existing state-of-the-art methods.

Figures (6)

• Figure 1: The comparison of regular multivariate time series forecasting and irregular multivariate time series forecasting.
• Figure 2: The overall framework of AiT. Raw observation series from different variables are independently embedded into dynamic variable embeddings via the Temporal Encoder. The Projection then integrates dynamic and static variable embeddings. The aggregated variable embedding is subsequently fed into the Spatial Encoder to capture variable correlations. Finally, the Predictor individually transforms the embedding of each variable into the forecasting series.
• Figure 3: The prediction error, average training time per epoch, and total inference time of AiT and its variants for irregular multivariate time series forecasting. A lower value denotes a better performance.
• Figure 4: The prediction error of AiT with various hyperparameter configurations for irregular multivariate time series forecasting. A lower value denotes superior prediction accuracy.
• Figure 5: The average training time per epoch and total inference time of ALinear and backbones for regular multivariate time series forecasting. A lower value denotes greater efficiency.