HyperIMTS: Hypergraph Neural Network for Irregular Multivariate Time Series Forecasting

TL;DR

HyperIMTS addresses irregular multivariate time series forecasting by representing observations as nodes in a hypergraph connected via temporal and variable hyperedges. The method uses three sequential message-passing steps to learn both time-aware and overall variable dependencies without padding, enabling irregularity-aware learning. Empirical results across five datasets show HyperIMTS achieves competitive or superior forecasting accuracy with lower computational cost than padding-based and many state-of-the-art models, supported by extensive ablations and efficiency analyses. The approach offers a scalable, padding-free framework that effectively models complex dependencies in IMTS, with future work including multimodal extensions and optimization of attention mechanisms.

Abstract

Irregular multivariate time series (IMTS) are characterized by irregular time intervals within variables and unaligned observations across variables, posing challenges in learning temporal and variable dependencies. Many existing IMTS models either require padded samples to learn separately from temporal and variable dimensions, or represent original samples via bipartite graphs or sets. However, the former approaches often need to handle extra padding values affecting efficiency and disrupting original sampling patterns, while the latter ones have limitations in capturing dependencies among unaligned observations. To represent and learn both dependencies from original observations in a unified form, we propose HyperIMTS, a Hypergraph neural network for Irregular Multivariate Time Series forecasting. Observed values are converted as nodes in the hypergraph, interconnected by temporal and variable hyperedges to enable message passing among all observations. Through irregularity-aware message passing, HyperIMTS captures variable dependencies in a time-adaptive way to achieve accurate forecasting. Experiments demonstrate HyperIMTS's competitive performance among state-of-the-art models in IMTS forecasting with low computational cost.

Figures (7)

• Figure 1: Existing methods for processing IMTS sample. (a) Canonical padding approach, which significantly increases the amount of data. (b) Patch-aligned padding approach, which also increase the amount of data. (c) Set views all observations as its unordered items. (d) Bipartite graph uses observation edges to connect variable and time nodes. It cannot model dependencies between variables without aligned observations, like $V_2$ and $V_3$, which require shared timestamps.
• Figure 2: Illustration of the proposed efficient hypergraph representation for IMTS. (a) Original IMTS sample, where $V_1$, $V_2$, and $V_3$ represent three different variables. (b) The corresponding hypergraph representation. From top to bottom, variable hyperedges, observation nodes, and temporal hyperedges are displayed. Each observation node connects to the associated variable hyperedge above and the temporal hyperedge below. Gradient color lines between hyperedges indicate hyperedge-to-hyperedge message passing.
• Figure 3: The architecture of HyperIMTS. It first converts input IMTS samples with empty forecast targets into the proposed efficient hypergraph representation. Three types of message passing are used sequentially: (a) Temporal and variable hyperedge embeddings are updated via node-to-hyperedge message passing; (b) Inter-variable correlations are modeled during irregularity-aware hyperedge-to-hyperedge message passing, where time-aware and overall variable similarities are merged based on time alignment; (c) Both temporal and variable hyperedge embeddings are used for unified hyperedge-to-node updates.
• Figure 4: Model efficiency comparison on MIMIC-III, with 36 hours of lookback length, 3 forecast timestamps, 96 variables, and a batch size of 32. Our proposed model, HyperIMTS, achieves the lowest MSE while maintaining high computational efficiency, as measured by training time and memory footprints.
• Figure 5: Forecasting performance with varying lookback lengths and fixed forecast horizons.