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Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline

Xvyuan Liu, Xiangfei Qiu, Xingjian Wu, Zhengyu Li, Chenjuan Guo, Jilin Hu, Bin Yang

arXiv:2505.11250v4cs.LG

TL;DR

Irregular, missing observations and the computational cost of existing methods make accurate, practical IMTS forecasting challenging. APN uses adaptive time-aware patch aggregation and a query module, and outperforms existing state-of-the-art methods on multiple real-world datasets in efficiency and accuracy.

  • Problem

    IMTS forecasting must contend with irregular, missing observations and existing models’ high computational costs, despite its importance for early warning and proactive decision-making.

    Source: §1 · p. 1

  • Method

    APN uses TAPA’s adaptive, time-aware aggregation to form regularized patches from irregular observations, then integrates history with a query module and predicts via a shallow MLP.

    Source: §1 · p. 2

  • Results

    APN outperforms existing state-of-the-art methods on multiple real-world datasets in both efficiency and accuracy.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The paper concludes that aggregation-based adaptive patching supports a streamlined, efficient IMTS forecasting framework while preserving observed-data fidelity.

    Source: §3.2 · p. 3, §5 · p. 7

    APN is sensitive to core hyperparameters, especially Dte, so practical use requires tuning for dataset-specific characteristics.

    Source: §4.4 · p. 7

Abstract

from arXiv · show

The forecasting of irregular multivariate time series (IMTS) is crucial in key areas such as healthcare, biomechanics, climate science, and astronomy. However, achieving accurate and practical predictions is challenging due to two main factors. First, the inherent irregularity and data missingness in irregular time series make modeling difficult. Second, most existing methods are typically complex and resource-intensive. In this study, we propose a general framework called APN to address these challenges. Specifically, we design a novel Time-Aware Patch Aggregation (TAPA) module that achieves adaptive patching. By learning dynamically adjustable patch boundaries and a time-aware weighted averaging strategy, TAPA transforms the original irregular sequences into high-quality, regularized representations in a channel-independent manner. Additionally, we use a simple query module to effectively integrate historical information while maintaining the model's efficiency. Finally, predictions are made by a shallow MLP. Experimental results on multiple real-world datasets show that APN outperforms existing state-of-the-art methods in both efficiency and accuracy.

1 Introduction

APN targets the challenges of irregular observations and missing data in IMTS forecasting while seeking a simpler, more efficient model. It combines adaptive patching with historical-information integration and reports improved accuracy and efficiency on multiple real-world datasets.

  • IMTS forecasting is challenged by irregular observations and missing data, while complex neural-ODE, GNN, and Transformer approaches incur high computational costs and long runtimes.Source: §1 · pp. 1–2
  • Fixed patching used by tPatchGNN and TimeCHEAT (Liu, Cao, and Chen 2025) cannot adapt to local density or reliably preserve complete semantic context.Source: §1 · p. 1
  • A simple query module integrates historical context from the patch representations, and a shallow MLP makes predictions.Source: §1 · p. 2
  • APN uses TAPA to learn adjustable patch boundaries and time-aware weighted averages, producing channel-independent regularized representations that adapt to information density and preserve semantics.Source: §1 · p. 2
  • APN outperforms existing state-of-the-art methods in forecasting accuracy and computational efficiency on multiple real-world datasets.Source: §1 · p. 2

2 Related Work

Prior IMTSF methods address irregular sampling with continuous-time dynamics or graph and attention models. Patch-based work progresses from fixed-span segmentation toward adaptive patching, while this paper proposes aggregation over observed data to avoid interpolation artifacts and information loss.

2.1 Progress in Irregular Multivariate Time Series Forecasting

  • Prior IMTSF work uses continuous-time ODE/SDE models, including Neural Flows (Bilos et al. 2021a) and GRU-ODE-Bayes, alongside graph and attention methods such as GraFITi.tPatchGNN combines time-aligned patches with Transformers and adaptive GNNs for intra- and inter-patch dependencies.Source: §2.1 · p. 2

2.2 Progress in Patch-based Irregular Multivariate Time Series Forecasting

  • Early IMTSF patch methods, including tPatchGNN and TimeCHEAT (Liu, Cao, and Chen 2025), use fixed spans that can yield sparse or redundant patches.Fixed segmentation is ill-suited to IMTS's non-uniform data distribution.Source: §2.2 · p. 2
  • Adaptive patching methods such as HDMixer learn flexible boundaries but use interpolation-based resampling, which can fabricate misleading points across sparse or missing IMTS intervals.The resulting artifacts can undermine model reliability.Source: §2.2 · p. 2
  • TAPA learns dynamic soft windows and aggregates original observations, avoiding interpolation distortions while ensuring every data point contributes to relevant patches.Its aggregation-based adaptive patching is designed specifically for IMTS.Source: §2.2 · p. 2

3 Methodology

APN separates irregularity handling from forecasting: TAPA converts irregular histories into regularized patch representations, then query-based aggregation and a simple MLP produce predictions at queried times. Its compact downstream modules are enabled by front-loading the handling of irregularity into TAPA.

3.1 Problem Definition

  • The forecasting task is to predict future observed values for all variables from historical observations and a set of prediction queries.Source: §3.1 · p. 3

3.2 Framework Overview

  • APN uses a two-stage pipeline that front-loads irregularity handling into TAPA before lightweight query-based contextualization and MLP forecasting.TAPA transforms raw observations into regularized patch representations without interpolation; query-based aggregation summarizes historical context for each variable before the decoder predicts.Source: §3.2 · p. 3

3.3 Time-Aware Patch Aggregation (TAPA)

  • TAPA replaces rigid segmentation with channel-independent soft, time-aware aggregation, learning patch centers and scales to produce regularized representations without interpolation.Its two steps are adaptive patching and weighted aggregation of raw observations.Source: §3.3 · p. 3, §3.2 · p. 3

Adaptive Patching: Learning Dynamic Temporal Windows

  • TAPA learns dynamic temporal windows that can widen in sparse regions and narrow in dense ones, adapting patch scope to local information density.The learned window width remains strictly positive during optimization.Source: Adaptive Patching: Learning Dynamic… · p. 3

Weighted Aggregation: From Raw Observations to Rich Representations

  • Positive soft-window weights yield normalized weighted averages in which every observation contributes to every patch, avoiding the information loss of hard segmentation.Learnable time embeddings are concatenated with raw values, and a learnable positive temperature adjusts the softness of window edges.Source: Weighted Aggregation: From Raw… · pp. 3–4

3.4 Query-based Aggregation

  • For each channel, a learnable query scores position-aware patches by dot product, softmax weights them into a context vector, and layer normalization stabilizes decoder input.This avoids complex inter-patch interactions such as multi-head self-attention.Source: §3.4 · p. 5

3.5 Forecasting Decoder

  • A two-layer MLP predicts each queried value from the aggregated context and query-time encoding, demonstrating that the learned representations support a simple decoder.The model is trained end-to-end with mean squared error.Source: §3.5 · p. 5

4 Experiments

Across four IMTS datasets, APN achieves leading or highly competitive forecasting accuracy, while ablations, sensitivity analyses, and efficiency comparisons assess its components, hyperparameters, and deployment characteristics.

4.1 Setup

  • APN was evaluated on four domain-spanning IMTS datasets against eleven baselines, using 80/10/10 splits and five-seed mean and standard-deviation reporting.Experiments used MSE loss, AdamW, early stopping, and validation-set hyperparameter tuning for APN and baselines.Source: §4.1 · p. 5

4.2 Main results

  • APN achieves optimal or highly competitive forecasting on all four datasets, reducing MSE and MAE versus GraFITi by approximately 2.64% and 3.61%, respectively.The paper attributes this performance to TAPA’s soft aggregation over raw observations in adaptively learned temporal windows, with a streamlined query module and MLP decoder.Source: §4.2 · p. 6, Table 2

4.3 Ablation Studies

  • Removing query-based aggregation caused the largest degradation; hard-cut averaging and fixed random windows also reduced performance, supporting query prioritization, weighted soft aggregation, and adaptive patching.The ablations compare query-based aggregation with a linear layer, weighted aggregation with hard-cut patch averaging, and adaptive patching with fixed random partitions.Source: Table 3 · p. 6, §4.3 · p. 6

4.5 Scalability and Efficiency Analysis

  • On USHCN at batch size 32, APN shows significant advantages over three representative baselines across all four reported computational-efficiency metrics.Figure 4 measures peak GPU memory, parameter count, training time, and inference time; the text attributes the advantages to TAPA’s condensed representations and streamlined architecture.Source: Figure 4 · p. 7, §4.5 · p. 7

4.4 Parameter Sensitivity

  • Performance is stable across hidden dimension D and reasonable patch-count P ranges, but oversized Dte significantly degrades PhysioNet and MIMIC, supporting moderate time encoding and dataset-specific tuning.The analysis finds that larger D brings no significant improvement for most datasets, while performance generally remains robust across a reasonable range of P.Source: §4.4 · pp. 6–7, Figure 3 · p. 7

5 Conclusion

APN is an efficient framework for irregular multivariate time-series forecasting, centered on TAPA’s adaptive aggregation of raw observations into regularized representations. Experiments on public benchmarks show it outperforms existing state-of-the-art methods in prediction accuracy and computational efficiency.

5 Conclusion

  • TAPA learns dynamic patch boundaries and uses time-aware soft weighting to aggregate all raw observations into regularized patch representations.Unlike fixed patching or interpolation, the aggregation-based design ensures full data coverage and handles variations in information density.Source: §5 · p. 7
  • APN combines TAPA’s representations with a concise query module and shallow MLP to make predictions in a streamlined architecture.The design is intended to retain efficiency while leveraging the aggregated representations.Source: §5 · p. 7
  • Experiments on multiple public IMTS benchmark datasets show APN significantly outperforms existing state-of-the-art methods in prediction accuracy and computational efficiency.Source: §5 · p. 7

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