Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting

Boyuan Li; Zhen Liu; Yicheng Luo; Qianli Ma

cs.LGFeb 25, 2026

Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting

Authors: Boyuan Li, Zhen Liu, Yicheng Luo, Qianli Ma

Organizations: School of Computer Science and Engineering, South China University of Technology

Abstract

Irregular Multivariate Time Series (IMTS) are characterized by uneven intervals between consecutive timestamps, which carry sampling pattern information valuable and informative for learning temporal and variable dependencies. In addition, IMTS often exhibit diverse dependencies across multiple time scales. However, many existing multi-scale IMTS methods use resampling to obtain the coarse series, which can alter the original timestamps and disrupt the sampling pattern information. To address the challenge, we propose ReIMTS, a Recursive multi-scale modeling approach for Irregular Multivariate Time Series forecasting. Instead of resampling, ReIMTS keeps timestamps unchanged and recursively splits each sample into subsamples with progressively shorter time periods. Based on the original sampling timestamps in these long-to-short subsamples, an irregularity-aware representation fusion mechanism is proposed to capture global-to-local dependencies for accurate forecasting. Extensive experiments demonstrate an average performance improvement of 27.1% in the forecasting task across different models and real-world datasets. Our code is available at https://github.com/Ladbaby/PyOmniTS.

Figures & tables

Figure 1: Existing multi-scale methods for IMTS resample the coarse series to balance differences in sampling densities across different variables. In the original sample from the healthcare dataset PhysioNet’12, liver function marker Bilirubin and heart rate (HR) exhibit a dense-to-sparse sampling pattern reflecting urgent to mild clinical monitoring, which is disrupted in the coarse series.

Figure 2: The architecture of ReIMTS with three scale levels. For the original IMTS sample on the top left, ReIMTS recursively splits it into subsamples with shorter time periods at each scale level. ReIMTS is compatible with most IMTS models, and we use graph neural networks as backbones here to illustrate multi-scale variable representation learning. Local representations from lower scale levels are fused with global ones from upper scale levels. The decoder in the lowest scale concatenates representations and decodes them into forecast predictions.

Figure 3: Comparison of our method and existing approaches. (a) ReIMTS preserves the original sampling pattern while remaining compatible with most IMTS backbones. (b) Sample-space resampling methods. (c) Patch-based methods for IMTS. (d) Representation-space resampling methods.

Description	MIMIC-III	MIMIC-IV	PhysioNet’12	Human Activity	USHCN
Max length	96	971	47	131	337
# Variable	96	100	36	12	5
# Sample	21,250	17,874	11,981	1,359	1,114
Avg # obs.	144.6	304.8	308.6	362.2	313.5
Avg # obs. (padding)	9,216.0	92,000.0	1,692.0	1,573.2	1,685.0

Table 1: Summary of five irregular time series datasets.

Algorithm		MIMIC-III	MIMIC-IV	PhysioNet’12	Human Activity	USHCN	Vs Ours
PrimeNet	original	9.04 $\pm$ 0.00	6.25 $\pm$ 0.00	7.93 $\pm$ 0.00	26.84 $\pm$ 0.02	4.57 $\pm$ 0.00
PrimeNet	$+$ ReIMTS	4.76 $\pm$ 0.19	3.58 $\pm$ 0.03	3.01 $\pm$ 0.03	0.82 $\pm$ 0.02	1.71 $\pm$ 0.06	$\uparrow$ 62.3%
mTAN	original	8.51 $\pm$ 0.14	5.09 $\pm$ 0.12	3.75 $\pm$ 0.02	0.89 $\pm$ 0.03	5.65 $\pm$ 0.67
mTAN	$+$ ReIMTS	6.37 $\pm$ 0.05	4.04 $\pm$ 0.10	3.51 $\pm$ 0.02	0.89 $\pm$ 0.01	1.70 $\pm$ 0.01	$\uparrow$ 24.3%
TimeCHEAT	original	4.41 $\pm$ 0.05	2.50 $\pm$ 0.01	3.27 $\pm$ 0.11	0.68 $\pm$ 0.04	1.73 $\pm$ 0.04
TimeCHEAT	$+$ ReIMTS	4.40 $\pm$ 0.03	2.02 $\pm$ 0.03	2.90 $\pm$ 0.01	0.52 $\pm$ 0.01	1.62 $\pm$ 0.06	$\uparrow$ 12.1%

Table 2: Experimental results for our method (

+

ReIMTS ) with respective baselines, evaluated by MSE (mean

\pm

std)

\times 10^{-1}

on five irregular multivariate time series datasets. The best results are indicated in bold . Average improvements (error reductions) are marked with

\uparrow

Algorithm		MIMIC-III	MIMIC-IV	PhysioNet’12	Human Activity	USHCN
Regular	MOIRAI	8.66 $\pm$ 0.00	4.29 $\pm$ 0.00	4.92 $\pm$ 0.00	1.08 $\pm$ 0.00	12.14 $\pm$ 0.00
	Ada-MSHyper	6.16 $\pm$ 0.01	3.89 $\pm$ 0.01	4.06 $\pm$ 0.02	1.48 $\pm$ 0.04	2.36 $\pm$ 0.07
	Autoformer	7.08 $\pm$ 0.08	5.45 $\pm$ 0.16	4.14 $\pm$ 0.04	0.98 $\pm$ 0.07	4.12 $\pm$ 0.29
	Scaleformer	5.50 $\pm$ 0.07	4.55 $\pm$ 0.13	4.02 $\pm$ 0.02	1.01 $\pm$ 0.05	5.18 $\pm$ 0.96
	TimesNet	5.78 $\pm$ 0.01	3.82 $\pm$ 0.01	4.08 $\pm$ 0.01	1.21 $\pm$ 0.03	2.20 $\pm$ 0.09
	NHITS	5.83 $\pm$ 0.01	3.95 $\pm$ 0.01	3.84 $\pm$ 0.01	0.98 $\pm$ 0.01	3.09 $\pm$ 0.19

Table 3: Experimental results for other state-of-the-art regular and irregular baselines on five irregular multivariate time series datasets evaluated by MSE (mean

\pm

std)

\times 10^{-1}

. The best and second-best results are indicated in bold and underlined , respectively. ‘ME’ indicates memory error.

Ablation	MIMIC-III	MIMIC-IV	PhysioNet’12	Human Activity	USHCN
ReIMTS	4.07 $\pm$ 0.02	1.79 $\pm$ 0.05	2.83 $\pm$ 0.01	0.42 $\pm$ 0.00	1.66 $\pm$ 0.02
rp sample	4.99 $\pm$ 0.05	1.92 $\pm$ 0.04	2.83 $\pm$ 0.01	0.45 $\pm$ 0.01	1.69 $\pm$ 0.03
rp split	5.02 $\pm$ 0.04	2.36 $\pm$ 0.03	3.20 $\pm$ 0.01	0.61 $\pm$ 0.02	2.31 $\pm$ 0.09
rp IARF	4.20 $\pm$ 0.02	1.84 $\pm$ 0.02	2.79 $\pm$ 0.00	0.47 $\pm$ 0.01	1.89 $\pm$ 0.05
w/o IARF	4.77 $\pm$ 0.08	2.07 $\pm$ 0.04	3.06 $\pm$ 0.00	0.54 $\pm$ 0.00	1.69 $\pm$ 0.04

Table 4: Ablation results of ReIMTS and its four variants on five irregular multivariate time series datasets using GraFITi as the backbone.

Figure 4: Model efficiency comparison on MIMIC-III, with a 36-hour lookback length, 3 forecast timestamps, 96 variables, and a batch size of 32. ReIMTS uses GraFITi as backbone in the figure, which achieves the best efficiency compared to other multi-scale IMTS methods, including Warpformer, HD-TTS, and Hi-Patch.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Scale level	MIMIC-III	MIMIC-IV	PhysioNet’12	Human Activity	USHCN
2	4.09 $\pm$ 0.03	1.79 $\pm$ 0.05	2.86 $\pm$ 0.01	0.42 $\pm$ 0.00	1.66 $\pm$ 0.02
3	4.07 $\pm$ 0.02	1.95 $\pm$ 0.05	2.83 $\pm$ 0.01	0.71 $\pm$ 0.00	1.80 $\pm$ 0.03
4	4.10 $\pm$ 0.02	2.00 $\pm$ 0.02	2.84 $\pm$ 0.01	0.44 $\pm$ 0.00	2.01 $\pm$ 0.02

Appendix

Table 5: Effect of the number of scale levels on five datasets. A larger number of scale levels performs better on datasets with longer maximum lengths and a sufficient number of samples.

Panel of Figure 5 — Figure 5: Effect of different time period lengths on PhysioNet’12, Human Activity, and USHCN.

Algorithm		MIMIC-III	MIMIC-IV	PhysioNet’12	Human Activity	USHCN	Vs Ours
Regular	MOIRAI	5.79 $\pm$ 0.00	4.00 $\pm$ 0.00	4.94 $\pm$ 0.00	1.91 $\pm$ 0.00	8.18 $\pm$ 0.00
	Ada-MSHyper	5.22 $\pm$ 0.00	4.28 $\pm$ 0.01	4.50 $\pm$ 0.00	2.61 $\pm$ 0.04	3.25 $\pm$ 0.07
	Autoformer	5.47 $\pm$ 0.03	5.20 $\pm$ 0.00	4.53 $\pm$ 0.03	2.18 $\pm$ 0.06	3.84 $\pm$ 0.12
	Scaleformer	4.93 $\pm$ 0.03	4.64 $\pm$ 0.08	4.45 $\pm$ 0.02	2.25 $\pm$ 0.05	3.37 $\pm$ 0.12
	TimesNet	5.03 $\pm$ 0.01	4.25 $\pm$ 0.01	4.54 $\pm$ 0.01	2.26 $\pm$ 0.02	3.19 $\pm$ 0.04
	NHITS	4.92 $\pm$ 0.01	4.13 $\pm$ 0.01	4.29 $\pm$ 0.01	2.16 $\pm$ 0.01	3.63 $\pm$ 0.06

Appendix

Table 6: Experimental results on five irregular multivariate time series datasets, evaluated using MAE (mean

\pm

std)

\times 10^{-1}

. The experimental setup is the same as in Table 3 . ‘ME’ indicates Memory Error.

Algorithm		MIMIC-III	MIMIC-IV	PhysioNet’12	Human Activity	USHCN	Vs Ours
Regular	MOIRAI	9.68 $\pm$ 0.00	4.75 $\pm$ 0.00	5.36 $\pm$ 0.00	1.02 $\pm$ 0.00	8.85 $\pm$ 0.00
	Ada-MSHyper	6.73 $\pm$ 0.05	4.30 $\pm$ 0.03	4.46 $\pm$ 0.02	1.60 $\pm$ 0.01	4.30 $\pm$ 0.03
	Scaleformer	7.36 $\pm$ 0.08	4.84 $\pm$ 0.11	4.34 $\pm$ 0.03	1.54 $\pm$ 0.04	4.97 $\pm$ 0.06
	NHITS	7.43 $\pm$ 0.02	5.16 $\pm$ 0.20	4.60 $\pm$ 0.01	1.10 $\pm$ 0.01	4.52 $\pm$ 0.09
	Pyraformer	6.49 $\pm$ 0.02	4.71 $\pm$ 0.00	4.30 $\pm$ 0.01	1.23 $\pm$ 0.01	3.99 $\pm$ 0.03
	PatchTST	5.90 $\pm$ 0.01	3.36 $\pm$ 0.00	3.91 $\pm$ 0.01	0.87 $\pm$ 0.01	4.28 $\pm$ 0.04

Appendix

Table 7: Experimental results of varying forecast horizons on five irregular multivariate time series datasets evaluated using MSE (mean

\pm

std)

\times 10^{-1}

, with the lookback length following Table 3 and forecast horizons set to the rest length of the whole series, which are 12 hours for MIMIC-III, MIMIC-IV, and PhysioNet’12, 1000 milliseconds for Human Activity, and 1 year for USHCN. ‘ME’ indicates memory error.

Panel of Figure 6 — Figure 6: Efficiency comparisons on MIMIC-IV, PhysioNet’12, Human Activity, and USHCN with a batch size of 32. ReIMTS demonstrates significantly lower GPU memory usage than other multi-scale methods Warpformer, HD-TTS, and Hi-Patch on most datasets, while maintaining similar training time. Compared to the original backbone GraFITi, ReIMTS achieves comparable efficiency.

Panel of Figure 7 — Figure 7: Visualization of forecast results on all five datasets, under the same settings as in Table 2 . Compared to original backbone GraFITi (in green), ReIMTS (in orange) is closer to the ground truth (in blue).

Panel of Figure 8 — Figure 8: The t-SNE visualization of multi-scale representations in ReIMTS+GRU-D on classification dataset PAM. Red boxs indicate the region of interest, which mainly contain samples from class 2. (a) Without ReIMTS, samples from class 2 are very close to ones from class 5 and 7. (b) After applying ReIMTS, samples from class 2 are more distant from others, leading to improved performance. It should be noted that class 3 and class 2 have similar colors, where samples from class 3 are mostly outside of the region of interest.

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