DBGL: Decay-aware Bipartite Graph Learning for Irregular Medical Time Series Classification

Jian Chen; Yuzhu Hu; Xiaoyan Yuan; Yuxuan Hu; Jinfeng Xu; Yipeng Du; Wenhao Yuan; Wei Wang

cs.LGApr 12, 2026

DBGL: Decay-aware Bipartite Graph Learning for Irregular Medical Time Series Classification

Authors: Jian Chen, Yuzhu Hu, Xiaoyan Yuan, Yuxuan Hu, Jinfeng Xu, Yipeng Du, Wenhao Yuan, Wei Wang,

Organizations: Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China · Shenzhen MSU-BIT University, China · Department of Data Science, City University of Hong Kong, China · Engineering Research Centre of Applied Technology on Machine Translation and Artificial Intelligence, Macao Polytechnic University

Abstract

Irregular Medical Time Series play a critical role in the clinical domain to better understand the patient's condition. However, inherent irregularity arising from heterogeneous sampling rates, asynchronous observations, and variable gaps poses key challenges for reliable modeling. Existing methods often distort temporal sampling irregularity and missingness patterns while failing to capture variable decay irregularity, resulting in suboptimal representations. To address these limitations, we introduce DBGL, Decay-Aware Bipartite Graph Learning for Irregular Medical Time Series. DBGL first introduces a patient-variable bipartite graph that simultaneously captures irregular sampling patterns without artificial alignment and adaptively models variable relationships for temporal sampling irregularity modeling, enhancing representation learning. To model variable decay irregularity, DBGL designs a novel node-specific temporal decay encoding mechanism that captures each variable's decay rates based on sampling interval, yielding a more accurate and faithful representation of irregular temporal dynamics. We evaluate the performance of DBGL on four publicly available datasets, and the results show that DBGL outperforms all baselines.

Figures & tables

Variable	$\lambda$	Variable	$\lambda$
HR	1.73	Temp	0.0265
Creatinine	0.1399	Lactate	13.00
ALP	14.71	PaCO2	0.0225
ALT	14.62	AST	13.89

Table 1: Representative variable decay rates (

\lambda

) on the P12 dataset.

Figure 1: Framework of our proposed DBGL. DBGL first models the IMTS as patient-variable bipartite graphs. Furthermore, a novel mechanism called temporal decay encoding with node-specific updates is used to obtain a robust representation for classification.

	Methods	P19		Physionet		MIMIC-III		P12
	Methods	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
Non-Graph	GRU-D	88.7 $\pm$ 1.2	57.6 $\pm$ 2.3	79.1 $\pm$ 6.9	42.7 $\pm$ 7.2	82.2 $\pm$ 1.8	43.3 $\pm$ 2.1	79.6 $\pm$ 0.6	41.7 $\pm$ 1.8
	ODE-RNN	87.1 $\pm$ 1.0	52.6 $\pm$ 3.2	75.5 $\pm$ 2.8	33.7 $\pm$ 4.1	81.0 $\pm$ 0.6	42.3 $\pm$ 0.7	78.8 $\pm$ 0.6	37.4 $\pm$ 2.6
	IP-Net	90.2 $\pm$ 0.2	58.6 $\pm$ 0.8	86.8 $\pm$ 0.6	55.8 $\pm$ 1.4	84.1 $\pm$ 0.1	47.1 $\pm$ 0.9	83.7 $\pm$ 0.3	46.3 $\pm$ 1.3
	SeFT	84.0 $\pm$ 0.3	49.3 $\pm$ 0.5	75.5 $\pm$ 0.2	29.4 $\pm$ 0.9	67.9 $\pm$ 0.2	23.2 $\pm$ 0.4	78.1 $\pm$ 0.5	35.9 $\pm$ 0.8
	mTAND	82.9 $\pm$ 0.9	32.3 $\pm$ 1.5	86.9 $\pm$ 1.3	52.5 $\pm$ 1.3	83.8 $\pm$ 0.3	46.6 $\pm$ 0.5	85.3 $\pm$ 0.3	49.3 $\pm$ 1.0

Table 2: Performance comparison (AUROC & AUPRC, %). The best results are in bold and the second-best results are in underlined .

Method	10%		20%		30%		40%		50%
Method	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
GRU-D	68.6 $\pm$ 2.3	35.8 $\pm$ 2.2	68.2 $\pm$ 2.1	34.5 $\pm$ 2.9	66.8 $\pm$ 3.3	32.7 $\pm$ 4.6	65.8 $\pm$ 4.0	31.3 $\pm$ 5.2	65.1 $\pm$ 4.1	30.4 $\pm$ 5.5
mTAND	74.9 $\pm$ 0.6	37.7 $\pm$ 0.6	74.0 $\pm$ 1.3	36.5 $\pm$ 1.5	71.4 $\pm$ 3.8	34.1 $\pm$ 3.7	70.6 $\pm$ 3.6	33.2 $\pm$ 3.7	70.1 $\pm$ 3.5	32.5 $\pm$ 3.6
$\text{DGM}^{2}$ -O	76.3 $\pm$ 1.1	39.3 $\pm$ 1.5	76.1 $\pm$ 1.1	38.2 $\pm$ 1.7	74.8 $\pm$ 2.2	36.8 $\pm$ 2.6	72.0 $\pm$ 5.3	34.3 $\pm$ 5.0	70.4 $\pm$ 5.9	32.7 $\pm$ 5.7
MTGNN	71.2 $\pm$ 2.1	30.5 $\pm$ 1.5	70.3 $\pm$ 3.3	29.7 $\pm$ 2.8	68.9 $\pm$ 4.2	28.5 $\pm$ 3.3	68.1 $\pm$ 4.7	27.7 $\pm$ 3.6	67.6 $\pm$ 5.2	27.2 $\pm$ 3.8
Raindrop	73.2 $\pm$ 1.6	32.4 $\pm$ 0.9	73.0 $\pm$ 1.6	31.7 $\pm$ 1.1	72.2 $\pm$ 2.6	31.1 $\pm$ 2.7	71.5 $\pm$ 3.5	30.6 $\pm$ 3.5	70.8 $\pm$ 4.2	29.7 $\pm$ 4.3

Table 3: Performance comparison (AUROC & AUPRC, %) under different variable discard ratios on P12 dataset. The best results are highlighted in bold and the second-best results are in underlined .

Figure 2: Comparison of Positive-class Predicted Probabilities.

Method	P19		Physionet		MIMIC-III		P12
	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
w/o TDE	92.9 $\pm$ 0.7	64.3 $\pm$ 2.0	88.7 $\pm$ 0.8	59.1 $\pm$ 2.2	84.6 $\pm$ 1.1	48.2 $\pm$ 2.4	87.2 $\pm$ 0.5	53.3 $\pm$ 1.9
w/o SNA	92.4 $\pm$ 0.6	65.0 $\pm$ 1.0	88.2 $\pm$ 1.1	56.7 $\pm$ 5.1	84.9 $\pm$ 0.3	49.1 $\pm$ 1.0	87.3 $\pm$ 0.6	53.3 $\pm$ 2.3
w/o HVS	92.3 $\pm$ 0.5	64.9 $\pm$ 1.2	87.1 $\pm$ 2.3	55.6 $\pm$ 3.8	84.5 $\pm$ 1.8	46.9 $\pm$ 4.1	86.9 $\pm$ 0.5	53.1 $\pm$ 0.8
w/o CB	92.8 $\pm$ 0.5	65.3 $\pm$ 1.4	88.5 $\pm$ 1.4	58.0 $\pm$ 4.8	84.9 $\pm$ 0.3	49.5 $\pm$ 0.9	87.7 $\pm$ 0.5	54.2 $\pm$ 1.7
w/o MCV	93.1 $\pm$ 0.3	66.1 $\pm$ 1.4	88.9 $\pm$ 0.5	59.5 $\pm$ 1.1	85.1 $\pm$ 0.2	50.0 $\pm$ 0.2	87.9 $\pm$ 0.2	54.6 $\pm$ 0.5

Table 4: Ablation study results (AUROC & AUPRC, %) on four clinical datasets. The best results are highlighted in bold .

Kernel	P19		Physionet		MIMIC-III		P12
	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
Exp	92.9 $\pm$ 0.3	65.2 $\pm$ 0.6	88.8 $\pm$ 0.7	58.2 $\pm$ 1.9	84.9 $\pm$ 0.2	49.9 $\pm$ 0.5	87.0 $\pm$ 0.3	53.0 $\pm$ 1.0
MLP + Linear	93.2 $\pm$ 0.7	65.6 $\pm$ 0.9	89.3 $\pm$ 0.4	60.8 $\pm$ 2.2	84.8 $\pm$ 0.2	49.5 $\pm$ 1.0	87.6 $\pm$ 0.3	54.2 $\pm$ 0.5
MLP + Gaussian	93.3 $\pm$ 0.4	66.1 $\pm$ 1.6	89.3 $\pm$ 0.4	60.7 $\pm$ 2.4	84.6 $\pm$ 0.9	48.3 $\pm$ 2.5	87.7 $\pm$ 0.5	54.5 $\pm$ 1.3
MLP + Exp	93.3 $\pm$ 0.5	66.3 $\pm$ 1.4	89.1 $\pm$ 0.3	60.8 $\pm$ 2.2	85.2 $\pm$ 0.4	50.2 $\pm$ 1.0	88.1 $\pm$ 0.4	56.3 $\pm$ 1.0

Table 5: Performance comparison of different kernel types (AUROC & AUPRC, %). The best results are highlighted in bold .

Figure 3: Comparison of graph construction.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Datasets	# Samples	# Variables	# Max Length	Missing Ratio	Task
P19	38803	34	60	94.9%	Sepsis Prediction
P12	11988	36	215	88.4%	Stay Predcition
MIMIC-III	21107	16	292	65.5%	Mortality Prediction
Physionet	3997	36	215	84.9%	Mortality Prediction

Appendix

Table 6: Dataset statistics

Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$
ALP	14.7113	FiO2	0.2458	NISysABP	6.0698	ALT	14.6235
GCS	1.0948	Na	0.0420	AST	13.8853	Glucose	0.0493
PaCO2	0.0225	Albumin	0.0853	HCO3	0.1094	PaO2	0.0280
BUN	0.0854	HCT	0.0379	Platelets	0.0505	Bilirubin	0.8760
HR	1.7301	RespRate	4.1157	Cholesterol	7.0000	K	0.0368
SaO2	0.0408	Creatinine	0.1399	Lactate	13.0000	SysABP	0.1403

Appendix

Table 7: Variable-specific decay rates (

\lambda

) on the P12 dataset. Higher

\lambda

indicates faster-changing.

Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$
Heart rate	0.0759	Temp	0.1131	BaseExcess	14.0	SpO2	0.0822
SBP	0.0813	HCO3	0.0900	MAP	0.0820	DBP	0.0798
FiO2	0.4244	Resp	0.0818	EtCO2	0.1071	pH	0.0953
PaCO2	0.7904	SaO2	16.0	AST	16.235	BUN	16.0
Alkalinephos	15.0	Calcium	0.1144	Chloride	0.0782	Creatinine	0.1134
Bilirubin_direct	15.0	Glucose	0.1376	Lactate	3.7805	Magnesium	0.0850

Appendix

Table 8: Variable-specific decay rates (

\lambda

) on the P19 dataset. Higher

\lambda

indicates faster-changing.

Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$
ALP	16.5173	ALT	14.4846	AST	16.0	Albumin	0.1164
BUN	0.0400	Bilirubin	14.0	Cholesterol	2.0	Creatinine	0.0502
DiasABP	0.0212	FiO2	0.3273	GCS	13.5627	Glucose	0.0586
HCO3	0.0791	HCT	0.0392	HR	12.0	K	0.0429
Lactate	12.8876	MAP	0.0371	MechVent	9.4304	Mg	14.0
NIDiasABP	0.0272	NIMAP	1.0679	NISysABP	11.0	Na	0.0441

Appendix

Table 9: Variable-specific decay rates (

\lambda

) on the Physionet dataset. Higher

\lambda

indicates faster-changing.

Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$
Weight	6098.3438	HR	11.8839	MAP	138.8822	DBP	4277.9697
SBP	581.1183	SpO2	2053.2156	RR	11829.0942	CRR	517.8212
Glucose	17.7346	pH	182.4216	Temperature	163.4556	FiO2	18.1914
GCS-EO	14.107	GCS-MR	26.0087	GCS-T	10.5168	GCS-VR	15.660

Appendix

Table 10: Variable-specific decay rates (

\lambda

) on the MIMIC-III dataset. Higher

\lambda

indicates faster-changing.

Dataset	Statistic	p-value
P12	668.4338	3.87e-118
P19	446.4491	5.97e-74
Physionet	267.0967	5.56e-38
MIMIC-III	697.995	4.97e-139

Appendix

Table 11: Kruskal–Wallis test results for variable-specific decay rates (

\lambda

) across datasets.

Model	Time (min/epoch)	Space (MiB)	AUPRC (%)
ODE-RNN	5.06	2582	33.7 $\pm$ 4.1
GRU-D	1.32	796	42.7 $\pm$ 7.2
SeFT	0.07	684	29.4 $\pm$ 0.9
mTAND	0.05	4658	52.5 $\pm$ 1.3
DGM 2 -O	0.06	684	50.4 $\pm$ 3.2
Raindrop	0.17	4864	41.2 $\pm$ 3.6

Appendix

Table 12: Training time and memory consumption per epoch of different models.

B	Space (MiB)	Time (s/epoch)	V	Space (MiB)	Time (s/epoch)	L	Space (MiB)	Time (s/epoch)	C	Space (MiB)	Time (s/epoch)
128	2670	56	36	3806	30	215	3806	30	512	2950	28
256	3806	30	72	5258	35	430	6294	66	1024	3064	28
512	6034	18	144	8154	48	860	11254	192	2048	3238	29
1024	10776	12	288	14208	71	1290	16316	338	4096	3806	30
2048	19700	9	432	20306	89	1720	21288	525	8172	4968	31

Appendix

Table 13: GPU memory usage and training time per epoch under different settings (B=batch size, V=number of variables, L=sequence length, C=codebook size).

Model	P19	Physionet	MIMIC-III	P12
KEDGN	0.11	0.14	0.61	0.29
DBGL	0.18	0.16	0.84	0.50

Appendix

Table 14: Inference time (seconds) of DBGL and KEDGN on four datasets.

Model	P19	Physionet	MIMIC-III	P12
KEDGN	1.76	0.93	5.92	1.61
DBGL	2.03	0.81	4.86	1.92

Appendix

Table 15: Training time per batch (seconds) of DBGL and KEDGN on four datasets.

Model	P19	PhysioNet	MIMIC-III	P12
KEDGN	10.9 $\pm$ 1.7 / 21.3 $\pm$ 3.0	15.8 $\pm$ 1.2 / 22.5 $\pm$ 2.4	15.8 $\pm$ 2.1 / 21.5 $\pm$ 4.2	15.0 $\pm$ 1.1 / 19.8 $\pm$ 1.7
DBGL	9.2 $\pm$ 1.6 / 18.2 $\pm$ 3.2	14.5 $\pm$ 1.5 / 21.1 $\pm$ 2.1	14.3 $\pm$ 1.0 / 20.0 $\pm$ 2.1	14.2 $\pm$ 1.4 / 18.9 $\pm$ 2.6

Appendix

Table 16: ECE (%) and Brier Score (%) comparison between DBGL and KEDGN across clinical datasets. Results are presented as mean

\pm

standard deviation.

Subset	P19		Physionet		MIMIC-III		P12
	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
Subset 1	90.8 $\pm$ 0.3	61.0 $\pm$ 1.6	87.0 $\pm$ 1.5	55.1 $\pm$ 4.5	83.7 $\pm$ 0.5	46.1 $\pm$ 1.2	85.9 $\pm$ 0.6	50.8 $\pm$ 1.0
Subset 2	91.0 $\pm$ 0.2	61.6 $\pm$ 1.2	86.5 $\pm$ 2.6	54.6 $\pm$ 3.3	84.0 $\pm$ 0.3	45.8 $\pm$ 1.3	85.7 $\pm$ 0.7	50.8 $\pm$ 1.9
All	93.3 $\pm$ 0.5	66.3 $\pm$ 1.4	89.1 $\pm$ 0.3	60.8 $\pm$ 2.2	85.2 $\pm$ 0.4	50.2 $\pm$ 1.0	88.1 $\pm$ 0.4	56.3 $\pm$ 1.0

Appendix

Table 17: Performance on different training subsets across four clinical datasets (AUROC & AUPRC, %).

ICU Type	Samples	AUROC
Medical ICU	3872	93.2 $\pm$ 0.5
SIC Surgical ICU	9	98.6 $\pm$ 2.9

Appendix

Table 18: P19 dataset: performance across ICU types.

ICU Type	Coronary Care Unit	Cardiac Surgery Recovery Unit	Medical ICU	SIC Surgical ICU
Samples	219	231	419	339
AUROC	81.9 $\pm$ 1.5	83.4 $\pm$ 1.9	85.0 $\pm$ 0.5	90.4 $\pm$ 0.3

Appendix

Table 19: P12 dataset: performance across ICU types.

ICU Type	Coronary Care Unit	Cardiac Surgery Recovery Unit	Medical ICU	SIC Surgical ICU
Samples	64	91	153	91
AUROC	90.3 $\pm$ 2.4	99.4 $\pm$ 0.6	84.8 $\pm$ 0.5	85.4 $\pm$ 1.2

Appendix

Table 20: Physionet dataset: performance across ICU types.

	Method	10%		20%		30%		40%		50%
	Method	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
MIMIC-III	GRU-D	81.0 $\pm$ 0.6	42.1 $\pm$ 0.8	80.3 $\pm$ 0.9	41.7 $\pm$ 1.0	79.2 $\pm$ 1.8	41.0 $\pm$ 1.4	78.5 $\pm$ 2.1	40.4 $\pm$ 1.6	77.9 $\pm$ 2.2	39.9 $\pm$ 1.8
	mTAND	81.2 $\pm$ 0.2	42.1 $\pm$ 0.8	80.4 $\pm$ 1.1	41.9 $\pm$ 1.2	79.7 $\pm$ 1.4	41.0 $\pm$ 1.7	79.3 $\pm$ 1.4	40.4 $\pm$ 2.0	78.8 $\pm$ 1.6	39.8 $\pm$ 2.3
	$\text{DGM}^{2}$ -O	78.8 $\pm$ 0.5	34.2 $\pm$ 0.9	78.3 $\pm$ 0.8	33.9 $\pm$ 1.1	77.6 $\pm$ 1.2	33.4 $\pm$ 1.2	77.3 $\pm$ 1.3	33.1 $\pm$ 1.2	76.8 $\pm$ 1.5	32.6 $\pm$ 1.4
	MTGNN	78.8 $\pm$ 1.1	34.5 $\pm$ 1.4	78.0 $\pm$ 1.6	34.0 $\pm$ 1.3	77.1 $\pm$ 2.2	33.5 $\pm$ 1.5	76.3 $\pm$ 2.5	32.8 $\pm$ 1.9	75.6 $\pm$ 3.2	32.2 $\pm$ 2.4
	Raindrop	78.2 $\pm$ 1.1	33.7 $\pm$ 0.9	77.5 $\pm$ 1.3	33.5 $\pm$ 0.9	76.4 $\pm$ 2.1	32.8 $\pm$ 1.4	76.0 $\pm$ 2.0	32.5 $\pm$ 1.4	75.7 $\pm$ 2.0	32.3 $\pm$ 1.4

Appendix

Table 21: Performance comparison (AUROC & AUPRC, %) under different discarding ratios on three clinical datasets. The best results are highlighted in bold and the second-best results are in underlined .

Figure 4: Effect of the number of EdgeSAGE layers.

Figure 5: Comparison of Positive-class Predicted Probabilities.

Dataset	P19	Physionet	MIMIC-III	P12
Utilization Rate	0.4973	0.4977	0.4982	0.4978

Appendix

Table 22: Soft codebook utilization rates across different datasets.

Panel of Figure 6 — Figure 6: T-SNE visualization of partial variable representations on three datasets.

Model	Accuracy (%)	Precision (%)	Recall (%)	F1 score (%)
Transformer	83.5 $\pm$ 1.5	84.8 $\pm$ 1.5	86.0 $\pm$ 1.2	85.0 $\pm$ 1.3
Trans-mean	83.7 $\pm$ 2.3	84.9 $\pm$ 2.6	86.4 $\pm$ 2.1	86.4 $\pm$ 2.1
GRU-D	83.3 $\pm$ 1.6	84.6 $\pm$ 1.2	84.6 $\pm$ 1.2	84.8 $\pm$ 1.2
SeFT	67.1 $\pm$ 2.2	70.0 $\pm$ 2.4	68.2 $\pm$ 1.5	68.5 $\pm$ 1.8
mTAND	74.6 $\pm$ 4.3	74.3 $\pm$ 4.0	79.5 $\pm$ 2.8	76.8 $\pm$ 3.4
IP-Net	74.3 $\pm$ 3.8	75.6 $\pm$ 2.1	77.9 $\pm$ 2.2	76.6 $\pm$ 2.8

Appendix

Table 23: Performance comparison of different models on the dataset. Values are reported as mean

\pm

std (%).

Variable	$\lambda$	Variable	$\lambda$	Variable	$\lambda$
v0	1.0451	v1	0.00887	v2	0.00662
v3	0.05265	v4	0.00910	v5	0.00660
v6	0.04641	v7	0.04618	v8	0.00823
v9	0.00720	v10	0.00836	v11	0.02725
v12	0.01110	v13	0.00728	v14	0.00806
v15	0.00756	v16	0.00714	—	—

Appendix

Table 24: Variable-specific

\lambda

values

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A Time-Aware Bag-of-Receptive-Fields for Interpretable Irregular Time Series Classification

Francesco Spinnato

Department of Computer Science, University of Pisa, Italy · ISTI-CNR, Pisa, Italy

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Irregular time series, characterized by non-uniform sampling intervals, missing observations, and variable lengths, are ubiquitous in healthcare, mobility, and environmental monitoring, yet effective and interpretable classifiers for this setting are limited. Existing approaches often rely on imputation, which can obscure the temporal structure of the data, or require complex neural architectures that are opaque and difficult to explain. In this work, we extend the Bag-Of-Receptive-Fields (BORF), a fast, deterministic, and interpretable transform for time series, to the irregular setting. Our key contribution is a time-weighted normalization scheme in which each observation is weighted proportionally to its associated time delta, making pattern extraction sensitive to the actual temporal distribution of samples rather than only their index position. This requires deriving an efficient sliding-window recurrence for the time-weighted standard deviation, preserving the linear time complexity of BORF. We benchmark the resulting method against state-of-the-art irregular time series classifiers on datasets from the PYRREGULAR repository, demonstrating competitive classification performance with the added benefit of human-interpretable explanations.

Abstract

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