Domain Generalization under Sampling Pattern Shifts in Irregular Time Series

Changhun Kim; Joohyung Lee; Kwanhyung Lee; Donghwee Yoon; Grigorios Chrysos; Eunho Yang

cs.LGSep 27, 2026

Domain Generalization under Sampling Pattern Shifts in Irregular Time Series

Authors: Changhun Kim, Joohyung Lee, Kwanhyung Lee, Donghwee Yoon, Grigorios Chrysos, Eunho Yang

Organizations: University of Wisconsin–Madison · AITRICS · KAIST

Abstract

Irregularly sampled multivariate time series (ISMTS) are prevalent in real-world applications, where both observation times and available measurements can vary substantially across domains. While recent models increasingly exploit such sampling information for prediction, its robustness under sampling pattern shifts remains underexplored. We introduce HAR-C, to the best of our knowledge the first controlled benchmark for sampling pattern shifts in ISMTS, and show that sampling shifts alone can substantially degrade performance, induce sampling-specific shortcuts, and remain challenging for existing domain generalization (DG) methods. Motivated by these findings, we propose PRISM, a DG framework that first learns complementary feature-centric and sampling-centric representations without task labels, and subsequently performs robust supervised training across diverse sampling variations to discourage brittle shortcut reliance. Extensive experiments on controlled and real-world ISMTS benchmarks demonstrate that PRISM consistently improves robustness to unseen sampling shifts over existing methods. Our code is available at https://anonymous.4open.science/r/PRISM.

Figures & tables

Figure 1: Hospital-level sampling pattern variations on eICU dataset.

Algorithm	Random	Regular	Desync	Fixed-Feat.	Rand-Feat.	First	Last	Mid	Avg.
ERM	79.92 $\pm$ 0.55	80.97 $\pm$ 0.81	68.91 $\pm$ 0.98	54.05 $\pm$ 4.27	54.48 $\pm$ 0.26	67.25 $\pm$ 1.52	61.10 $\pm$ 3.20	65.06 $\pm$ 2.50	66.47 $\pm$ 0.95
ARM	80.39 $\pm$ 0.49	81.32 $\pm$ 0.82	68.15 $\pm$ 0.92	56.54 $\pm$ 3.56	56.74 $\pm$ 0.65	73.12 $\pm$ 0.88	70.54 $\pm$ 0.87	72.18 $\pm$ 1.04	69.87 $\pm$ 0.60
CORAL	80.05 $\pm$ 0.54	81.51 $\pm$ 0.67	70.26 $\pm$ 1.22	53.97 $\pm$ 3.49	54.91 $\pm$ 0.48	67.12 $\pm$ 1.90	60.34 $\pm$ 3.60	67.10 $\pm$ 2.86	66.91 $\pm$ 0.88
DANN	81.94 $\pm$ 0.24	82.72 $\pm$ 0.73	70.30 $\pm$ 0.90	51.82 $\pm$ 4.97	54.41 $\pm$ 0.53	69.21 $\pm$ 1.25	60.59 $\pm$ 2.66	68.12 $\pm$ 1.20	67.39 $\pm$ 0.98
GroupDRO	79.86 $\pm$ 0.21	81.41 $\pm$ 0.55	68.45 $\pm$ 0.84	54.79 $\pm$ 3.99	55.01 $\pm$ 0.43	66.53 $\pm$ 1.08	61.43 $\pm$ 2.15	66.78 $\pm$ 1.51	66.78 $\pm$ 0.68
IB_ERM	80.51 $\pm$ 0.45	81.45 $\pm$ 0.84	68.94 $\pm$ 0.97	53.87 $\pm$ 4.17	56.10 $\pm$ 0.53	64.53 $\pm$ 1.34	61.17 $\pm$ 3.46	66.10 $\pm$ 2.81	66.58 $\pm$ 1.26

Table 1: Comparison of PRISM and existing DG methods on HAR-C. Models are evaluated on the source-matched Random condition and seven target sampling pattern shifts.

Algorithm	Northeast		West		South		Midwest		Avg.
Algorithm	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
ERM	85.30 $\pm$ 0.20	57.91 $\pm$ 0.35	76.89 $\pm$ 0.20	43.77 $\pm$ 0.19	78.59 $\pm$ 0.20	40.96 $\pm$ 0.28	78.09 $\pm$ 0.34	37.27 $\pm$ 0.98	79.72 $\pm$ 0.15	44.98 $\pm$ 0.25
ARM	74.08 $\pm$ 1.25	45.82 $\pm$ 0.99	68.76 $\pm$ 1.18	37.86 $\pm$ 1.05	69.96 $\pm$ 1.30	33.90 $\pm$ 0.76	72.64 $\pm$ 0.48	31.48 $\pm$ 0.47	71.36 $\pm$ 0.60	37.26 $\pm$ 0.43
CORAL	85.08 $\pm$ 0.24	58.16 $\pm$ 0.27	76.99 $\pm$ 0.29	43.75 $\pm$ 0.33	79.47 $\pm$ 0.18	41.97 $\pm$ 0.20	78.58 $\pm$ 0.14	39.25 $\pm$ 0.25	80.03 $\pm$ 0.08	45.78 $\pm$ 0.11
DANN	83.28 $\pm$ 0.31	55.97 $\pm$ 0.40	77.90 $\pm$ 0.18	44.64 $\pm$ 0.35	77.38 $\pm$ 0.29	40.04 $\pm$ 0.36	77.19 $\pm$ 0.31	35.29 $\pm$ 0.57	78.94 $\pm$ 0.16	43.98 $\pm$ 0.24
GroupDRO	84.36 $\pm$ 0.30	57.40 $\pm$ 0.27	76.99 $\pm$ 0.27	43.85 $\pm$ 0.33	77.33 $\pm$ 0.33	39.32 $\pm$ 0.36	77.39 $\pm$ 0.39	37.76 $\pm$ 0.45	79.02 $\pm$ 0.13	44.58 $\pm$ 0.16

Table 2: Comparison of PRISM and existing DG methods on eICU under leave-one-region-out evaluation. AUROC and AUPRC are reported for Northeast, West, South, and Midwest target regions.

Incremental construction
Variant	HAR-C		eICU
Variant	Avg.	Worst	AUROC	AUPRC
ERM	66.47 $\pm$ 0.95	54.05 $\pm$ 4.27	79.72 $\pm$ 0.15	44.98 $\pm$ 0.25
+ Complementary pretraining	72.02 $\pm$ 0.43	56.29 $\pm$ 3.73	81.87 $\pm$ 0.07	47.58 $\pm$ 0.15
+ Sampling variations	79.58 $\pm$ 0.17	73.85 $\pm$ 0.18	82.17 $\pm$ 0.07	47.91 $\pm$ 0.15
+ Worst-view objective (PRISM)	80.57 $\pm$ 0.19	74.72 $\pm$ 0.21	82.47 $\pm$ 0.04	48.25 $\pm$ 0.08

Table 3: Ablation study of PRISM. Top: incremental construction from ERM. Bottom: component removal. Worst: lowest target-condition accuracy on HAR-C. eICU results are averaged over regions.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

	HAR-C	eICU	PAM
Task	Activity recognition	In-hospital mortality	Activity recognition
# Classes	6	2	7
# Features $F$	6	11	12
Sequence length $T$	128	24	50
Time window	2.56 s	24 h	—
Observed fraction	20% (25/128 steps)	38.5% (native)	24.9% (native)

Appendix

Table A4: Dataset statistics for the three benchmarks. Observed fraction is the share of the

T\times F

lattice that carries a measurement: on HAR-C it is injected by subsampling a fully observed signal at a 20% rate (

\lfloor 128\times 0.2\rfloor=25

of 128 steps, synchronised across channels), whereas on eICU and PAM it is the native charting or recording density. eICU is evaluated leave-one-region-out, so its split sizes depend on the held-out region; the Northeast fold is shown, with negative / positive mortality counts in parentheses. HAR-C holds out 20% of the training subjects for validation.

Dataset	Pretrain $(r_{t},r_{f})$	Downstream $(r_{t},r_{f})$	$K$
HAR-C	$(0.5,0.4)$	$(0.5,0.4)$	4
PAM	$(0.5,0.4)$	$(0.5,0.4)$	4
eICU	$(0.5,0)$	$(0.2,0)$	4

Appendix

Table A5: Sampling augmentation settings used for pretraining and downstream robust learning.

Algorithm	Bias-aligned	Unbiased	Bias-conflicting
ERM	93.99 $\pm$ 2.44	58.00 $\pm$ 0.69	42.59 $\pm$ 1.86
ARM	77.51 $\pm$ 1.30	57.61 $\pm$ 1.35	44.36 $\pm$ 1.56
CORAL	97.76 $\pm$ 0.15	54.54 $\pm$ 0.69	34.89 $\pm$ 0.94
DANN	98.03 $\pm$ 0.08	57.79 $\pm$ 0.61	40.18 $\pm$ 0.95
GroupDRO	97.48 $\pm$ 0.18	57.67 $\pm$ 0.76	40.83 $\pm$ 1.20
IB_ERM	93.20 $\pm$ 2.91	54.87 $\pm$ 0.73	36.73 $\pm$ 1.24

Appendix

Table A6: Sampling-specific shortcut analysis on HAR-C at

\rho=0.9

. At test time, the sampling cue is bias-aligned, unbiased, or bias-conflicting with the ground-truth label.

Algorithm	10%	20%	30%	40%	50%	Avg.
ERM	85.46 $\pm$ 0.47	79.67 $\pm$ 1.54	67.82 $\pm$ 3.54	57.24 $\pm$ 4.85	50.33 $\pm$ 4.66	68.11 $\pm$ 2.39
ARM	85.63 $\pm$ 0.43	80.10 $\pm$ 1.75	69.86 $\pm$ 3.96	59.39 $\pm$ 4.45	53.35 $\pm$ 5.04	69.66 $\pm$ 2.55
CORAL	85.85 $\pm$ 0.45	80.51 $\pm$ 1.73	69.01 $\pm$ 3.92	59.70 $\pm$ 4.82	53.87 $\pm$ 4.90	69.79 $\pm$ 2.69
DANN	85.34 $\pm$ 0.46	79.51 $\pm$ 1.73	69.01 $\pm$ 3.68	57.30 $\pm$ 4.23	52.03 $\pm$ 4.65	68.64 $\pm$ 2.31
GroupDRO	85.65 $\pm$ 0.32	79.47 $\pm$ 1.59	67.52 $\pm$ 3.23	57.31 $\pm$ 3.93	51.26 $\pm$ 4.15	68.24 $\pm$ 2.16
IB_ERM	85.66 $\pm$ 0.37	80.49 $\pm$ 1.44	68.58 $\pm$ 3.67	58.78 $\pm$ 4.34	52.14 $\pm$ 4.40	69.13 $\pm$ 2.33

Appendix

Table A7: Comparison of PRISM and existing DG methods on PAM under leave-fixed-sensors-out evaluation. A fixed fraction of sensors is entirely unobserved at test time, with the missing-sensor ratio varied from 10% to 50%.

Pretraining objective
Variant	Random	Regular	Desync	Fixed-Feat.	Rand-Feat.	First	Last	Mid	Avg.
ERM	79.92 $\pm$ 0.55	80.97 $\pm$ 0.81	68.91 $\pm$ 0.98	54.05 $\pm$ 4.27	54.48 $\pm$ 0.26	67.25 $\pm$ 1.52	61.10 $\pm$ 3.20	65.06 $\pm$ 2.50	66.47 $\pm$ 0.95
w/o $\mathcal{L}_{\mathrm{feat}}$ & w/o sampling variations	81.12 $\pm$ 0.39	83.47 $\pm$ 0.42	73.29 $\pm$ 0.90	55.18 $\pm$ 3.88	57.09 $\pm$ 0.63	73.36 $\pm$ 1.00	70.89 $\pm$ 2.31	72.31 $\pm$ 1.50	70.84 $\pm$ 0.68
w/o $\mathcal{L}_{\mathrm{samp}}$ & w/o sampling variations	82.86 $\pm$ 0.25	85.61 $\pm$ 0.33	78.93 $\pm$ 0.55	58.59 $\pm$ 3.49	58.32 $\pm$ 0.57	75.47 $\pm$ 0.62	66.17 $\pm$ 1.44	70.67 $\pm$ 0.91	72.08 $\pm$ 0.70
w/o $\mathcal{L}_{\mathrm{feat}}$	83.47 $\pm$ 0.20	85.73 $\pm$ 0.15	82.50 $\pm$ 0.28	74.60 $\pm$ 1.15	74.36 $\pm$ 0.25	80.66 $\pm$ 0.20	78.87 $\pm$ 0.23	79.98 $\pm$ 0.29	80.02 $\pm$ 0.14
w/o $\mathcal{L}_{\mathrm{samp}}$	84.08 $\pm$ 0.13	86.31 $\pm$ 0.21	83.07 $\pm$ 0.16	74.50 $\pm$ 1.19	74.68 $\pm$ 0.18	81.01 $\pm$ 0.14	79.27 $\pm$ 0.24	80.84 $\pm$ 0.23	80.47 $\pm$ 0.15

Appendix

Table A8: Ablation study of PRISM on HAR-C. We ablate

\mathcal{L}_{\mathrm{feat}}

\mathcal{L}_{\mathrm{samp}}

E_{\mathrm{feat}}

E_{\mathrm{samp}}

, and the sampling-variation and worst-view components of downstream training.

Pretraining objective
Variant	Northeast		West		South		Midwest		Avg.
Variant	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC	AUROC	AUPRC
ERM ( Vapnik, 1991 )	85.30 $\pm$ 0.20	57.91 $\pm$ 0.35	76.89 $\pm$ 0.20	43.77 $\pm$ 0.19	78.59 $\pm$ 0.20	40.96 $\pm$ 0.28	78.09 $\pm$ 0.34	37.27 $\pm$ 0.98	79.72 $\pm$ 0.15	44.98 $\pm$ 0.25
w/o $\mathcal{L}_{\mathrm{feat}}$ & w/o sampling variations	83.75 $\pm$ 0.25	55.65 $\pm$ 0.52	77.94 $\pm$ 0.16	44.70 $\pm$ 0.26	76.71 $\pm$ 0.21	38.52 $\pm$ 0.30	76.89 $\pm$ 0.21	35.66 $\pm$ 0.47	78.82 $\pm$ 0.07	43.63 $\pm$ 0.15
w/o $\mathcal{L}_{\mathrm{samp}}$ & w/o sampling variations	86.04 $\pm$ 0.10	58.48 $\pm$ 0.24	78.12 $\pm$ 0.11	44.86 $\pm$ 0.25	79.41 $\pm$ 0.18	41.41 $\pm$ 0.32	79.23 $\pm$ 0.15	37.85 $\pm$ 0.34	80.70 $\pm$ 0.06	45.65 $\pm$ 0.15
w/o $\mathcal{L}_{\mathrm{feat}}$	85.08 $\pm$ 0.09	57.62 $\pm$ 0.27	78.69 $\pm$ 0.19	45.61 $\pm$ 0.25	79.42 $\pm$ 0.08	42.05 $\pm$ 0.12	79.76 $\pm$ 0.16	40.25 $\pm$ 0.20	80.74 $\pm$ 0.07	46.38 $\pm$ 0.06

Appendix

Table A9: Ablation study of PRISM on eICU under leave-one-region-out evaluation. We evaluate the same pretraining, encoder, and downstream-objective ablations as on HAR-C across the four target regions.

Algorithm	Random	Regular	Desync	Fixed-Feat.	Rand-Feat.	First	Last	Mid	Avg.
Medium CNN
ERM	77.78 $\pm$ 0.17	81.25 $\pm$ 0.57	66.81 $\pm$ 0.95	54.98 $\pm$ 3.12	55.85 $\pm$ 0.48	69.82 $\pm$ 0.81	65.24 $\pm$ 1.24	69.09 $\pm$ 0.91	67.60 $\pm$ 0.38
MLDG	80.48 $\pm$ 0.21	84.03 $\pm$ 0.29	71.75 $\pm$ 0.91	56.36 $\pm$ 2.86	55.55 $\pm$ 0.50	71.67 $\pm$ 1.28	67.01 $\pm$ 0.97	72.34 $\pm$ 0.54	69.90 $\pm$ 0.43
ManyDG	78.92 $\pm$ 0.45	82.90 $\pm$ 0.47	70.24 $\pm$ 0.62	52.69 $\pm$ 2.95	55.00 $\pm$ 0.61	71.12 $\pm$ 1.09	63.35 $\pm$ 1.41	69.44 $\pm$ 1.05	67.96 $\pm$ 0.75
Mixup	79.61 $\pm$ 0.32	59.91 $\pm$ 4.40	45.72 $\pm$ 2.87	45.48 $\pm$ 3.00	42.73 $\pm$ 2.06	60.02 $\pm$ 1.67	40.90 $\pm$ 2.61	53.13 $\pm$ 2.42	53.44 $\pm$ 1.87
MMD	77.94 $\pm$ 0.33	80.97 $\pm$ 0.57	67.86 $\pm$ 0.63	56.98 $\pm$ 2.78	55.80 $\pm$ 0.44	69.27 $\pm$ 0.83	63.39 $\pm$ 1.08	68.21 $\pm$ 0.89	67.55 $\pm$ 0.33

Appendix

Table A10: Architecture generalization on HAR-C. We compare PRISM and DG baselines across Medium CNN, Large CNN, SeFT, mTAND, and GRU-D under the eight sampling conditions.

Figure A10: Examples of HAR-C observations under diverse sampling pattern shifts. Each condition retains 150 observations while varying their temporal and feature-wise locations; color indicates the standardized feature value.

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ITGPT: Generative Pretraining on Irregular Timeseries

Antoine Honoré, Ming Xiao

⋆Division of Information Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden

Time Series Single-Cell Foundation Models Self-Supervised Learning Transformer Architectures Openai

Open paper AskPDF arXiv

Timeseries regression models often struggle to leverage large volumes of labeled multimodal data, particularly when the data are irregularly sampled or contain missing values. This is common in domains like healthcare and predictive maintenance, where data are collected from unreliable sources, and labeling requires expert knowledge or costly equipments. Transformer-based large language models have proven effective on structured data such as text through self-supervised learning (SSL) and generative pretraining (GPT) frameworks. However, such models lack the flexibility to efficiently process irregularly sampled multimodal timeseries data. In this paper, we introduce ITGPT, an attention-based architecture designed for handling multimodal, irregularly sampled timeseries by allowing training with both SSL losses and GPT-like objectives. We evaluate its performance on a healthcare task with the TIHM dataset, and a predictive maintenance task with the CompX dataset. Our results demonstrate that ITGPT achieves state-of-the-art performance without requiring resampling, feature fusion or explicit data imputation. Furthermore, when labels are scarce, ITGPT effectively leverages unlabeled data through SSL and GPT training, outperforming the purely supervised approach. This represents an important step towards efficiently using large and unstructured timeseries datasets for practical inference tasks.

Abstract

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