Recurrent Neural Networks for Multivariate Time Series with Missing Values
Open accessAbstract
Multivariate time series data in practical applications, such as health care, geoscience, and biology, are characterized by a variety of missing values. In time series prediction and other related tasks, it has been noted that missing values and their missing patterns are often correlated with the target labels, a.k.a., informative missingness. There is very limited work on exploiting the missing patterns for effective imputation and improving prediction performance. In this paper, we develop novel deep learning models, namely GRU-D, as one of the early attempts. GRU-D is based on Gated Recurrent Unit (GRU), a state-of-the-art recurrent neural network. It takes two representations of missing patterns, i.e., masking and time interval, and effectively incorporates them into a deep model architecture so that it not only captures the long-term temporal dependencies in time series, but also utilizes the missing patterns to achieve better prediction results. Experiments of time series classification tasks on real-world clinical datasets (MIMIC-III, PhysioNet) and synthetic datasets demonstrate that our models achieve state-of-the-art performance and provide useful insights for better understanding and utilization of missing values in time series analysis.
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Existing GRU-D integrates temporal decay within its hidden states and an automated imputation mechanism to handle missing data, and consequently exhibits superior predictive accuracy compared to standard GRU on incomplete datasets.
“Existing GRU-D integrates temporal decay within its hidden states in conjunction with an automated imputation mechanism to handle missing data. Consequently, GRU-D exhibits superior predictive accuracy compared to the standard GRU architecture when applied to incomplete datasets.”
From AI-Driven Predictions of Readmission and Mortality for Improved Discharge Decisions in Critical Care: A Retrospective Study (2026) · cites this paper as [22]
Another dominant topic in the DL papers is completeness, which the ML community almost exclusively refers to as missing data.
“Another dominant topic is completeness to which the ML community almost exclusively refers to as missing data119,125–128,133–135,182.”
From The METRIC-framework for assessing data quality for trustworthy AI in medicine: A systematic review (2024) · cites this paper as [135]
Che et al. found an informative pattern in the MIMIC-III critical care dataset displaying a correlation between missing rates of variables and ICD9-diagnosis labels.
“Che et al.135 find an informative pattern in the case of the MIMIC-III critical care dataset226 which displays a correlation between missing rates of variables and ICD9-diagnosis labels.”
From The METRIC-framework for assessing data quality for trustworthy AI in medicine: A systematic review (2024) · cites this paper as [135]
A primary limitation of GRU-D is the assumption that variables at the initial time step are fully observed.
“A primary limitation of GRU-D, however, is the assumption that variables at the initial time step are fully observed.”
From AI-Driven Predictions of Readmission and Mortality for Improved Discharge Decisions in Critical Care: A Retrospective Study (2026) · cites this paper as [22]
The Methods > Notations section assumes the first observation occurs at time-stamp 0, but does not say that every variable is observed then. Methods > GRU-D describes how missing variables are handled without stating an initial-step requirement. The Discussions > Limitations section does not identify that requirement as a limitation; searches for initial-step and first-observation assumptions found no passage establishing the claim. No page numbers are available in our copy. (LLM, conf=0.73)
Experimental — accuracy not yet measuredRNN is more suitable for prediction or recognition of sequences; CNN is more suitable for recognition of spatial arrangement features.
“The former is more suitable for prediction or recognition of sequences, such as natural language processing [59] and time series prediction [60,61]. The latter is more suitable for the recognition of spatial arrangement features, such as the shapes in graphics and images [62].”
From Machine Learning Based Toxicity Prediction: From Chemical Structural Description to Transcriptome Analysis (2018) · cites this paper as [60]
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Heilbroner, S. P., Carter, C., Vidmar, D. M., Mueller, E. T., Stumpe, M. C., & Miotto, R. (2025) · Communications Medicine · doi:10.1038/s43856-025-00973-w · Cited by 1 · see citing works
Heo, Y., Kim, M., Han, S.-S., Kim, T.-H., Heo, J., Kim, D., Kim, W. J., Lee, S.-J., Kwon, O. B., Kim, Y., et al. (2026) · Diagnostics · doi:10.3390/diagnostics16060874
“GRU-D [22] was proposed to address this issue as a GRU-based model that directly handles missing values.”
- Authors
- Che, Z., Purushotham, S., Cho, K., Sontag, D., & Liu, Y.
- Affiliations
- University of Southern California (US)
- New York University (US)
- Massachusetts Institute of Technology (US)
- Corresponding author
- Che, Zhengping
- Venue
- Scientific Reports
- Published
- 2018-04-17
- Volume
- 8
- Issue
- 1
- Pages
- 6085-6085
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC5904216
- OpenAlex
- W2964010366
- Cited by
- 2,370
- References
- 46
- Citations by year
- 2026: 355 · 2025: 316 · 2024: 277 · 2023: 277 · 2022: 256 · 2021: 292 · 2020: 272 · 2019: 197 · 2018: 94 · 2017: 27 · 2016: 6
- FWCI
- 152.35
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Scientific Reports (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, other-oa)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Time Series Analysis and Forecasting
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning in Healthcare
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- multivariate time series, missing data, informative missingness, time series imputation, time series forecasting, time series classification, gated recurrent unit, masking, time intervals, clinical time series, MIMIC-III, PhysioNet
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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