A Diffusion Model for Traffic Data Imputation

Bo Lu; Qinghai Miao; Yahui Liu; Tariku Sinshaw Tamir; Hongxia Zhao; Xiqiao Zhang; Yisheng Lv; Fei-Yue Wang

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2025 > In Press, Accepted Manuscript

B. Lu, Q. Miao, Y. Liu, T. Tamir, H. Zhao, X. Zhang, Y. Lv, and F.-Y. Wang, “A diffusion model for traffic data imputation,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 3, pp. 1–12, Mar. 2025.

Citation:

B. Lu, Q. Miao, Y. Liu, T. Tamir, H. Zhao, X. Zhang, Y. Lv, and F.-Y. Wang, “A diffusion model for traffic data imputation,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 3, pp. 1–12, Mar. 2025.

B. Lu, Q. Miao, Y. Liu, T. Tamir, H. Zhao, X. Zhang, Y. Lv, and F.-Y. Wang, “A diffusion model for traffic data imputation,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 3, pp. 1–12, Mar. 2025.

Citation:

B. Lu, Q. Miao, Y. Liu, T. Tamir, H. Zhao, X. Zhang, Y. Lv, and F.-Y. Wang, “A diffusion model for traffic data imputation,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 3, pp. 1–12, Mar. 2025.

PDF( 2568 KB)

A Diffusion Model for Traffic Data Imputation

Funds: This work was partially supported by the National Natural Science Foundation of China (62271485), and the SDHS Science and Technology Project (HS2023B044)

More Information

Author Bio:
Bo Lu received the B.S. degree in computer science and technology from the Chengdu University of Information Technology in 2021. He is currently a master student in ... at the Institute of Automation, Chinese Academy of Sciences as well as the School of Artificial Intelligence, University of Chinese Academy of Sciences. His research interests include artificial intelligence generated content and computer vision

Qinghai Miao (Senior Member, IEEE) received the Ph.D. degree in control theory and control engineering from the Graduate University of Chinese Academy of Sciences in 2007. From 2017 to 2018, he was a Visiting Scholar with the School of Informatics, the University of Edinburgh, UK. He is currently an Associate Professor with the School of Artificial Intelligence, University of Chinese Academy of Sciences. His research interests include parallel intelligence, machine learning, computer vision, intelligent transportation systems

Yahui Liu received the B.E. degree from Xiamen University in 2021. She is currently a master student in ... at the Institute of Automation, Chinese Academy of Sciences as well as the School of Artificial Intelligence, University of Chinese Academy of Sciences. Her research interests include motion prediction and vision-based autonomous driving

Tariku Sinshaw Tamir received the B.Sc. degree in electrical engineering from Haramaya University, Ethiopia in 2011, the M.Sc. degree in control engineering from Addis Ababa University, Ethiopia in 2015, and the Ph.D. degree in control theory and control engineering from the Institute of Automation, Chinese Academy of Sciences in 2023. He is currently a Postdoctoral Researcher at Guangdong University of Technology. His research interests include modeling, control, and optimization of complex systems; 3D printing; and smart manufacturing. He was a recipient of the Excellent International Student Award in 2021 and 2022 from the University of Chinese Academy of Sciences. He has authored more than 20 referred journal and conference papers

Hongxia Zhao (Senior Member, IEEE) received the Ph.D. degree in control theory and control engineering from the Chinese Academy of Sciences in 2009. She is currently an Assistant Professor with the State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences. Her research interests include intelligent control, data analysis, and traffic modeling and prediction

Xiqiao Zhang received the B.E. degree in traffic engineering, the M.E. degree in transportation planning and management, and the Ph.D. degree in bridge and tunnel engineering from Harbin Institute of Technology, in 2001, 2004, and 2008, respectively. He is currently an Associate Professor with the Department of Transportation Engineering, the School of Transportation Science and Technology, Harbin Institute of Technology. His research interests include traffic data analysis, traffic control, dynamic traffic modeling

Yisheng Lv (Senior Member, IEEE) received the B.E. and M.E. degrees in transportation engineering from Harbin Institute of Technology in 2005 and 2007, respectively, and the Ph.D. degree in control theory and control engineering from the Chinese Academy of Sciences in 2010. He is a Professor with the State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences. His research interests include traffic data analysis, dynamic traffic modeling, and parallel traffic management and control systems

Fei-Yue Wang (Fellow, IEEE) received the Ph.D. degree in computer and systems engineering from Rensselaer Polytechnic Institute, USA in 1990. He joined the University of Arizona, USA in 1990, and became a Professor and the Director of the Robotics and Automation Lab and Program in Advanced Research for Complex Systems. In 1999, he founded the Intelligent Control and Systems Engineering Center at the Institute of Automation, Chinese Academy of Sciences (CAS), and in 2002, was appointed as the Director of the Key Laborabory of Complex Systems and Intelligence Science, CAS. From 2006 to 2010, he was Vice President for Research, Education, and Academic Exchanges with the Institute of Automation, CAS. In 2011, he became the State Specially Appointed Expert and the Director of the State Key Laboratory for Management and Control of Complex Systems. His research interests include methods and applications for parallel systems, social computing, parallel intelligence, and knowledge automation. He was the Founding Editor-in-Chief (EiC) of the International Journal of Intelligent Control and Systems (1995–2000), Founding EiC of IEEE ITS Magazine (2006–2007), EiC of IEEE Intelligent Systems (2009–2012), EiC of IEEE Transactions on ITS (2009–2016), and EiC of IEEE Transactions on Computational Social Systems (2017–2020). He is currently the EiC of IEEE Transactions on Intelligent Vehicles, Founding EiC of IEEE/CAA Journal of Automatica Sinica, and Chinese Journal of Command and Control. Since 1997, he was the General or Program Chair of more than 20 IEEE, INFORMS, ACM, and ASME conferences. He was the President of IEEE ITS Society (2005–2007), Chinese Association for Science and Technology, Beijing, China, in 2005, American Zhu Kezhen Education Foundation (2007–2008), and Vice President of the ACM China Council (2010–2011). Since 2008, he has been the Vice President and Secretary General of Chinese Association of Automation. Dr. Wang has been elected as Fellow of INCOSE, IFAC, ASME, and AAAS. In 2007, he was the recipient of the National Prize in Natural Sciences of China, Outstanding Scientist by ACM for his research contributions in intelligent control and social computing, IEEE ITS Outstanding Application and Research Awards in 2009, 2011and 2015, respectively, and IEEE SMC Norbert Wiener Award in 2014
Corresponding author: Hongxia Zhao, e-mail: hongxia.zhao@ia.ac.cn; Xiqiao Zhang, e-mail: zxqjuly@hit.edu.cn
Received Date: 2024-03-03
Revised Date: 2024-04-17
Accepted Date: 2024-05-31

Available Online: 2025-01-10

Abstract

Abstract

Imputation of missing data has long been an important topic and an essential application for intelligent transportation systems (ITS) in the real world. As a state-of-the-art generative model, the diffusion model has proven highly successful in image generation, speech generation, time series modelling etc. and now opens a new avenue for traffic data imputation. In this paper, we propose a conditional diffusion model, called the implicit-explicit diffusion model, for traffic data imputation. This model exploits both the implicit and explicit feature of the data simultaneously. More specifically, we design two types of feature extraction modules, one to capture the implicit dependencies hidden in the raw data at multiple time scales and the other to obtain the long-term temporal dependencies of the time series. This approach not only inherits the advantages of the diffusion model for estimating missing data, but also takes into account the multiscale correlation inherent in traffic data. To illustrate the performance of the model, extensive experiments are conducted on three real-world time series datasets using different missing rates. The experimental results demonstrate that the model improves imputation accuracy and generalization capability.
- Data imputation,
- diffusion model,
- implicit feature,
- time series,
- traffic data

FullText(HTML)

References(64)

References

[1]	D. Xu, H. Peng, C. Wei, X. Shang, and H. Li, “Traffic state data imputation: An efficient generating method based on the graph aggregator,” IEEE Trans. Intelligent Transportation Systems, vol. 23, no. 8, pp. 13084–13093, 2022. doi: 10.1109/TITS.2021.3119638
[2]	M. Kantardzic, “Data mining: Concepts, models, methods, and algorithms,” Technometrics, vol. 45, no. 3, p. 277, 2003.
[3]	Q. Miao, Y. Lv, M. Huang, X. Wang, and F.-Y. Wang, “Parallel learning: Overview and perspective for computational learning across syn2real and sim2real,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 603–631, 2023. doi: 10.1109/JAS.2023.123375
[4]	W. Zou, Y. Sun, Y. Zhou, Q. Lu, Y. Nie, T. Sun, and L. Peng, “Limited sensing and deep data mining: A new exploration of developing city-wide parking guidance systems,” IEEE Intelligent Transportation Systems Magazine, vol. 14, no. 1, pp. 198–215, 2022. doi: 10.1109/MITS.2020.2970185
[5]	C. Zhao, Y. Lv, J. Jin, Y. Tian, J. Wang, and F.-Y. Wang, “Decast in transverse for parallel intelligent transportation systems and smart cities: Three decades and beyond,” IEEE Intelligent Transportation Systems Magazine, vol. 14, no. 6, pp. 6–17, 2022. doi: 10.1109/MITS.2022.3199557
[6]	S. Feng, Z. Song, Z. Li, Y. Zhang, and L. Li, “Robust platoon control in mixed traffic flow based on tube model predictive control,” IEEE Trans. Intelligent Vehicles, vol. 6, no. 4, pp. 711–722, 2021. doi: 10.1109/TIV.2021.3060626
[7]	X. Ge, Q.-L. Han, X.-M. Zhang, and D. Ding, “Communication resource-efficient vehicle platooning control with various spacing policies,” IEEE/CAA J. Autom. Sinica, 2023.
[8]	J. Zhan, Z. Ma, and L. Zhang, “Data-driven modeling and distributed predictive control of mixed vehicle platoons,” IEEE Trans. Intelligent Vehicles, vol. 8, no. 1, pp. 572–582, 2023. doi: 10.1109/TIV.2022.3168591
[9]	J. Wang, J. Wang, and Q.-L. Han, “Receding-horizon trajectory planning for under-actuated autonomous vehicles based on collaborative neurodynamic optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 11, pp. 1909–1923, 2022. doi: 10.1109/JAS.2022.105524
[10]	V. G. Stepanyants and A. Y. Romanov, “A survey of integrated simulation environments for connected automated vehicles: Requirements, tools, and architecture,” IEEE Intelligent Transportation Systems Magazine, 2023.
[11]	A. T. Hudak, N. L. Crookston, J. S. Evans, D. E. Hall, and M. J. Falkowski, “Nearest neighbor imputation of species-level, plot-scale forest structure attributes from lidar data,” Remote Sensing of Environment, vol. 112, no. 5, pp. 2232–2245, 2008. doi: 10.1016/j.rse.2007.10.009
[12]	D. Cai, X. He, J. Han, and T. S. Huang, “Graph regularized nonnegative matrix factorization for data representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 33, no. 8, pp. 1548–1560, 2011. doi: 10.1109/TPAMI.2010.231
[13]	J. Liu, P. Musialski, P. Wonka, and J. Ye, “Tensor completion for estimating missing values in visual data,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 35, no. 1, pp. 208–220, 2012.
[14]	X. Chen, M. Lei, N. Saunier, and L. Sun, “Low-rank autoregressive tensor completion for spatiotemporal traffic data imputation,” IEEE Trans. Intelligent Transportation Systems, vol. 23, no. 8, pp. 12301–12310, 2021.
[15]	X. Chen, Z. He, and J. Wang, “Spatial-temporal traffic speed patterns discovery and incomplete data recovery via SVD-combined tensor decomposition,” Transportation Research Part C: Emerging Technologies, vol. 86, pp. 59–77, 2018. doi: 10.1016/j.trc.2017.10.023
[16]	T. Chen and C. Guestrin, “XGBoost: A scalable tree boosting system,” in Proc. 22nd ACM SIGKDD Int. Conf. Knowledge Discovery and Data Mining, 2016, pp. 785–794.
[17]	S. Harford, F. Karim, and H. Darabi, “Generating adversarial samples on multivariate time series using variational autoencoders,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 9, pp. 1523–1538, 2021. doi: 10.1109/JAS.2021.1004108
[18]	T. Lintonen and T. Räty, “Self-learning of multivariate time series using perceptually important points,” IEEE/CAA J. Autom. Sinica, vol. 6, p. 1318, 2019. doi: 10.1109/JAS.2019.1911777
[19]	J. Liu, F. Zheng, X. Liu, and G. Guo, “Dynamic traffic flow prediction based on long-short term memory framework with feature organization,” IEEE Intelligent Transportation Systems Magazine, vol. 14, no. 6, pp. 221–236, 2022. doi: 10.1109/MITS.2021.3116156
[20]	Z. Li, Y. Li, and L. Li, “A comparison of detrending models and multiregime models for traffic flow prediction,” IEEE Intelligent Transportation Systems Magazine, vol. 6, no. 4, pp. 34–44, 2014. doi: 10.1109/MITS.2014.2332591
[21]	I. Lana, J. Del Ser, M. Velez, and E. I. Vlahogianni, “Road traffic forecasting: Recent advances and new challenges,” IEEE Intelligent Transportation Systems Magazine, vol. 10, no. 2, pp. 93–109, 2018. doi: 10.1109/MITS.2018.2806634
[22]	S. Choi, H. Shon, and K. Huh, “Interpretable vehicle speed estimation based on dual attention network for 4WD off-road vehicles,” IEEE Trans. Intelligent Vehicles, 2023.
[23]	Y. Lv, Y. Duan, W. Kang, Z. Li, and F.-Y. Wang, “Traffic flow prediction with big data: A deep learning approach,” IEEE Trans. Intelligent Transportation Systems, vol. 16, no. 2, pp. 865–873, 2015.
[24]	Y. Duan, Y. Lv, Y.-L. Liu, and F.-Y. Wang, “An efficient realization of deep learning for traffic data imputation,” Transportation Research Part C: Emerging Technologies, vol. 72, pp. 168–181, 2016. doi: 10.1016/j.trc.2016.09.015
[25]	J. Xi, F. Zhu, P. Ye, Y. Lv, H. Tang, and F.-Y. Wang, “HMDRL: Hierarchical mixed deep reinforcement learning to balance vehicle supply and demand,” IEEE Trans. Intelligent Transportation Systems, vol. 23, no. 11, pp. 21861–21872, 2022. doi: 10.1109/TITS.2022.3191752
[26]	J. Xi, F. Zhu, Y. Chen, Y. Lv, C. Tan, and F. Wang, “DDRL: A decentralized deep reinforcement learning method for vehicle repositioning,” in Proc. IEEE Int. Intelligent Transportation Systems Conf., 2021, pp. 3984–3989.
[27]	J. Pan, C. Li, Y. Tang, W. Li, and X. Li, “Energy consumption prediction of a CNC machining process with incomplete data,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 987–1000, 2021. doi: 10.1109/JAS.2021.1003970
[28]	W. Du, B. Li, J. Chen, Y. Lv, and Y. Li, “A spatiotemporal hybrid model for airspace complexity prediction,” IEEE Intelligent Transportation Systems Magazine, vol. 15, no. 2, pp. 217–224, 2023. doi: 10.1109/MITS.2022.3204099
[29]	X. Jiang, X. Kong, and Z. Ge, “Augmented industrial data-driven modeling under the curse of dimensionality,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1445–1461, 2023. doi: 10.1109/JAS.2023.123396
[30]	J. Yoon, W. R. Zame, and M. van der Schaar, “Estimating missing data in temporal data streams using multi-directional recurrent neural networks,” IEEE Trans. Biomedical Engineering, vol. 66, no. 5, pp. 1477–1490, 2019. doi: 10.1109/TBME.2018.2874712
[31]	X. Yao, Y. Gao, D. Zhu, E. Manley, J. Wang, and Y. Liu, “Spatial origindestination flow imputation using graph convolutional networks,” IEEE Trans. Intelligent Transportation Systems, vol. 22, no. 12, pp. 7474–7484, 2021. doi: 10.1109/TITS.2020.3003310
[32]	Z. Wu, S. Pan, G. Long, J. Jiang, and C. Zhang, “Graph wavenet for deep spatial-temporal graph modeling,” arXiv preprint arXiv: 1906.00121, 2019.
[33]	Y. Liu, R. Yu, S. Zheng, E. Zhan, and Y. Yue, “NAOMI: Nonautoregressive multiresolution sequence imputation,” Advances in Neural Information Processing Systems, vol. 32, 2019.
[34]	M. Morsali, E. Frisk, and J. Åslund, “Spatio-temporal planning in ˚ multi-vehicle scenarios for autonomous vehicle using support vector machines,” IEEE Trans. Intelligent Vehicles, vol. 6, no. 4, pp. 611–621, 2021. doi: 10.1109/TIV.2020.3042087
[35]	W. Cao, D. Wang, J. Li, H. Zhou, L. Li, and Y. Li, “BRITS: Bidirectional recurrent imputation for time series,” Advances in Neural Information Processing Systems, vol. 31, 2018.
[36]	Q. Suo, W. Zhong, G. Xun, J. Sun, C. Chen, and A. Zhang, “GLIMA: Global and local time series imputation with multi-directional attention learning,” in Proc. IEEE Int. Conf. Big Data, 2020, pp. 798–807.
[37]	Z. Wei, H. Zhao, Z. Li, X. Bu, Y. Chen, X. Zhang, Y. Lv, and F.-Y. Wang, “STGSA: A novel spatial-temporal graph synchronous aggregation model for traffic prediction,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 226–238, 2023. doi: 10.1109/JAS.2023.123033
[38]	W. Du, D. Côté, and Y. Liu, “SAITS: Self-attention-based imputation x for time series,” Expert Systems With Applications, vol. 219, p. 119619, 2023. doi: 10.1016/j.eswa.2023.119619
[39]	Y. Liu, B. Tian, Y. Lv, L. Li, and F.-Y. Wang, “Point cloud classification using content-based transformer via clustering in feature space,” IEEE/CAA J. Autom. Sinica, vol. 10, p. 1, 2023. doi: 10.1109/JAS.2023.123003
[40]	Y. Tashiro, J. Song, Y. Song, and S. Ermon, “CSDI: Conditional scorebased diffusion models for probabilistic time series imputation,” Advances in Neural Information Processing Systems, vol. 34, pp. 24804–24816, 2021.
[41]	J. M. L. Alcaraz and N. Strodthoff, “Diffusion-based time series imputation and forecasting with structured state space models,” arXiv preprint arXiv: 2208.09399, 2022.
[42]	I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial networks,” Communi. the ACM, vol. 63, no. 11, pp. 139–144, 2020. doi: 10.1145/3422622
[43]	Y. Luo, X. Cai, Y. Zhang, J. Xu, et al., “Multivariate time series imputation with generative adversarial networks,” Advances in Neural Information Processing Systems, vol. 31, 2018.
[44]	Y. Lv, Y. Chen, L. Li, and F.-Y. Wang, “Generative adversarial networks for parallel transportation systems,” IEEE Intelligent Transportation Systems Magazine, vol. 10, no. 3, pp. 4–10, 2018. doi: 10.1109/MITS.2018.2842249
[45]	K. Sarda, A. Yerudkar, and C. D. Vecchio, “Missing data imputation for real time-series data in a steel industry using generative adversarial networks,” in Proc. Ann. Conf. IEEE Industrial Electronics Society, 2021, pp. 1–6.
[46]	X. Xiao, Y. Zhang, S. Yang, and X. Kong, “Efficient missing counts imputation of a bike-sharing system by generative adversarial network,” IEEE Trans. Intelligent Transportation Systems, vol. 23, no. 8, pp. 13443–13451, 2022. doi: 10.1109/TITS.2021.3124409
[47]	Y. Chen, Y. Lv, and F.-Y. Wang, “Traffic flow imputation using parallel data and generative adversarial networks,” IEEE Trans. Intelligent Transportation Systems, vol. 21, no. 4, pp. 1624–1630, 2020. doi: 10.1109/TITS.2019.2910295
[48]	J. Chen, K. Wu, Y. Yu, and L. Linbo, “CDP-GAN: Near-infrared and visible image fusion via color distribution preserved GAN,” IEEE/CAA J. Autom. Sinica, vol. 9, p. 1698, 2022. doi: 10.1109/JAS.2022.105818
[49]	J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, and S. Ganguli, “Deep unsupervised learning using nonequilibrium thermodynamics,” in Proc. Int. Conf. Machine Learning, 2015, pp. 2256–2265.
[50]	Y. Song and S. Ermon, “Generative modeling by estimating gradients of the data distribution,” Advances in Neural Information Processing Systems, vol. 32, 2019.
[51]	J. Ho, A. Jain, and P. Abbeel, “Denoising diffusion probabilistic models,” Advances in Neural Information Processing Systems, vol. 33, pp. 6840–6851, 2020.
[52]	Z. Kong, W. Ping, J. Huang, K. Zhao, and B. Catanzaro, “Diffwave: A versatile diffusion model for audio synthesis,” arXiv preprint arXiv: 2009.09761, 2020.
[53]	S. Bai, J. Z. Kolter, and V. Koltun, “An empirical evaluation of generic convolutional and recurrent networks for sequence modeling,” arXiv preprint arXiv: 1803.01271, 2018.
[54]	G. Guo, W. Yuan, J. Liu, Y. Lv, and W. Liu, “Traffic forecasting via dilated temporal convolution with peak-sensitive loss,” IEEE Intelligent Transportation Systems Magazine, vol. 15, no. 1, pp. 48–57, 2023. doi: 10.1109/MITS.2021.3119869
[55]	A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, “Attention is all you need,” Advances in Neural Information Processing Systems, vol. 30, 2017.
[56]	K. Liu, Z. Ye, H. Guo, D. Cao, L. Chen, and F.-Y. Wang, “Fiss GAN: A generative adversarial network for foggy image semantic segmentation,” IEEE/CAA J. Autom. Sinica, vol. 8, p. 1428, 2021. doi: 10.1109/JAS.2021.1004057
[57]	H. Huang, G. Zhou, N. Liang, Q. Zhao, and S. Xie, “Diverse deep matrix factorization with hypergraph regularization for multiview data representation,” IEEE/CAA J. Autom. Sinica, 2022.
[58]	A. Gu, T. Dao, S. Ermon, A. Rudra, and C. Ré, “HIPPO: Recurrent x memory with optimal polynomial projections,” Advances in Neural Information Processing Systems, vol. 33, pp. 1474–1487, 2020.
[59]	Y. Li, R. Yu, C. Shahabi, and Y. Liu, “Diffusion convolutional recurrent neural network: Data-driven traffic forecasting,” arXiv preprint arXiv: 1707.01926, 2017.
[60]	H. V. Jagadish, J. Gehrke, A. Labrinidis, Y. Papakonstantinou, J. M. Patel, R. Ramakrishnan, and C. Shahabi, “Big data and its technical challenges,” Communi. the ACM, vol. 57, no. 7, pp. 86–94, 2014. doi: 10.1145/2611567
[61]	I. R. White, P. Royston, and A. M. Wood, “Multiple imputation using chained equations: Issues and guidance for practice,” Statistics in Medicine, vol. 30, no. 4, pp. 377–399, 2011. doi: 10.1002/sim.4067
[62]	L. Ljung, “Prediction error estimation methods,” Circuits, Systems and Signal Processing, vol. 21, pp. 11–21, 2002. doi: 10.1007/BF01211648
[63]	X. Miao, Y. Wu, J. Wang, Y. Gao, X. Mao, and J. Yin, “Generative semi-supervised learning for multivariate time series imputation,” in Proc. AAAI Conf. Artificial Intelligence, vol. 35, no. 10, 2021, pp. 8983–8991.
[64]	K. Swanson, “Message passing neural networks for molecular property prediction,” Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, USA, 2019.

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(6) / Tables(7)

Get Citation

PDF

XML

Article Metrics

Article views (17) PDF downloads(7)

A Diffusion Model for Traffic Data Imputation

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content