{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T20:19:02Z","timestamp":1783455542371,"version":"3.55.0"},"reference-count":53,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"7","license":[{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T00:00:00Z","timestamp":1782864000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62403425"],"award-info":[{"award-number":["62403425"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2025M781449"],"award-info":[{"award-number":["2025M781449"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Ind. Inf."],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1109\/tii.2026.3674530","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T20:10:04Z","timestamp":1775679004000},"page":"6034-6045","source":"Crossref","is-referenced-by-count":0,"title":["Slack More, Predict Better: Proximal Relaxation for Probabilistic Latent Variable Model-Based Soft Sensors"],"prefix":"10.1109","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1933-5035","authenticated-orcid":false,"given":"Zehua","family":"Zou","sequence":"first","affiliation":[{"name":"Hangzhou International Innovation Institute, Beihang University, Hangzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-6749-5121","authenticated-orcid":false,"given":"Yiran","family":"Ma","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Industrial Control Technology, College of Control science and Engineering, Zhejiang University, Hangzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4038-1616","authenticated-orcid":false,"given":"Yulong","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0592-214X","authenticated-orcid":false,"given":"Zhengnan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Data Science, The Chinese University of Hong Kong, Shenzhen, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0253-9053","authenticated-orcid":false,"given":"Zeyu","family":"Yang","sequence":"additional","affiliation":[{"name":"Zhejiang Key Laboratory of Industrial Solid Waste Thermal Hydrolysis Technology and Intelligent Equipment, Huzhou Key Laboratory of Intelligent Sensing and Optimal Control for Industrial Systems, School of Engineering, Huzhou University, Huzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6870-263X","authenticated-orcid":false,"given":"Jinhao","family":"Xie","sequence":"additional","affiliation":[{"name":"MOE of the Key Laboratory of Bioinorganic and Synthetic Chemistry, the Key Lab of Low-Carbon Chem &amp; Energy Conservation of Guangdong Province, School of Chemistry, Sun Yat-Sen University, Guangzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4170-5579","authenticated-orcid":false,"given":"Xiaoyu","family":"Jiang","sequence":"additional","affiliation":[{"name":"Hangzhou International Innovation Institute, Beihang University, Hangzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5785-0741","authenticated-orcid":false,"given":"Zhichao","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Lab of General AI, School of Intelligence Science and Technology, Peking University, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-7566-5"},{"key":"ref2","volume-title":"Machine learning: A probabilistic perspective","author":"Murphy","year":"2012"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2025.3597838"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2024.3504736"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2018.2889774"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2017.1285773"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00196"},{"key":"ref8","first-page":"1","article-title":"Variational inference for Bayesian mixtures of factor analysers","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Ghahramani","year":"1999"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2024.3386890"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2025.3563546"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2022.3198833"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1561\/9781680839135"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TIM.2022.3160542"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2024.107031"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2025.3621125"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2019.104198"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2022.3183211"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2024.3495020"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2023.3281336"},{"key":"ref20","first-page":"1","article-title":"Auto-encoding variational Bayes","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Kingma","year":"2014"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1613\/jair.1.14258"},{"key":"ref22","first-page":"1","article-title":"PyTorch: An imperative style, high-performance deep learning library","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Paszke","year":"2019"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1561\/2400000003"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2019.2951348"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3060704"},{"key":"ref26","first-page":"15243","article-title":"Large-scale wasserstein gradient flows","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Mokrov","year":"2021"},{"key":"ref27","first-page":"12356","article-title":"The Wasserstein proximal gradient algorithm","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Salim","year":"2020"},{"key":"ref28","first-page":"6185","article-title":"Variational Wasserstein gradient flow","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Fan","year":"2022"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2023.3271226"},{"key":"ref30","first-page":"1","article-title":"FeynmanKac correctors in diffusion: Annealing, guidance, and product of experts","volume-title":"Proc. Int. Conf. Mach. Learn.","author":"Skreta","year":"2025"},{"issue":"6","key":"ref31","first-page":"1","article-title":"Debiased recommendation via Wasserstein causal balancing","volume":"43","author":"Wang","year":"2025","journal-title":"ACM Trans. Inf. Syst."},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TIFS.2024.3516584"},{"key":"ref33","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71050-9","volume-title":"Optimal Transport: Old and New","volume":"338","author":"Villani","year":"2009"},{"key":"ref34","first-page":"1","article-title":"DistDF: Time-series forecasting needs joint-distribution Wasserstein alignment","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Wang","year":"2026"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/s13373-017-0101-1"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-55978-8"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2021.3129888"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.arcontrol.2022.09.005"},{"key":"ref39","first-page":"1","article-title":"Proximal diffusion neural sampler","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Guo","year":"2026"},{"key":"ref40","first-page":"1","article-title":"Debiased collaborative filtering with kernel-based causal balancing","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Li","year":"2024"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/4175.001.0001"},{"key":"ref42","first-page":"1","article-title":"Particle-based variational inference with preconditioned functional gradient flow","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Dong","year":"2023"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v38i14.29472"},{"key":"ref44","first-page":"154","volume-title":"Miscellaneous Notes on Optimization Theory and Related Topics","author":"Border","year":"2015"},{"key":"ref45","first-page":"1","article-title":"Sinkhorn distances: Lightspeed computation of optimal transport","volume-title":"Proc. Adv. Neural Inf. Process. Syst.","author":"Cuturi","year":"2013"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2004.04.013"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2019.2947622"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2019.2951622"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2021.107230"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2018.2809730"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2020.3010331"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2022.3215448"},{"key":"ref53","first-page":"1","article-title":"iTransformer: Inverted transformers are effective for time series forecasting","volume-title":"Proc. Int. Conf. Learn. Representations","author":"Liu","year":"2024"}],"container-title":["IEEE Transactions on Industrial Informatics"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/9424\/11595910\/11477839.pdf?arnumber=11477839","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T19:48:20Z","timestamp":1783453700000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/11477839\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7]]},"references-count":53,"journal-issue":{"issue":"7"},"URL":"https:\/\/doi.org\/10.1109\/tii.2026.3674530","relation":{},"ISSN":["1551-3203","1941-0050"],"issn-type":[{"value":"1551-3203","type":"print"},{"value":"1941-0050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7]]}}}