{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T05:02:59Z","timestamp":1789707779401,"version":"4.0.1"},"reference-count":21,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T00:00:00Z","timestamp":1789344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Although recommendation systems based on neural collaborative filtering (NCF) can achieve high rating accuracy, the point estimates they generate do not express prediction confidence. Existing variants that account for uncertainty, such as Monte Carlo dropout, deep ensemble models, and single-head Bayesian networks, can only capture epistemic uncertainty. We propose BayesNCF-v2, a single-model Bayesian neural collaborative filtering framework that combines a Bayes-by-Backprop output layer with a heteroscedastic head trained under the Gaussian NLL, thereby jointly learning aleatoric and epistemic uncertainty. Across five seeds and three datasets, compared to standard NCF, it reduces ECE by 25\u201373% and NLL by 7\u201320%, while its calibration performance shows no statistically significant difference from heteroscedastic MC dropout and approaches that of a heteroscedastic deep ensemble consisting of five models, despite having significantly fewer parameters. For cold-start users, the learned aleatoric variance increases, thereby reducing the ECE for cold-start users on three datasets. These results hold consistently across both random and temporal partitions, demonstrating that heteroscedastic aleatoric modeling is the main driver of calibration in these experiments.<\/jats:p>","DOI":"10.3390\/e28091025","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T14:15:04Z","timestamp":1789395304000},"page":"1025","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Uncertainty-Calibrated Collaborative Filtering via Heteroscedastic Bayesian Neural Networks"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1749-8955","authenticated-orcid":false,"given":"Xiaowei","family":"Wang","sequence":"first","affiliation":[{"name":"The College of Cybersecurity, Shandong University of Political Science and Law, Jinan 250013, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"He, X., Liao, L., Zhang, H., Nie, L., Hu, X., and Chua, T.S. 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