Coherent information deletion: Bayes' theorem and generalized Bayesian unlearning

[2602.09061] Coherent Information Deletion: Bayesian, Generalized Bayesian and Possibilistic Unlearning Skip to main content Search Submit Donate Log in Statistics > Methodology arXiv:2602.09061 (stat) [Submitted on 8 Feb 2026 ( v1 ), last revised 12 Oct 2026 (this version, v5)] Title: Coherent Information Deletion: Bayesian, Generalized Bayesian and Possibilistic Unlearning Authors: Hans Montcho , Håvard Rue , Maurizio Filippone View PDF HTML (experimental) Abstract: Bayes' theorem admits an information processing interpretation due to Zellner (1988): under the Shannon information criterion, the posterior is the unique rule that processes prior and data information without information loss. We revisit these ideas from the perspective of information deletion. Given a posterior based on a complete dataset, what distribution should replace it when a subset of the data is removed? For ordinary Bayesian inference, we show that the corresponding information deletion objective is uniquely minimized by the leave-data-out posterior. We then extend the framework beyond likelihood-based inference from Bayes to the generalized Bayesian updating of Bissiri et al.(2016} based on loss functions. Requiring deletion to be coherent under sequential removal of loss contributions yields a deletion rule that exactly recovers the generalized posterior based only on the retained information. We further develop an axiomatic theory, beyond probabilistic inference, for possibilistic deletion and show that the same information-deletion perspective leads to a principled rule for exact possibilistic unlearning. Finally, restricting these exact deletion principles to tractable families leads naturally to variational Bayesian, generalized Bayesian, and maxitive possibilistic unlearning. Comments: Extended the deletion rule to generalized Bayes and Possibilistic inference Subjects: Methodology (stat.ME) ; Information Theory (cs.IT); Statistics Theory (math.ST) Cite as: arXiv:2602.09061 [stat.ME] (or arXiv:2602.09061v5 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2602.09061 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hans Montcho [ view email ] [v1] Sun, 8 Feb 2026 23:43:29 UTC (16 KB) [v2] Tue, 19 May 2026 16:33:49 UTC (16 KB) [v3] Thu, 27 Aug 2026 19:32:17 UTC (18 KB) [v4] Thu, 8 Oct 2026 19:40:43 UTC (29 KB) [v5] Mon, 12 Oct 2026 10:21:03 UTC (29 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2026-02 Change to browse by: cs cs.IT math math.IT math.ST stat stat.TH References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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