Extended feature allocation models

Mathematics > Statistics Theory [Submitted on 14 Feb 2025 (v1), last revised 16 Jun 2026 (this version, v3)] Title:Extended feature allocation models View PDF HTML (experimental)Abstract:Feature allocation models are Bayesian nonparametric tools tailored to data in which each observation can simultaneously exhibit multiple characteristics, or features. A fundamental limitation of standard formulations is that feature labels are assumed to be independent and identically distributed, and therefore play no role in posterior inference. The present paper introduces a unified Bayesian framework for extended feature allocation models, in which feature labels and proportions are modeled jointly, thereby enabling the simultaneous discovery of features and learning of dependencies among their labels. Building on point process theory, we develop a full Bayesian analysis of these models. Within this general setting, we also characterize previously proposed priors as those leading to poor predictive distributions, which cannot capture label dependencies and are insensitive to the observed frequency spectrum. Our methodology is designed to move beyond such standard formulations by leveraging the information carried by feature labels. We demonstrate the usefulness of our approach by introducing: (i) a Cox process prior that clusters genomic variant embeddings while predicting new variants and new variant clusters; (ii) a determinantal point process prior for repeated forest surveys, where prediction concerns both the number and the locations of unobserved trees. Submission history From: Lorenzo Ghilotti [view email][v1] Fri, 14 Feb 2025 16:08:42 UTC (1,566 KB) [v2] Mon, 3 Mar 2025 10:11:44 UTC (1,566 KB) [v3] Tue, 16 Jun 2026 09:05:33 UTC (1,261 KB) Current browse context: math.ST References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) 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.