Algebraic implicitization techniques in the graphical models program

[2608.27636] Algebraic implicitization techniques in the graphical models program Skip to main content Search Submit Donate Log in Mathematics > Statistics Theory arXiv:2608.27636 (math) [Submitted on 27 Aug 2026] Title: Algebraic implicitization techniques in the graphical models program Authors: Liam Solus View PDF HTML (experimental) Abstract: Many aspects of daily life now rely on technology driven by advanced techniques for analyzing multivariate data. Graphical models provide the general framework within which much of these analyses take place. However, different data types require different graphical models, with each requiring its own basic mathematical theory to guide sound statistical inference. Developing this theory for a family of graphical models requires solutions to fundamental questions, where emerging mathematical approaches are utilizing what can collectively be called algebraic implicitization techniques. These notes provide an introduction to the basics of graphical models and the algebraic implicitization techniques now appearing in instances of the graphical models program. Comments: This is a preprint of a chapter intended for publication in a Springer Lecture Notes in Mathematics series based on the lectures given at the 43rd Finnish Summer School on Probability and Statistics in Lammi, Finland. It surveys basic results on graphical models and algebraic techniques, with the intent of being broadly accessible Subjects: Statistics Theory (math.ST) ; Algebraic Geometry (math.AG) Cite as: arXiv:2608.27636 [math.ST] (or arXiv:2608.27636v1 [math.ST] for this version) https://doi.org/10.48550/arXiv.2608.27636 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Liam Solus [ view email ] [v1] Thu, 27 Aug 2026 19:21:28 UTC (125 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2026-08 Change to browse by: math math.AG stat stat.TH References & Citations NASA ADS 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) Major funding support from

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