{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/estimating-mutual-information-via-geodesic-k","title":"Estimating Mutual Information via Geodesic $k$NN","arxiv_id":"2110.13883","date":"2021-10-26","proceeding":null,"authors":["Alexander Marx","Jonas Fischer"],"abstract":"Estimating mutual information (MI) between two continuous random variables $X$ and $Y$ allows to capture non-linear dependencies between them, non-parametrically. As such, MI estimation lies at the core of many data science applications. Yet, robustly estimating MI for high-dimensional $X$ and $Y$ is still an open research question. In this paper, we formulate this problem through the lens of manifold learning. That is, we leverage the common assumption that the information of $X$ and $Y$ is captured by a low-dimensional manifold embedded in the observed high-dimensional space and transfer it to MI estimation. As an extension to state-of-the-art $k$NN estimators, we propose to determine the $k$-nearest neighbors via geodesic distances on this manifold rather than from the ambient space, which allows us to estimate MI even in the high-dimensional setting. An empirical evaluation of our method, G-KSG, against the state-of-the-art shows that it yields good estimations of MI in classical benchmark and manifold tasks, even for high dimensional datasets, which none of the existing methods can provide.","url_abs":"https://arxiv.org/abs/2110.13883v2","url_pdf":"https://arxiv.org/pdf/2110.13883v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"estimating-mutual-information-via-geodesic-k","repo_url":"https://github.com/a-marx/geodesic-mi","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2110.13883","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}