{"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/efficient-approximate-minimum-entropy","title":"Efficient Approximate Minimum Entropy Coupling of Multiple Probability Distributions","arxiv_id":"2006.07955","date":"2020-06-14","proceeding":null,"authors":["Cheuk Ting Li"],"abstract":"Given a collection of probability distributions $p_{1},\\ldots,p_{m}$, the minimum entropy coupling is the coupling $X_{1},\\ldots,X_{m}$ ($X_{i}\\sim p_{i}$) with the smallest entropy $H(X_{1},\\ldots,X_{m})$. While this problem is known to be NP-hard, we present an efficient algorithm for computing a coupling with entropy within 2 bits from the optimal value. More precisely, we construct a coupling with entropy within 2 bits from the entropy of the greatest lower bound of $p_{1},\\ldots,p_{m}$ with respect to majorization. This construction is also valid when the collection of distributions is infinite, and when the supports of the distributions are infinite. Potential applications of our results include random number generation, entropic causal inference, and functional representation of random variables.","url_abs":"https://arxiv.org/abs/2006.07955v1","url_pdf":"https://arxiv.org/pdf/2006.07955v1.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":"efficient-approximate-minimum-entropy","repo_url":"https://github.com/cheuktingli/psitip","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2006.07955","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}