{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:25Z","timestamp":1760240005175,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T00:00:00Z","timestamp":1551744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Given a dataset, we quantify the size of patterns that must always exist in the dataset. This is done formally through the lens of Ramsey theory of graphs, and a quantitative bound known as Goodman\u2019s theorem. By combining statistical tools with Ramsey theory of graphs, we give a nuanced understanding of how far away a dataset is from correlated, and what qualifies as a meaningful pattern. This method is applicable to a wide range of datasets. As examples, we analyze two very different datasets. The first is a dataset of repeated voters (    n = 435    ) in the 1984 US congress, and we quantify how homogeneous a subset of congressional voters is. We also measure how transitive a subset of voters is. Statistical Ramsey theory is also used with global economic trading data (    n = 214    ) to provide evidence that global markets are quite transitive. While these datasets are small relative to Big Data, they illustrate the new applications we are proposing. We end with specific calls to strengthen the connections between Ramsey theory and statistical methods.<\/jats:p>","DOI":"10.3390\/axioms8010029","type":"journal-article","created":{"date-parts":[[2019,3,5]],"date-time":"2019-03-05T11:19:50Z","timestamp":1551784790000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Using Ramsey Theory to Measure Unavoidable Spurious Correlations in Big Data"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2808-8502","authenticated-orcid":false,"given":"Micheal","family":"Pawliuk","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0908-7571","authenticated-orcid":false,"given":"Michael Alexander","family":"Waddell","sequence":"additional","affiliation":[{"name":"Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1007\/s10699-016-9489-4","article-title":"The deluge of spurious correlations in big data","volume":"22","author":"Calude","year":"2017","journal-title":"Found. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1080\/00029890.1959.11989408","article-title":"On sets of acquaintances and strangers at any party","volume":"66","author":"Goodman","year":"1959","journal-title":"Am. Math. Mon."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1112\/plms\/s2-30.1.264","article-title":"On a Problem of Formal Logic","volume":"s2-30","author":"Ramsey","year":"1930","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1080\/00029890.1972.11993198","article-title":"Acquaintance graph party problem","volume":"79","author":"Schwenk","year":"1972","journal-title":"Am. Math. Mon."},{"key":"ref_5","unstructured":"Lichman, M. (2013). UCI Machine Learning Repository, School of Information and Computer Science, University of California. Available online: http:\/\/archive.ics.uci.edu\/ml."},{"key":"ref_6","unstructured":"(1985). Congressional Quarterly Almanac, 98th Congress, 2nd session 1984, Congressional Quarterly Inc."},{"key":"ref_7","unstructured":"WITS (2017). WITS Historical Trading Data, World Bank."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1112\/jlms\/s2-39.2.246","article-title":"A disproof of a conjecture of Erd\u0151s in Ramsey theory","volume":"2","author":"Thomason","year":"1989","journal-title":"J. Lond. Math. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.jctb.2013.05.002","article-title":"Monochromatic triangles in three-coloured graphs","volume":"103","author":"Cummings","year":"2013","journal-title":"J. Comb. Theory Ser. B"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mubayi, D., and Suk, A. (arXiv, 2017). A survey of quantitative bounds for hypergraph Ramsey problems, arXiv.","DOI":"10.1112\/blms.12133"},{"key":"ref_11","unstructured":"Alon, N., and Spencer, J.H. (2015). The Probabilistic Method, Wiley. [4th ed.]."},{"key":"ref_12","unstructured":"Sj\u00f6land, E. (arXiv, 2014). Enumeration of monochromatic three term arithmetic progressions in two-colorings of cyclic groups, arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"385","DOI":"10.4171\/rmi\/499","article-title":"On monochromatic solutions of equations in groups","volume":"23","author":"Cameron","year":"2007","journal-title":"Rev. Mat. Iberoam."},{"key":"ref_14","first-page":"53","article-title":"The minimum number of monochromatic 4-term progressions in \n\t\t  Zp","volume":"1","author":"Wolf","year":"2010","journal-title":"J. Comb."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1016\/j.jcta.2011.12.004","article-title":"Monochromatic 4-term arithmetic progressions in 2-colorings of Zn","volume":"119","author":"Lu","year":"2012","journal-title":"J. Comb. Theory Ser. A"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/1\/29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:36:25Z","timestamp":1760186185000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/8\/1\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,5]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["axioms8010029"],"URL":"https:\/\/doi.org\/10.3390\/axioms8010029","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2019,3,5]]}}}