{ "_id": "6a1eb59fb25058d4daaddd63", "Package": "shattering", "Title": "Estimate the Shattering Coefficient for a Particular Dataset", "Version": "1.0.7", "Authors@R": "person(given = \"Rodrigo\",\nfamily = \"F. de Mello\",\nrole = c(\"aut\", \"cre\"),\nemail = \"mellorf@gmail.com\",\ncomment = c(ORCID = \"0000-0002-0435-3992\"))", "Description": "The Statistical Learning Theory (SLT) provides the\ntheoretical background to ensure that a supervised algorithm\ngeneralizes the mapping f:X -> Y given f is selected from its\nsearch space bias F. This formal result depends on the\nShattering coefficient function N(F,2n) to upper bound the\nempirical risk minimization principle, from which one can\nestimate the necessary training sample size to ensure the\nprobabilistic learning convergence and, most importantly, the\ncharacterization of the capacity of F, including its under and\noverfitting abilities while addressing specific target\nproblems. In this context, we propose a new approach to\nestimate the maximal number of hyperplanes required to shatter\na given sample, i.e., to separate every pair of points from one\nanother, based on the recent contributions by Har-Peled and\nJones in the dataset partitioning scenario, and use such\nfoundation to analytically compute the Shattering coefficient\nfunction for both binary and multi-class problems. As main\ncontributions, one can use our approach to study the complexity\nof the search space bias F, estimate training sample sizes, and\nparametrize the number of hyperplanes a learning algorithm\nneeds to address some supervised task, what is specially\nappealing to deep neural networks. Reference: de Mello, R.F.\n(2019) \"On the Shattering Coefficient of Supervised Learning\nAlgorithms\" ; de Mello, R.F., Ponti, M.A.\n(2018, ISBN: 978-3319949888) \"Machine Learning: A Practical\nApproach on the Statistical Learning Theory\".", "License": "GPL-3", "Encoding": "UTF-8", "RoxygenNote": "7.1.1.9001", "NeedsCompilation": "no", "Packaged": { "Date": "2026-06-02 10:38:29 UTC", "User": "root" }, "Author": "Rodrigo F. de Mello [aut, cre]\n()", "Maintainer": "Rodrigo F. de Mello ", "Config/pak/sysreqs": "cmake make libicu-dev libuv1-dev", "Repository": "https://mellorf.r-universe.dev", "Date/Publication": "2021-08-21 12:50:02 UTC", "RemoteUrl": "https://github.com/cran/shattering", "RemoteRef": "HEAD", "RemoteSha": "0ba348d25ac129d4884fe4696f506b55195bbadd", "MD5sum": "85acdbd2b41fb25d9e1c85128ad4473c", "_user": "mellorf", "_type": "src", "_file": "shattering_1.0.7.tar.gz", "_fileid": "a4e36bc5f6cea675953a31235149804219775c54c63059aa95356f604ab9c0ac", "_filesize": 129670, 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