{"id":224,"date":"2022-04-05T18:39:00","date_gmt":"2022-04-05T18:39:00","guid":{"rendered":"https:\/\/groups.cs.umass.edu\/equate-ml\/?p=224"},"modified":"2022-04-07T18:15:59","modified_gmt":"2022-04-07T18:15:59","slug":"paper-towards-practical-mean-bounds-for-small-samples","status":"publish","type":"post","link":"https:\/\/groups.cs.umass.edu\/equate-ml\/2022\/04\/05\/paper-towards-practical-mean-bounds-for-small-samples\/","title":{"rendered":"Paper: Towards Practical Mean Bounds for Small Samples"},"content":{"rendered":"\n<p>Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding\u2019s inequality that use weaker assumptions but produce much looser (wider) intervals. In 1969, Anderson proposed a mean confidence interval strictly better than or equal to Hoeffding\u2019s whose only assumption is that the distribution\u2019s support is contained in an interval [a, b]. For the first time since then, we present a new family of bounds that compares favorably to Anderson\u2019s. We prove that each bound in the family has guaranteed coverage, i.e., it holds with probability at least 1\u2212\u03b1 for all distributions on an interval [a, b]. Furthermore, one of the bounds is tighter than or equal to Anderson\u2019s for all samples. In simulations, we show that for many distributions, the gain over Anderson\u2019s bound is substantial.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"http:\/\/proceedings.mlr.press\/v139\/phan21a\/phan21a.pdf\">Paper<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Historically, to bound the mean for small sample sizes, practitioners have had to choose between using methods with unrealistic assumptions about the unknown distribution (e.g., Gaussianity) and methods like Hoeffding\u2019s inequality that use weaker assumptions but produce much looser (wider) intervals. In 1969, Anderson proposed a mean confidence interval strictly better than or equal to &hellip; <a href=\"https:\/\/groups.cs.umass.edu\/equate-ml\/2022\/04\/05\/paper-towards-practical-mean-bounds-for-small-samples\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Paper: Towards Practical Mean Bounds for Small Samples&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":188,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[32,33,26],"class_list":["post-224","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai-ml","tag-32","tag-icml","tag-paper","group-blog","hfeed"],"_links":{"self":[{"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/posts\/224","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/comments?post=224"}],"version-history":[{"count":1,"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/posts\/224\/revisions"}],"predecessor-version":[{"id":225,"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/posts\/224\/revisions\/225"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/media\/188"}],"wp:attachment":[{"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/media?parent=224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/categories?post=224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/groups.cs.umass.edu\/equate-ml\/wp-json\/wp\/v2\/tags?post=224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}