{"id":12696,"date":"2021-11-15T19:06:09","date_gmt":"2021-11-16T00:06:09","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=12696"},"modified":"2026-06-02T14:59:26","modified_gmt":"2026-06-02T18:59:26","slug":"tr-153-the-use-of-chi-squared-statistics-in-determining-dependence-trees","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1989\/tr-153-the-use-of-chi-squared-statistics-in-determining-dependence-trees\/","title":{"rendered":"TR-153: The Use of Chi-Squared Statistics in Determining Dependence Trees"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-153: The Use of Chi-Squared Statistics in Determining Dependence Trees\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n<p>Carleton University<br>\n<a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1989\/\">Technical Report<\/a> <strong>TR-153<\/strong><br>\nMarch 1989<\/p>\n\n\n\n<h2 id=\"the-use-of-chi-squared-statistics-in-determining-dependence-trees\" class=\"wp-block-heading tr_t1\">The Use of Chi-Squared Statistics in Determining Dependence Trees<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">R.S. Valiveti &amp; B.J. Oommen<\/div>\n<\/div>\n<\/div>\n\n\n\n<div>\n<h3>Abstract<\/h3>\n<p>In several pattern-recognition applications, it is often neccesary to approximate prob\u00adability distributions with well defined, parametrized q.ensity functions. For the case of discrete-valued functions (and for the cases when the features are not necessarily normally distributed), a method known as the dependence-tree exists. This method is based on the metric known as the Expected Mutual Information Measure. This paper studies the suitability of a chi-squared based metric for the same purpose. For a restricted class of distributions, these two metrics are shown to be equivalent and stochastically optimal. For the general cases, the latter metric is almost as efficient as the optimal one, but is computationally far superior.<\/p>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/tr-153.pdf\">TR-153.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-153 March 1989 The Use of Chi-Squared Statistics in Determining Dependence Trees R.S. Valiveti &amp; B.J. Oommen Abstract In several pattern-recognition applications, it is often neccesary to approximate prob\u00adability distributions with well defined, parametrized q.ensity functions. For the case of discrete-valued functions (and for the cases when the features are not [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11903,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-12696","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12696","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=12696"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12696\/revisions"}],"predecessor-version":[{"id":12697,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12696\/revisions\/12697"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11903"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=12696"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=12696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}