{"version":"1.0","provider_name":"Microsoft Research","provider_url":"https:\/\/www.microsoft.com\/en-us\/research","author_name":"Ralf Herbrich","author_url":"https:\/\/www.microsoft.com\/en-us\/research\/people\/rherb\/","title":"Kernel Methods for Measuring Independence - Microsoft Research","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"8MTSCMEI0F\"><a href=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/kernel-methods-for-measuring-independence\/\">Kernel Methods for Measuring Independence<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.microsoft.com\/en-us\/research\/publication\/kernel-methods-for-measuring-independence\/embed\/#?secret=8MTSCMEI0F\" width=\"600\" height=\"338\" title=\"&#8220;Kernel Methods for Measuring Independence&#8221; &#8212; Microsoft Research\" data-secret=\"8MTSCMEI0F\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/\/# sourceURL=https:\/\/www.microsoft.com\/en-us\/research\/wp-includes\/js\/wp-embed.min.js\n\/* ]]> *\/\n<\/script>\n","description":"We introduce two new functionals, the constrained covariance and the kernel mutual information, to measure the degree of independence of random variables. These quantities are both based on the covariance between functions of the random variables in reproducing kernel Hilbert spaces (RKHSs). We prove that when the RKHSs are universal, both functionals are zero if [&hellip;]"}