{"id":185832,"date":"2011-01-10T00:00:00","date_gmt":"2011-01-12T08:28:45","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/optimal-moment-estimation-in-data-streams\/"},"modified":"2016-08-22T11:30:38","modified_gmt":"2016-08-22T18:30:38","slug":"optimal-moment-estimation-in-data-streams","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/optimal-moment-estimation-in-data-streams\/","title":{"rendered":"Optimal Moment Estimation in Data Streams"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We close the problem of understanding the space complexity of pth moment estimation in data streams for 0  p = 2 by giving the first optimal upper and lower bounds. In this problem, a high-dimensional vector receives a long sequence of coordinate-wise updates, and we must output a low relative-error approximation of the pth moment at the end of the stream while keeping a memory footprint exponentially smaller than the vector length. This problem has applications in network traffic monitoring, databases, and simply computing distance measures across massive datasets.<\/p>\n<p>We obtain the upper bound by showing an invariance principle for sums of boundedly independent p-stable random variables, which may be of independent interest.  Our main ingredient in this proof is the introduction of an approximation theoretic tool we dub &#8220;FT-mollification&#8221;, which has since found other applications in agnostic learning, pseudorandomness, and approximation theory. We obtain the lower bound by showing a direct sum property for the one way communication complexity of the GapHamming problem.<\/p>\n<p>Joint work with Daniel M. Kane (Harvard) and David P. Woodruff (IBM Almaden)<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We close the problem of understanding the space complexity of pth moment estimation in data streams for 0 p = 2 by giving the first optimal upper and lower bounds. In this problem, a high-dimensional vector receives a long sequence of coordinate-wise updates, and we must output a low relative-error approximation of the pth moment [&hellip;]<\/p>\n","protected":false},"featured_media":195946,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-185832","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/b_Yq5QRDOCU","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185832","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185832\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/195946"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=185832"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=185832"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=185832"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=185832"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=185832"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=185832"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=185832"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=185832"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=185832"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=185832"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}