{"id":192683,"date":"2015-08-18T00:00:00","date_gmt":"2015-08-18T12:53:30","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/provable-non-convex-projections-for-high-dimensional-learning-problems-part2\/"},"modified":"2016-07-15T15:26:12","modified_gmt":"2016-07-15T22:26:12","slug":"provable-non-convex-projections-for-high-dimensional-learning-problems-part2","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/provable-non-convex-projections-for-high-dimensional-learning-problems-part2\/","title":{"rendered":"Provable Non-convex Projections for High-dimensional Learning Problems -Part2"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Typical high-dimensional learning problems such as sparse regression, low-rank matrix completion, robust PCA etc can be solved using projections onto non-convex sets. However, providing theoretical guarantees for such methods is difficult due to the non-convexity in projections. In this talk, we will discuss some of our recent results that show that non-convex projections based methods can be used to solve several important problems in this area such as: a) sparse regression, b) low-rank matrix completion, c) robust PCA.<\/p>\n<p>In this talk, we will give an overview of the state-of-the-art for these problems and also discuss how simple non-convex techniques can significantly outperform state-of-the-art convex relaxation based techniques and provide solid theoretical results as well. For example, for robust PCA, we provide first provable algorithm with time complexity O(n<sup>2<\/sup> r) which matches the time complexity of normal SVD and is faster than the usual nuclear+L<sub>1<\/sub>-regularization methods that incur O(n<sup>3<\/sup>) time complexity. This talk is based on joint works with Ambuj Tewari, Purushottam Kar, Praneeth Netrapalli, Animashree Anandkumar, U N Niranjan, and Sujay Sanghavi.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Typical high-dimensional learning problems such as sparse regression, low-rank matrix completion, robust PCA etc can be solved using projections onto non-convex sets. However, providing theoretical guarantees for such methods is difficult due to the non-convexity in projections. In this talk, we will discuss some of our recent results that show that non-convex projections based methods [&hellip;]<\/p>\n","protected":false},"featured_media":199231,"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-192683","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/X0oS8KythN4","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192683","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\/192683\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/199231"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=192683"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=192683"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=192683"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=192683"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=192683"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=192683"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=192683"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=192683"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=192683"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=192683"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}