{"id":456750,"date":"2018-01-04T00:00:34","date_gmt":"2018-01-04T08:00:34","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=456750"},"modified":"2018-01-25T09:59:55","modified_gmt":"2018-01-25T17:59:55","slug":"understanding-over-parametrization-through-matrix-sensing","status":"publish","type":"msr-video","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/video\/understanding-over-parametrization-through-matrix-sensing\/","title":{"rendered":"Understanding Over-parametrization Through Matrix Sensing"},"content":{"rendered":"<p>We study the problem of recovering a low-rank matrix from linear measurements using an over-parameterized model. We show that the gradient descent process on the square loss function, starting from a small initialization, can converge to the ground truth matrix. Although the total number of observations is much smaller than the total number of parameters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study the problem of recovering a low-rank matrix from linear measurements using an over-parameterized model. We show that the gradient descent process on the square loss function, starting from a small initialization, can converge to the ground truth matrix. Although the total number of observations is much smaller than the total number of parameters.<\/p>\n","protected":false},"featured_media":456840,"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":[13561,13546],"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-456750","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/D4HLmgGwt1o","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/456750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":3,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/456750\/revisions"}],"predecessor-version":[{"id":456846,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/456750\/revisions\/456846"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media\/456840"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=456750"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=456750"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=456750"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=456750"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=456750"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=456750"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=456750"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=456750"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=456750"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=456750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}