{"id":450075,"date":"2017-11-13T00:00:37","date_gmt":"2017-11-13T08:00:37","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=450075"},"modified":"2017-12-12T08:58:09","modified_gmt":"2017-12-12T16:58:09","slug":"foundations-of-data-science-lecture-8-low-rank-approximation-lra-via-length-squared-sampling","status":"publish","type":"msr-video","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/video\/foundations-of-data-science-lecture-8-low-rank-approximation-lra-via-length-squared-sampling\/","title":{"rendered":"Foundations of Data Science &#8211; Lecture 8 &#8211; Low Rank Approximation (LRA) via Length Squared Sampling"},"content":{"rendered":"<p>Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science. This mini-course covers these areas, providing intuition and rigorous proofs. Connections between Geometry and Probability will be brought out. Text Book: <a href=\"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/foundations-of-data-science-2\/\">Foundations of Data Science<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science. This mini-course covers these areas, providing intuition and rigorous proofs. Connections between Geometry and Probability will be brought out. Text [&hellip;]<\/p>\n","protected":false},"featured_media":450081,"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-450075","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\/plgmGhyVIdM","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/450075","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":2,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/450075\/revisions"}],"predecessor-version":[{"id":450084,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/450075\/revisions\/450084"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media\/450081"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=450075"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=450075"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=450075"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=450075"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=450075"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=450075"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=450075"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=450075"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=450075"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=450075"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}