\n the optimal linear predictor for vector data (without proof). Here, let us derive the optimallinear predictor in the vector case. Suppose that {21, 12, . .., In } denote training data samples,where each r; E Rd. Suppose {y1, y2, . .., Un } denote corresponding (scalar) labels.a. Show that the mean squared-error loss function for multivariate linear regression can bewritten in the following form:MSE(w) = ly – Xw\/3where X is an n x (d + 1) matrix and where the first column of X is all-ones. What isthe dimension of w and y? What do the coordinates of w represent?b. Theoretically prove that the optimal linear regression weights are given by:w = (XX) ‘xTy.What algebraic assumptions on X did you make in order to derive the above closed form?\n <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
the optimal linear predictor for vector data (without proof). Here, let us derive the optimallinear predictor in the vector case. Suppose that {21, 12, . .., In } denote training data samples,where each r; E Rd. Suppose {y1, y2, . .., Un } denote corresponding (scalar) labels.a. Show that the mean squared-error loss function for […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/228797"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=228797"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/228797\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=228797"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=228797"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=228797"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}