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High Dimensional Statistics - MIT Mathematics

High Dimensional Statistics Lecture Notes (This version: November 5, 2019). Philippe Rigollet and Jan-Christian Hu tter Spring 2017. Preface These lecture notes were written for the course , High Dimensional Statistics at MIT. They build on a set of notes that was prepared at Prince- ton University in 2013-14 that was modified (and hopefully improved) over the years. Over the past decade, Statistics have undergone drastic changes with the development of high- Dimensional statistical inference. Indeed, on each indi- vidual, more and more features are measured to a point that their number usually far exceeds the number of observations.

Nov 05, 2019 · Notation Functions, sets, vectors [n] Set of integers [n] = f1;:::;ng Sd 1 Unit sphere in dimension d 1I() Indicator function jxj q ‘ q norm of xde ned by jxj q= P i jx ij q 1 q for q>0 jxj 0 ‘ 0 norm of xde ned to be the number of nonzero coordinates of x f(k) k-th derivative of f e j j-th vector of the canonical basis Ac complement of set A conv(S) Convex hull of set S.

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