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SUMMARY:Lichen Zhang (MIT Mathematics)
DTSTART:20221027T220000Z
DTEND:20221027T224500Z
DTSTAMP:20260423T003257Z
UID:SPAMS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SPAMS/21/">S
 ketching as a tool for fast optimization</a>\nby Lichen Zhang (MIT Mathema
 tics) as part of MIT Simple Person's Applied Mathematics Seminar\n\nLectur
 e held in Room: 2 - 132 in the Simons Building.\n\nAbstract\n\\noindent Sk
 etching is a powerful tool with many applications including regression\, l
 ow-rank approximation\, and preconditioning. Given an n-by-d matrix A with
  n much larger than d\, sketching describes a distribution on random matri
 ces such that an element S of this distribution is an s-by-n matrix such t
 hat for any d-dimensional $ vector x\, || SAx ||_2^2 <= (1+eps) || Ax ||_2
 ^2$ \, and $ s = poly(d\, 1/eps\, 1/delta) $ is independent of n.\n\n\\vsp
 ace{1ex}\n\n\\noindent In this talk\, I survey another direction that uses
  sketching to speed up optimization algorithms. I’ll show how to design 
 a good distribution of sketching matrices so that they can be used for \\\
 \\n1). Compressed gradient descent\, \n2). Linear programming and empirica
 l risk minimization. \\\\\n\n\\vspace{1ex}\n\n\\noindent We will see how s
 ketching enables us to develop novel data structures for numerical linear 
 algebra problems\, which are the backbones of recent breakthroughs in fast
  optimization algorithms. If time permits\, I’ll also touch on using dif
 ferential privacy (in a very surprising way) to improve the performance of
  the sketching data structure. \\\\\n
LOCATION:https://researchseminars.org/talk/SPAMS/21/
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