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SUMMARY:Topics in Convex Optimisation - Ryota Tomioka\, University of Toky
 o
DTSTART:20070322T130000Z
DTEND:20070322T150000Z
UID:TALK6898@talks.cam.ac.uk
CONTACT:Frederik Eaton
DESCRIPTION:This week\, Ryota Tomioka will present some topics in convex o
 ptimisation. The primary reference will be subsections of Boyd and Vandenb
 erghe\, "Convex Optimization":http://www.stanford.edu/~boyd/cvxbook/bv_cvx
 book.pdf\n\nThere is also a paper:\n\n"Performance Guarantees for Regulari
 zed Maximum Entropy Density Estimation":http://www.cs.princeton.edu/~mdudi
 k/DudikPhSc04.pdf\nM Dudik\, SJ Phillips\, RE Schapire - 17th Annual Confe
 rence on Learning Theory\, 2004\n\nThe topics are:\n\n1. Convex function (
 3.1\; p67)\n\n2. Legendre-Fenchel transformation (conjugate function) (3.3
 \; p90)\n\n3. norm and dual norm (appendix A.1)\n\n4. Convex optimization 
 problem (4.2\; p136)\n\n5. Lagrangian function (5.1.2\; p216)\n\n6. Lagran
 gian dual problem (5.2\; p223)\n\n7. Complementary slackness (5.5.2\; p242
 )\n\n8. Karush-Kuhn-Tucker (KKT) conditions (5.5.3\; p243)\n\n9. Maximum l
 ikelihood and maximum entropy (see Dudik et al. 2004)\n\n10. Duality in in
 formation geometry\n\n1-4 are basic definitions from sections 2\,3\,4\n\n5
 -8 are from section 5 "duality"\n\n9-10 are examples of duality in ML (not
  in the book)\n\nHere are some interesting blogs talking about the connect
 ion between Fourier transformation and Legendre transformation:\n\nhttp://
 sigfpe.blogspot.com/2005/10/quantum-mechanics-and-fourier-legendre.html\nh
 ttp://math.ucr.edu/home/baez/qg-spring2004/discussion.html#idempotent\n
LOCATION:5th floor meeting room\, Engineering Department
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