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Topics in Convex Optimisation

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If you have a question about this talk, please contact Frederik Eaton.

This week, Ryota Tomioka will present some topics in convex optimisation. The primary reference will be subsections of Boyd and Vandenberghe, Convex Optimization

There is also a paper:

Performance Guarantees for Regularized Maximum Entropy Density Estimation M Dudik, SJ Phillips, RE Schapire – 17th Annual Conference on Learning Theory, 2004

The topics are:

1. Convex function (3.1; p67)

2. Legendre-Fenchel transformation (conjugate function) (3.3; p90)

3. norm and dual norm (appendix A.1)

4. Convex optimization problem (4.2; p136)

5. Lagrangian function (5.1.2; p216)

6. Lagrangian dual problem (5.2; p223)

7. Complementary slackness (5.5.2; p242)

8. Karush-Kuhn-Tucker (KKT) conditions (5.5.3; p243)

9. Maximum likelihood and maximum entropy (see Dudik et al. 2004)

10. Duality in information geometry

1-4 are basic definitions from sections 2,3,4

5-8 are from section 5 “duality”

9-10 are examples of duality in ML (not in the book)

Here are some interesting blogs talking about the connection between Fourier transformation and Legendre transformation:

http://sigfpe.blogspot.com/2005/10/quantum-mechanics-and-fourier-legendre.html http://math.ucr.edu/home/baez/qg-spring2004/discussion.html#idempotent

This talk is part of the Machine Learning Reading Group @ CUED series.

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