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udaykamath 04-04-2013 10:18 AM

SVM equation from Slides
 
Prof Yaser.
Even though its not related to book chapter but the slide but thought it made sense here in this discussion.

In SVM slides Lecture 14

On page 13 we had just converted the problem to minimization and had

minimize Lagrangian(alpha)=....

On page 14 we have

maximize Lagrangian w.r.t alpha subject to...

How did this change?

Also page 15

we convert the maximize problem to minimize problem by inverting the sign.

So the jump from first minimize to maximize of lagrangian is not clear.

Thanks
Uday Kamath

yaser 04-04-2013 01:12 PM

Re: SVM equation from Slides
 
Quote:

Originally Posted by udaykamath (Post 10137)
In SVM slides Lecture 14

On page 13 we had just converted the problem to minimization and had

minimize Lagrangian(alpha)=....

On page 14 we have

maximize Lagrangian w.r.t alpha subject to...

How did this change?

Thank you for asking. In slide 13, minimization is w.r.t. some of the variables, and for the rest of the variables it is maximization (per Lagrange/KKT method). The minimization has already been done in the derivation in slide 13, so only the maximization part remains in slide 14.

udaykamath 04-04-2013 02:38 PM

Re: SVM equation from Slides
 
thanks for your answer, so Lagrange(w,b,alpha) minimization means w.r.t to minimize w and b and maximize w.rt. alpha.

Also, you mention in the video that the KKT condition, the first one, of replacing the min yn(wXn+b) =1 is equivalent to using the inequality using the slack time square and adjusting. You mention that you will explain that in the Q&A, but no one asked that in Q&A and was wondering if you can here or some place give and explanation of the slack square thing and how min gets changed to non minimum with adding equality.

Thanks again for the wonderful lectures and book!
Forever indebted!
Uday

yaser 04-04-2013 03:17 PM

Re: SVM equation from Slides
 
Quote:

Originally Posted by udaykamath (Post 10142)
thanks for your answer, so Lagrange(w,b,alpha) minimization means w.r.t to minimize w and b and maximize w.rt. alpha.

Also, you mention in the video that the KKT condition, the first one, of replacing the min yn(wXn+b) =1 is equivalent to using the inequality using the slack time square and adjusting. You mention that you will explain that in the Q&A, but no one asked that in Q&A and was wondering if you can here or some place give and explanation of the slack square thing and how min gets changed to non minimum with adding equality.

Thanks again for the wonderful lectures and book!
Forever indebted!
Uday

The slack argument is probably available online in writeups about KKT. The basic idea is to add a squared variable s^2 to one side of an inequality to make it equality, and because it is squared, there are no resrictions on the value of s itself.


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