Timeline for Relation between values of $ξ_i$ and $\alpha_i$ in SVM?

9 events

when toggle format	what		by	license	comment
Jun 26 at 19:42	comment	added	Ted Black		$\hat\alpha_i <C$ is a deduction from (12.15) and (12.12). $\mu_i$ is a slack variable; you can see that since none of the derivatives (12.10), (12.11) and (12.12) are partial derivatives w.r.t. $\mu_i$.
Jun 26 at 19:39	comment	added	hasanghaforian		@TedBlack So, I think that you are agree that $\hat\alpha_i < C$ is not a deduction. Although as I know $ξ_i$ is the slack variable and $\mu_i$ is one of Lagrangian multipliers.
Jun 26 at 19:26	comment	added	Ted Black		$\mu_i$ is a slack variable which hopefully has a positive value that forces $\xi_i$ to be optimised (to minimize the objective we would like $\xi_i \geq 0$).
Jun 26 at 18:33	history	edited	hasanghaforian	CC BY-SA 4.0	added 57 characters in body
Jun 26 at 18:22	comment	added	hasanghaforian		@TedBlack Thank you for your reply. But I said I think both $\mu_i$ and $ξ_i$ may be zero at the same time. Are not you agree with me?
Jun 25 at 17:17	comment	added	Ted Black		Since one of the constraints is $\mu_i \xi_i=0$, if we are on the edge of the margin $\xi_i=0$ and so $\mu_i >0$. Since $\alpha_i = C - \mu_i$, $\alpha_i < C$. From the positivity constraints $\alpha_i, \mu_i, \xi_i \geq 0 \; \forall i$, since in this case $\alpha_i \neq 0$, we get $\alpha_i > 0$.
Jun 25 at 4:42	history	edited	hasanghaforian	CC BY-SA 4.0	added 220 characters in body
Jun 24 at 18:35	history	edited	hasanghaforian	CC BY-SA 4.0	added 98 characters in body
Jun 24 at 18:26	history	asked	hasanghaforian	CC BY-SA 4.0