Axelle's answer explains how the two slack variables are different. We could replace the two slack variables by 1 by using the absolute value of the difference between the prediction and the target variable. This would make for a non-differentiable constraint function(which could be bothersome if one needs to derive the dual formulation or while deriving the KKT conditions) and this is why two different slack variables are introduced in the regression problem.
Why use two slack variables in the support vector regression formulation?
General Tech Learning Aids/Tools 2 years ago
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manpreet![Tuteehub forum best answer]()
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2 years ago
I am learning support com/tag/vector">vector regression but cannot fully understand the rational of the slack variable tricks in its formulation. The original optimization problem for SVR is as follows:
min{C∑Ni=1Lϵ(yi,w0+wTxi)+12||w||2}min{C∑i=1NLϵ(yi,w0+wTxi)+12||w||2}
where Lϵ(yi,w0+wTxi)=max{0,∣∣class="mi" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: normal; font-family: MathJax_Math-italic; font-size: 16.65px