Usually, the margin-based bound for SVM rely on the fact that we minimise Hinge loss. definition The \gamma-ramp loss is given by the following: \Phi_\gamma(t) = \begin{cases} 0 & \text{if } t \geq \gamma \\ 1 - \frac{t}{\gamma} & \text{if } 0 < t < \gamma \\ 1 & \text{if } t \leq 0 \end{cases} In relation with Hinge loss: \mathcal{l}^{\text{ramp}}(\textbf{w}, (\textbf{x},y)) = \min \{1, \mathcal{l}^{\text{hinge}}(\textbf{w}, (\textbf{x},y))\} = \min \{1, \max\{0, 1 - y \langle w, x \rangle\}\} Note that we use Hinge loss for SVM is due to the fact that ramp-loss is a non-convex functions, meaning it is more computationally efficient to minimise Hinge loss in comparison to ramp loss.
Usually, the margin-based bound for SVM rely on the fact that we minimise Hinge loss.
definition
The -ramp loss is given by the following:
In relation with Hinge loss:
Note that we use Hinge loss for SVM is due to the fact that ramp-loss is a non-convex functions, meaning it is more computationally efficient to minimise Hinge loss in comparison to ramp loss