# Error distribution of support vector machine

I am recently learning to use support vector machine as classification. I have some question about it and hope that it is not a dumb question.

As far as I know, For multinomial logistic model for classification, the error terms is assumed to be i.i.d double-exponential distribution. For probit model, it is assumed to be normal distribution.

How about support vector machine? Since we assume the data is linearly separable, does the error distribution related to the distance between the hyperplane and the support vector?

The margin $M = \frac{1}{||\beta||}$

where the hyperplane is $\{x: f(x) = x^T \beta + \beta_0 = 0\}$ and the decision rule for class $\{-1,1\}$ is simply $sign(x^T \beta + \beta_0)$.

and I think somehow the "variance" of the error is controlled by the cost and I can use it to control the bias-variance tradeoff?

For the hard-margin support vector machine, there is no real means of controlling the bias-variance trade-off. For that you need to use the soft-margin formulation, where the bias-variance trade-off is controlled by the regularisation parameter, $C$.