# What is the possible range of SVR parameters range?

I'm working on a regression problem. While tunning the Parameters of SVR I got the following values c=100, gamma= 10 and epsilon =100. For which I got 95 percent r-square. My question is what is the theoretical range of these parameters values.?

• What is $\gamma$? Is this the parameter in your basis function? – MachineLearner Mar 22 '19 at 8:44

I support vector regression the inverse regularization parameter $$C$$ can be selected from the interval $$[0,\infty)$$. In which $$C=0$$ means that we are very heavily regularizing and $$C\to \infty$$ no regularization.

The parameter $$\varepsilon$$ is also from the interval $$[0,\infty)$$. In which $$\varepsilon=0$$ forces the regression to penalize every point that is not exactly on the regression line. Whereas $$\varepsilon > 0$$ allows an indifference margin around the regression in which a deviation will not be counted as an error.

Additionally, there are slack variables of $$\xi\geq 0$$ and $$\hat{\xi}\geq 0$$. These are zero if a point is inside the indifference margin. If a data point lies above and outside the indifference margin we will have $$\xi>0$$ and if a data point lies below and outside the indifference margin we will have $$\hat{\xi}<0$$.

I think you mean the form parameter of your radial basis function when you talk about $$\gamma$$. If we have

$$\varphi(\boldsymbol{x}_i,\boldsymbol{x}_j|\gamma)=\exp\left[-\gamma||\boldsymbol{x}_i-\boldsymbol{x}_j||^2\right]$$

then $$\gamma \in (0,\infty)$$ (Note the minus sign in front of $$\gamma$$). For $$\gamma \to 0$$ we make the kernel flatter as $$\varphi \approx 1$$. If $$\gamma \to \infty$$ we will get a very peaked kernel. Which will be 1 when $$\boldsymbol{x}_i\approx \boldsymbol{x}_i$$ and almost zero everywhere else.

You should also have a look at the documentation for the implementation of these parameters. It might happen that these parameters are not implemented as you think (see note on $$\gamma$$).