# How do I interpret the length-scale parameter of the RBF kernel?

According to the Scikit-Learn documentation for the RBF kernel: The length scale of the kernel. If a float, an isotropic kernel is used. If an array, an anisotropic kernel is used where each dimension of l defines the length-scale of the respective feature dimension.

I am currently working on a problem where I am setting the length-scale of each individual feature (which I assume is synonymous with dimension here). My understanding is that a smaller length scale implies a more complex function.

My question is, can I use this parameter to explain how well a certain feature will help a model generalize to new data?

For example, if I have a data set which, after optimizing the length-scale value looks like this: [Feature_1: length-scale = 20] [Feature_2: length-scale = 1] [Feature_3: length-scale = 5]

Does this mean that, if I had to pick one feature which would help a model generalize to new data, it would be Feature_1? Is Feature_2 potentially causing my model to overfit? Are these fair assumptions to make?

Note: I am using support vector regression with this kernel.

Just to complete the answer, I like to track the complexity of a kernel model by evaluating the kernel matrix k(x1, x2) and computing its effective rank as in https://infoscience.epfl.ch/record/110188/files/RoyV07.pdf . A lower rank means a less complex model (because all the points look more similar in your implicit kernel space), whereas a higher effective rank allows learning very complex functions but you lose statistical power since in your kernel space all your points are "outliers", in the sense that they are apart from each other.