1
$\begingroup$

Say I have 10,000 data in 2-D and I want to fit a curve to them. There are many functional forms this curve could take -- polynomial, B-spline, trigonometric, and so on. I've decided that I only want to use 4 parameters.

Is there a way to figure out what is the most accurate functional form? That is, considering all possible functions with 4 parameters, which one fits the best in, e.g., an $L_2$ sense?

edit: maybe I should ask about the most accurate function with the same Vapnik-Chervonenkis dimension as a polynomial of degree $4$ rather than "4 parameters"?

  • 0
    @Lao Tzu: It depends on the nature of your data. The VC dimension is equivalent to the number of free independent parameters. Some classes of functions are better suited to particular types of data (in SVM this amounts to the choice of kernel). I recommend that you start with a Gaussian RBF or polynomial kernel and see with gives you better performance. Given that you have a reasonably sized data set with only two dimensions, you should be able to get a good results with either of these two kernels using a cross-validated assessment of the error.2011-07-02

0 Answers 0