1
$\begingroup$

I am searching for the VC-dimension of the following:

What is the VC-dimension of the infinite set of triangle wave functions with amplitude 1 and period parameter p on points on the line?
2πarcsin⁡(sin(2πx⁄p))

$\endgroup$
1
$\begingroup$

First of all, presumably you want the VC-dimension of your class of composed with the sign function, which yields a class of Boolean functions (otherwise, VC-dim is not defined). With that out of the way, the answer is: It's infinite. That will be the answer for any periodic function class that contains all possible frequencies and crosses the x-axis. For a concrete proof for this sine wave, see Theorem 9 here: https://www.cs.bgu.ac.il/~karyeh/fat-add.pdf

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.