I'm studying machine learning and I feel there is a strong relationship between the concept of VC dimension and the more classical (statistical) concept of degrees of freedom.

Can anyone explain such a connection?


As stated by Prof Yaser Abu-Mostafa-

Degrees of freedom are an abstraction of the effective number of parameters. The effective number is based on how many dichotomies one can get, rather than how many real-valued parameters are used. In the case of 2-dimensional perceptron, one can think of slope and intercept (plus a binary degree of freedom for which region goes to +1), or one can think of 3 parameters w_0,w_1,w_2 (though the weights can be simultaneously scaled up or down without affecting the resulting hypothesis). The degrees of freedom, however, are 3 because we have the flexibility to shatter 3 points, not because of one way or another of counting the number of parameters.

2-d perceptron

  • $\begingroup$ I think this is a quite non-standard definition of degrees of freedom! $\endgroup$ – kjetil b halvorsen Sep 11 '15 at 11:04

The VC dimension is very well explained in this paper in Section 2.1 and further, with the basic lemmas and proofs given. You can go through this.


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.