
#1




VC Dimension and Degrees of Freedom
Firstly, thank you to Professor Yaser for this wonderful course. I am learning a lot from it. I have a question regarding degrees of freedom and their relation to the VC dimension
In Lecture 7, the professor states that the VC dimension of a hypothesis set is equal to the number of degrees of freedom and shows that this indeed holds for positive rays and positive intervals. However in the case of a perceptron in R2, he has shown that the VC dimension is d+1, i.e. 3 but I can only see 2 degrees of freedom, the slope and intercept of the line. What am I missing here? 
#2




Re: VC Dimension and Degrees of Freedom
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#3




Re: VC Dimension and Degrees of Freedom
Another interesting "angle" on them is as dimensional vector subspaces of an dimensional vector space without considering the plane . This has the same VCdimension () even if the points can be chosen anywhere rather than on the hyperplane . Since no points on a ray can be separated, this is essentially the same as them acting on, say, a unit sphere, which has dimension . Half of this sphere is also the same as our plane by projection along the rays.

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