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? 
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.

All times are GMT 7. The time now is 12:17 AM. 
Powered by vBulletin® Version 3.8.3
Copyright ©2000  2021, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. AbuMostafa, Malik MagdonIsmail, and HsuanTien Lin, and participants in the Learning From Data MOOC by Yaser S. AbuMostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.