M=H? (Lecture 2 slide 1617)
I have a question regarding the value of M in the multiplebins Hoeffding bound slides.
M is supposed to be the number of different alternate hypotheses considered by the learning algorithm. At the same time, H is the space of possible hypotheses that can be considered by the algorithm (e.g., all linear functions, etc). I keep going back and forth in my mind about whether M=H. Specifically, suppose that for a SPECIFIC training set X, after looking at the data points in X, the algorithm only explored some subset of H, say G with G < H. Would it then be correct to set M = G and say that for the specific training set X, the probability of the hypothesis being bad is at most 2G*the hoeffding bound ? Or would this be incorrect since the theorem only deals with the behavior of the system over all possible X with the distribution P. Thanks! 
Re: M=H? (Lecture 2 slide 1617)
Thank you Professor for your reply. It makes sense now. I think trying to consider the space of hypothesis "actually explored" is not that useful, as you said, the space of possible hypothesis is independent of and and the resultant bound is a much more general and useful characterization of the learning model.

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