P(X) and Error Measure Doubts in Lecture 4
I have a couple of doubts from the 4th Lecture, any clarification would be really appreciated.
1. When talking about P(X), I gather that it was introduced in order to arrive at the Hoeffding's Inequality which is probabilistic in nature. However, even if whe are not making any assumptions about P(X), isn't it true that we are limiting the generalization prospects. As in, if we assume the input set having a particular P(X) we are really regarding the inputs distributed only along those lines. Please clarify if I have got it all wrong!
2.Error measures are supposed to be the average pointwise errors encountered using a hypothesis. How do we really calculate the E_out. considering we do not know the target function, we have taken a random out of sample input. So, e(h(X),f(X)) seems strange as f(X) is really unknown at this Input point.
