P(X) and Error Measure Doubts in Lecture 4

[pranav_s]

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 point-wise 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.

[yaser]

Originally Posted by pranav_s

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!

Your understanding of the role of is correct. The problem you foresee if we take a particular is not really a problem since we do not need to pick a particular . No points are emphasized or deemphasized by the assumption we made which is the mere existence of such .

2.Error measures are supposed to be the average point-wise 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.

The out-of-sample error is inherently unknown. If it were known, we would just minimize it and forget about learning from the data set. However, there are ways to estimate the out-of-sample error through a test or validation set. This will be discussed in detail in a later lecture.

[pranav_s]

Thank you sir, also the course is really interesting.