Theory of generalization - problem about E_out?

[jjepsuomi]

Hi,

I watched the lecture "Theory of generalization", but I didn't understand Mostafa's point about E_out at 52:50 of the lecture, even though I watched it multiple times...

Here is the link for that particular point in the video...it is the last part of the proof:

http://www.youtube.com/watch?v=6FWRijsmLtE&t=52m50s



Could someone maybe make his point clear for me? Thank you for any help! =)

[yaser]

Hi,

What we are able to prove is that the union bound can be tightened using the growth function instead of the number of hyptheses. In order to do that, we considered events involving two samples, because the growth function applies only to finite samples, and the two samples together are still finite (of size instead of ). However, we need to extend this result to the case we care about, where the events involve a sample () and the whole space (), and the growth function is not directly applicable. This is what the segment is about.

BTW, I added the direct inclusion of a video segment to your post using the [lecture6] tag (see the above sticky thread about including a lecture video segment).

[jjepsuomi]

Thank you very much for the explanation =) You are a superb lecturer!