[yaser]

Originally Posted by Averroes

I succeeded to understand most of it except (A.4) in the bottom of page 189. I can understand that you have applied Hoeffding Inequality to h*, but your explanation on how this applies to h* conditioned to the sup_H event, is hard to grasp for me.

Thank you for your post. The hypothesis is based on a fixed data set among the possible s. Once we know that such exists, the conditioned-upon statement does not matter. We have a fixed hypothesis and independently generated data sets , so we can apply Hoeffding to that in isolation.