Hoeffding inequality for multiple hypothesis
It's clear for me how inequality works for each hypothesis separately. But I don't understand why we need Hoeffding inequality for multiple hypothesis. If i have training data set of size 'N' then (for fixed tolerance 'e') Hoeffding upper bound is determined for each hypoyhesis. The only thing that remains is to find hypothesis with minimal insample rate. Why do we need to consider all hypothesis simultaneously? What information gives us Hoeffding inequality with factor 'M' in it? I undetstand example with coins but I can not relate it to learning problem.
Sorry for my english and thanks.
