max of a summation

Question

I have a nooby question regarding the max of a summation. How does one read the following:

$$ max \sum_{u \in V} log(Pr(N_{s}(u) | f(u))$$

Does the summation not just return a single value? If it does then how are you supposed to take a max from that?

Answer 1

In the paper there is a subscript $f$ under the $\max$, so it is finding the function $f$ out of some collection of functions that maximizes the sum.