Scientific name for the problem given in the description. (In machine learning what kind of problem it is termed as) Features marked as boolean values (around 50,000) , need to score a set of fixed output (around 25,000). 

I have wikipedia topics relevant to a particular url as features. And the output is the advertisement keywords which will perform well on those url. If I have the training data, i.e. advertisement keywords performance on urls. Given a url (I can extract the features i.e. relevant wikipedia topics), I need to predict which keyword might perform well on that url.

What is the scientific name for such kind of problems in which there is a big boolean input set and I need to score a big fixed output set. Can you name few algorithms for such kind of problems.
Ok. I think I'm getting a clearer picture. Firstly any name isn't going to be different just because the data is large. Of course in the big data community anyone is free to coin a term and time will show if it gets adopted (same goes with what we might consider a scientific name for that matter too).

Another thing is input output. These terms can be confusing as what is input by a comp scientist into a training model is both the input and output of what a statistician would define.

I'm not aware of a name for the problems but names for models addressing such a problem include logistic regression and probit regression. Both deal with a(n) (set of) independent variable(s) - the feature name in your case - and a resultant dependent variable - the binary relevancy. The regression looks at fitting a linear function to a hidden variable; whose threshold gives the binary result. Fitting an "input" training set then allows the scoring based on this linear function, whether you want a binary score or a real valued one (from the hidden variable) that will be more indicative of the probability of your prediction.