(I'm brand-new here. I have strong mathematical and computing backgrounds, but little knowledge of statistics. If this question belongs elsewhere, I would appreciate a pointer to where.)
I believe I'm really simply searching for the best term to do further research on and perhaps links to helpful resources on that. But any suggestions are welcome.
I'm looking to reduce by an order of magnitude or so the number of factors being used to calculate a result. What terms should I be researching in order to manage this?
For a complex process, we gather 500 - 1000 different factors and feed them into a (mostly) black-box process that chooses sensible defaults for the missing ones and returns a boolean result. We'd like to choose a much smaller set of factors, perhaps 30 - 50 of them, that when fed into the process yields the closest match to the full calculation. (Since we're returning yes or no, I guess "closest match" really means that for a few thousand sample cases the number on which they disagree is the smallest.) We know that some of the factors are closely correlated and some are much more independent, but don't yet have details on those.
Gathering the factors is the expensive part of the process. Running the calculations is fairly quick.
We have to do this for several dozen different large sets of factors, and I will probably write somewhat generic programs to do this for them once I figure out the technique.
I assume this is not a unique requirement. I'd like to know what I should be researching in order to handle this.
A web search on the title yields terms such as "Factor Analysis" and "Principal Components Analysis", both of which sound like good places to start. Is one of those the correct place to focus my research? Is there a different term? Or am I on the wrong track altogether?