How to get started on multivariate predictive modeling? I'm used to doing descriptive modeling where I'm very concerned with parsimony and interpretability, but now I have a project that calls for the opposite and I'd like advice on techniques I should look into.
I have a tool (an R function) that essentially creates random graphs based on 11 parameters. There are 4 statistics about the resulting graph that I care about--the number of nodes, the mean and standard deviation of the degree distribution, and the coefficient of variation of the area distribution (areas are assigned to each node as part of the R function). I'd like to input desired ranges for the statistics and find a set (or sets) of parameter values parameters that has relatively high probability of generating an output graph with those characteristics. I've run simulations  (and running more is no problem, but they do take 1-2 seconds each) to generate lots of data, and now I need to model. I don't care what model parameters mean, I don't care how parsimonious the model is, I just need predictive power.
My questions: (1) Where do I start? Should I be looking at GAMs or other non-parametric regression techniques? (2) I've been assuming that I would fit the 4 graph statistics as dependent on the parameter values.  It occurred to me recently that I could do it the other way around. Would that be reasonable?
 A: Interesting, if rather odd, problem... I'm assuming that working out the theoretical true relationship between your variables and the graphs they create is impractical for some reason.
Apologies if the following is all very obvious to you - it may just be a conversation starter:
For your question 1, I would start with plotting the data (each of the 11 candidate explanatory variables against each of the 4 response variables) and it could go anywhere from there depending on what your eyes tell you.  I would try simple transformations to linearize the relationships and plug them into a model before looking at GAMs, although they might be the answer in the end.
Even when the purpose is prediction, parsimony is important - you will find that the less variables you have the better your predictions generally.  This will show up well in my third suggestion which is (seeing as you have a virtually unlimited supply of data) to set aside a training set for fitting your models, and a testing set for testing their predictive power.
For your question 2, I don't see any advantage in looking at it the other way around.  Four response variables is probably easier to handle than 11.
