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?