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Hmm, not sure if we are discussing the same thing anymore. The std of errors in the neighborhood is an indication of distribution of an error I expect to make at a point. The actual absolute value of the error will not match the standard deviation, sure, but the information about the distribution of the error is still useful (at least in my use case).
indeed, the individual prediction can be way off, but what I want is information like in the interval 1.95-2.05 the std of error was 2, but in the interval 1.55-1.65 was 1.5. This should be doable by smoothing, the question is only how aggressive (length of window, parameters of kernel, etc.). In principle there is even no need for the second regressor, except for comfort of having more compact representation of smoothed surface.
Indeed, although I was hoping for this to be less of a concern, as I don't expect standard deviation of errors to be very noisy (given I do the smoothing right).
That is indeed a tricky part, and while I can image some ad-hoc strategies, I don't have a satisfactory answer to this now. I was hoping to get some insights from the (non existing?) references.
There are several methods that can be used to calculate the variable importance. For example one can calculate "total decrease in node impurities from splitting on the variable, averaged over all trees", in which case the answer to you question would be "all the samples". Do you have a specific method in mind?
You do not need a join distribution. If someone specifies the probabilities $P(R|L_i) = p_i$ for each region $L_i$, then you are free to do what you did when you had no regions. For each player in location $L_i$ sample from $[0,1]$ and reward those who were in $[0, p_i)$.
It is very difficult to understand what are you trying to do, and where the difficulty lies. You write that you would like to be able to specify a probability of reward conditional on the location. Why can't you do it? And based on what you want to assign this probability? Infer from data?
Also note that "equation" is not a good word, as these are expressions or formulas (if written in se = ... style). I second Dilip, in proposing not to use the second one at all.
