Are there any methodologies for combining the class probabilities from a classifier run on partitioned data? We have n datasets, all in the same format, managed by separate organizations. For legal/privacy reasons, the raw data cannot be retrieved from their servers. 
We run classifier models against the individual datasets. Are there any legitimate approaches to combining the predicted class probabilities to make inferences about the larger population?
Since this is a broad question, pointers to relevant literature would be greatly appreciated.
 A: I can think of two approaches. First, the simple one --
1) Fit your K separate models, privately
2) For each one, simulate a data set of that model's original size (or just share the parameter estimates, and have somebody else do the simulation)
3) Run a big regression on the pooled, simulated, data.
4) POSSIBLY weight the sub-datasets by the original goodness of fit, but I have no principled way of doing that.
As far as privacy goes, this is the same as sharing the estimated parameters, intervals, and N, which I assume is okay, and gives you a simple way of combining results, with outcomes that are easy to interpret and manipulate. I don't have a citation for this unfortunately, but nothing about it strikes me as unnaturally dangerous (given your options) -- your big worry will be goodness of fit in the component models though, so I would communicate thoroughly about that, to the extent you can to feel confident.
The second approach I know less about, but I have seen talks on models being fit in distributed systems, and thought perhaps a single model could be run on all your separated data without anyone seeing all of it at once. How, I have no clue, but I would look in that direction as well. A recent Stanford stats PhD was working on something like that for the lasso, but that's really all I know.
