Pinging @elastic/ml-core (:ml)

It's a good point about using double instead of float. float only stores 7 digits of accuracy, so if the dependent variable contained integers greater than 10 million then using float will lose more accuracy than sticking with integer. (integer will lose the fractions from the predictions, but for a number between 10 and 100 million float would make the units and fraction random.) double would be a reasonable compromise as it has 15 digits of accuracy. long has 19, but we'd only suffer the problem at the (unusual) extreme sizes, whereas integers over 10 million are not that uncommon.

I wonder if we should force the mapping for regression to always be double instead of it being float? I am not sure if the precision loss is a concern or not.

This change required bigger changes in the logic that calculates mappings as now Regression imposes constant mapping while Classification copies the mapping from dependent variable.
You might want to take another look @benwtrent and @droberts195.