LASSOLOESS and piecewise linear models. I favor splines, especially penalized smoothing splines via the R package pspline, using generalized cross validation to set the smoothing parameter. Tamino looks for breaks in the piecewise linear case to check for and test for significant changes. I use the first and higher derivatives of the spline.
Both methods are sound and good.
I don’t know how you might use a random forest regression for this purpose, but I bet there is a way. I doubt it is as good, though.
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