Recent advances in machine learning technology make it possible
to determine definitively whether or not interactions of any
degree need to be included in a predictive model. We can thus establish 
conclusively, for example, for a given set of predictors, that
an additive model (one with no interactions) cannot be improved upon
with interactions. Or alternatively, one might prove that a model with interaction
will outperform a model without them.

Further, we can now identify
precisely which interactions are supported by the data, and also
the degree of interaction, even in very high dimensional data. The tools
we use to achieve these results are extensions of Stanford University
Professor Jerome Friedman's TreeNet, developed by the authors and embedded
in the Salford Systems TreeNet 2.0 Pro Ex product. We illustrate the
concepts in the context of a real world regression model where we are
quickly able to identify all the important interactions with a modest
number of boosted tree ensemble models.