  Standard methods of using categorical variables as predictors either endow
them with an ordinal structure or assume they have no structure at all.
However, categorical variables often possess structure that is more complicated
than a linear ordering can capture. We develop a mathematical framework for
representing the structure of categorical variables and show how to generalize
decision trees to make use of this structure. This approach is applicable to
methods such as Gradient Boosted Trees which use a decision tree as the
underlying learner. We show results on weather data to demonstrate the
improvement yielded by this approach.
