  Based on decision trees, it is efficient to handle tabular data. Conventional
decision tree growth methods often result in suboptimal trees because of their
greedy nature. Their inherent structure limits the options of hardware to
implement decision trees in parallel. Here is a compact representation of
binary decision trees to overcome these deficiencies. We explicitly formulate
the dependence of prediction on binary tests for binary decision trees and
construct a function to guide the input sample from the root to the appropriate
leaf node. And based on this formulation we introduce a new interpretation of
binary decision trees. Then we approximate this formulation via continuous
functions. Finally, we interpret the decision tree as a model combination
method. And we propose the selection-prediction scheme to unify a few learning
methods.
