Rethink Decision Tree Traversal

We will show how to evaluate binary decision tree traversal in the language of matrix computation motivated by \textit{QuickScorer} in \cite{lucchese2015quickscorer}. Our main contribution is a novel matrix representation of the hierarchical structure of the decision tree. And we propose some equivalent algorithms of binary decision tree traversal based on rigorous theoretical analysis. The core idea is to find the relation between the input and exit leaf node. Here we not only understand decisions without the recursive traverse but also dive into the partitioning nature of tree-based methods.