  Based on decision trees, many fields have arguably made tremendous progress
in recent years. In simple words, decision trees use the strategy of
"divide-and-conquer" to divide the complex problem on the dependency between
input features and labels into smaller ones. While decision trees have a long
history, recent advances have greatly improved their performance in
computational advertising, recommender system, information retrieval, etc. We
introduce common tree-based models (e.g., Bayesian CART, Bayesian regression
splines) and training techniques (e.g., mixed integer programming, alternating
optimization, gradient descent). Along the way, we highlight probabilistic
characteristics of tree-based models and explain their practical and
theoretical benefits. Except machine learning and data mining, we try to show
theoretical advances on tree-based models from other fields such as statistics
and operation research. We list the reproducible resource at the end of each
method.
