Optimal Sparse Decision Trees
This addresses the issue of suboptimal models in interpretable machine learning for practitioners, though it is incremental as it focuses on binary variables.
The authors tackled the long-standing problem of decision tree algorithms lacking optimality guarantees by introducing the first practical algorithm for optimal decision trees for binary variables, achieving scalability, speed, and proof of optimality in experiments.
Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library. Our experiments highlight advantages in scalability, speed, and proof of optimality. The code is available at https://github.com/xiyanghu/OSDT.