Decision Stream: Cultivating Deep Decision Trees

Various modifications of decision trees have been extensively used during the past years due to their high efficiency and interpretability. Tree node splitting based on relevant feature selection is a key step of decision tree learning, at the same time being their major shortcoming: the recursive nodes partitioning leads to geometric reduction of data quantity in the leaf nodes, which causes an excessive model complexity and data overfitting. In this paper, we present a novel architecture - a Decision Stream, - aimed to overcome this problem. Instead of building a tree structure during the learning process, we propose merging nodes from different branches based on their similarity that is estimated with two-sample test statistics, which leads to generation of a deep directed acyclic graph of decision rules that can consist of hundreds of levels. To evaluate the proposed solution, we test it on several common machine learning problems - credit scoring, twitter sentiment analysis, aircraft flight control, MNIST and CIFAR image classification, synthetic data classification and regression. Our experimental results reveal that the proposed approach significantly outperforms the standard decision tree learning methods on both regression and classification tasks, yielding a prediction error decrease up to 35%

Optimal Sparse Decision Trees

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.Comment: 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canad