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

Decision trees and prescriber choices

Prescriber decisions are increasingly being pressured by a supply of economic information in the form of cost-effectivenessstudies, or similar evaluations, of a range of pharmaceuticals. These have been welcomed by Virginia Bottomley and a set of guidelines for these studies has been drawn up by the Department of Health and the pharmaceutical industry. Such economic studies are now being published in a wide range of journals and are increasingly being used in promotional literature and publicity handouts by the pharmaceutical companies. Many of these studies are using decision trees with which to represent clinical problems and perform analysis of the costs of treatment. This paper reviews the principles and practice of analysis using these techniques, providing guidance on the critical review of such studies