By Topic

Minimax-optimal classification with dyadic decision trees

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
C. Scott ; Dept. of Stat., Rice Univ., Houston, TX, USA ; R. D. Nowak

Decision trees are among the most popular types of classifiers, with interpretability and ease of implementation being among their chief attributes. Despite the widespread use of decision trees, theoretical analysis of their performance has only begun to emerge in recent years. In this paper, it is shown that a new family of decision trees, dyadic decision trees (DDTs), attain nearly optimal (in a minimax sense) rates of convergence for a broad range of classification problems. Furthermore, DDTs are surprisingly adaptive in three important respects: they automatically 1) adapt to favorable conditions near the Bayes decision boundary; 2) focus on data distributed on lower dimensional manifolds; and 3) reject irrelevant features. DDTs are constructed by penalized empirical risk minimization using a new data-dependent penalty and may be computed exactly with computational complexity that is nearly linear in the training sample size. DDTs comprise the first classifiers known to achieve nearly optimal rates for the diverse class of distributions studied here while also being practical and implementable. This is also the first study (of which we are aware) to consider rates for adaptation to intrinsic data dimension and relevant features.

Published in:

IEEE Transactions on Information Theory  (Volume:52 ,  Issue: 4 )