A System for Induction of Oblique Decision Trees

This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hill-climbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a decision tree. Oblique decision tree methods are tuned especially for domains in which the attributes are numeric, although they can be adapted to symbolic or mixed symbolic/numeric attributes. We present extensive empirical studies, using both real and artificial data, that analyze OC1's ability to construct oblique trees that are smaller and more accurate than their axis-parallel counterparts. We also examine the benefits of randomization for the construction of oblique decision trees.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

Comparison of the CPU and memory performance of StatPatternRecognition (SPR) and Toolkit for MultiVariate Analysis (TMVA)

High Energy Physics data sets are often characterized by a huge number of events. Therefore, it is extremely important to use statistical packages able to efficiently analyze these unprecedented amounts of data. We compare the performance of the statistical packages StatPatternRecognition (SPR) and Toolkit for MultiVariate Analysis (TMVA). We focus on how CPU time and memory usage of the learning process scale versus data set size. As classifiers, we consider Random Forests, Boosted Decision Trees and Neural Networks. For our tests, we employ a data set widely used in the machine learning community, "Threenorm" data set, as well as data tailored for testing various edge cases. For each data set, we constantly increase its size and check CPU time and memory needed to build the classifiers implemented in SPR and TMVA. We show that SPR is often significantly faster and consumes significantly less memory. For example, the SPR implementation of Random Forest is by an order of magnitude faster and consumes an order of magnitude less memory than TMVA on Threenorm data

Optimization of Signal Significance by Bagging Decision Trees

An algorithm for optimization of signal significance or any other classification figure of merit suited for analysis of high energy physics (HEP) data is described. This algorithm trains decision trees on many bootstrap replicas of training data with each tree required to optimize the signal significance or any other chosen figure of merit. New data are then classified by a simple majority vote of the built trees. The performance of this algorithm has been studied using a search for the radiative leptonic decay B->gamma l nu at BaBar and shown to be superior to that of all other attempted classifiers including such powerful methods as boosted decision trees. In the B->gamma e nu channel, the described algorithm increases the expected signal significance from 2.4 sigma obtained by an original method designed for the B->gamma l nu analysis to 3.0 sigma.Comment: 8 pages, 2 figures, 1 tabl