Tree Induction vs. Logistic Regression: A Learning-Curve Analysis

Abstract

Tree induction and logistic regression are two standard, off-the-shelf methods for building models for classification. We present a large-scale experimental comparison of logistic regression and tree induction, assessing classification accuracy and the quality of rankings based on class-membership probabilities. We use a learning-curve analysis to examine the relationship of these measures to the size of the training set. The results of the study show several remarkable things. (I) Contrary to prior observations, logistic regression does not generally outperform tree induction. (2) More specifically, and not surprisingly, logistic regression is better for smaller training sets and tree induction for larger data sets. Importantly, this often holds for training sets drawn from the same domain (i.e., the learning curves cross), so conclusions about induction-algorithm superiority on a given domain must be based on an analysis of the learning curves. (3) Contrary to conventional wisdom, tree induction is effective at producing probability-based rankings, although apparently comparatively less so for a given training--set size than at making classifications. Finally, (4) the domains on which tree induction and logistic regression are ultimately preferable can be characterized surprisingly well by a simple measure of signal-to-noise ratio.