Probabilistic Characterization of Random Decision Trees

Amit Dhurandhar, Alin Dobra; 9(Oct):2321--2348, 2008.

Abstract

In this paper we use the methodology introduced by Dhurandhar and Dobra (2009) for analyzing the error of classifiers and the model selection measures, to analyze decision tree algorithms. The methodology consists of obtaining parametric expressions for the moments of the generalization error (GE) for the classification model of interest, followed by plotting these expressions for interpretability. The major challenge in applying the methodology to decision trees, the main theme of this work, is customizing the generic expressions for the moments of GE to this particular classification algorithm. The specific contributions we make in this paper are: (a) we primarily characterize a subclass of decision trees namely, Random decision trees, (b) we discuss how the analysis extends to other decision tree algorithms and (c) in order to extend the analysis to certain model selection measures, we generalize the relationships between the moments of GE and moments of the model selection measures given in (Dhurandhar and Dobra, 2009) to randomized classification algorithms. An empirical comparison of the proposed method with Monte Carlo and distribution free bounds obtained using Breiman's formula, depicts the advantages of the method in terms of running time and accuracy. It thus showcases the use of the deployed methodology as an exploratory tool to study learning algorithms.

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