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When Efficient Model Averaging Out-Perform Bagging and Boosting Ian Davidson, SUNY Albany Wei Fan, IBM T.J.Watson Ensemble Techniques • Techniques such as boosting and bagging are methods of combining models. • Used extensively in ML and DM seems to work well in a large variety of situations. • But model averaging is the “correct” Bayesian method of using multiple models. • Does model averaging have a place in ML and DM? What is Model Averaging? Averaging of class probabilities weighted by posterior Integration Over Class Model Space Probability Posterior weighting Removes model uncertainty by averaging Prohibitive for large model spaces such as decision trees Efficient Model Averaging: PBMA and Random DT • PBMA (Davidson 04): parametric bootstrap model averaging – Use parametric model to generate multiple bootstraps computed from a single training set. • Random Decision Tree (Fan et al 03) – Construct each tree’s structure randomly • Categorical feature used once in a decision path • Random threshold for continuous features. – Leaf node statistics estimated from data. – Average probability of multiple trees. Our Empirical Study • Idea: When model uncertainty occurs, model averaging should perform well • Four specific but common situations when factoring in model uncertainty is beneficial – Class label noise – Many label problem – Sample selection bias – Small data sets Class Label Noise • Randomly flip 10% of labels Data Set with Many Classes Biased Training Sets • See ICDM 2005 for a formal analysis • See KDD 2006 to look at estimating accuracy • See ICDM 2006 for a case study Universe of Examples Two classes: red and green red: f2>f1 green: f2<=f1 Unbiased and Biased Samples Single Decision Tree Unbiased 97.1% Biased 92.1% Random Decision Tree Unbiased 96.9% Biased 95.9% Bagging Unbiased 97.82% Biased 93.52% PBMA Unbiased 99.08% Biased 94.55 Boosting Unbiased 96.405% Biased 92.7% Scope of This Paper • Identifies conditions where model averaging should outperform bagging and boosting. • Empirically verifies these claims. • Other questions: – Why does bagging and boosting perform badly in these conditions?
