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?

Posterior weighting

Class Probability

Integration Over Model Space

Averaging of class probabilities weighted by posterior

Removes model uncertainty by averaging

Prohibitive for large model spacessuch 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>f1green: 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?