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Mathematical Formulas for Ensemble methods

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This just shows mathematical formulas for some boosting, bagging, and tree ensemble methods in machine learning. Including explanation and diagrams

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Dumb and dumber

What happens if the feature distribution does
not allow simple classifiers to work well?

Simple classifiers (few parameters, simple
structure …)
1) Are good: do not usually overfit
2) Are bad: can not solve hard problems

,Exploiting weak classifiers

Instead of learning a single classifier

Learn many weak classifiers that are good at
difference parts of the input space

Output class: vote of each classifier

, Ensamble methods
We like that:
- Classifiers that are most ‘sure’ will vote with more
conviction
- Classifiers will be most ‘sure’ about a particular part of the
space
- On average, do better than single classifiers


How?
-Force a classifier ℎ𝑡 to learn different part of the input space?
- Weight the votes of each classifier 𝛼𝑡 ?

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