## 17. Learning: Boosting

“Wisdom of a weighted crowd of experts”

## Classifiers

Classifiers are tests that produce binary choices about samples. They are considered strong classifiers if their error rate is close to 0,  weak classifiers if their error rate is close to 0.5.

By using multiple classifiers with different weights, data samples can be sorted or grouped according to different characteristics.

## Decision tree stumps

Aside from classifiers, a decision tree can be used to sort positive and negative samples in a 2-dimension space. By adding weights to different tests, some samples can be emphasized over the others. The total sum of weights must always be constrained to 1 to ensure a proper distribution of samples.

## Dividing the space

By minimizing the error rate of the tests from the weights, the algorithm can cut the space to sort positive and negative examples.

## No over fitting

Boosting algorithms seems not to be over fitting, as the decision tree stumps tends to be very tightly close to outlying samples, only excluding them from the space.

## Decision boundaries

Separating positive and negative example with a straight line that is as far as possible from both positive and negative examples, a median that maximizes the space between positive and negative examples.

Constraints are applied to build a support vector (u) and define a constant b that allow to sort positive examples from negative ones. The width of a “street” between the positive and negative values is maximized.

Going through the algebra, the resulting equation show that the optimization depends only on the dot product of pair of samples.

The decision rule that defines if a sample is positive or negative only depends on the dot product of the sample vector and the unknown vector.

### No local maximum

Such support vector algorithm can be proven to be evolving in a convex space, meaning that it will never be blocked at a local maximum.

### Non linearity

The algorithm cannot find a median between data which cannot be linearly separable. A transformation can however be applied to the space to reorganize the samples so that they can be linearly separable. Certain transformations can however create an over fitting model that becomes useless by only sorting the example data.