The winnow algorithm is a technique from machine learning for learning a linear classifier from labeled examples. It is very similar to the perceptron algorithm. However, the perceptron algorithm uses an additive weight-update scheme, while Winnow uses a multiplicative scheme that allows it to perform much better when many dimensions are irrelevant (hence its name winnow). It is a simple algorithm that scales well to high-dimensional data. During training, Winnow is shown a sequence of positive and negative examples. From these it learns a decision hyperplane that can then be used to label novel examples as positive or negative. The algorithm can also be used in the online learning setting, where the learning and the classification phase are not clearly separated.

Algorithm

, that is, each instance is described as a set of Boolean-valued features, it applies the typical prediction rule for linear classifiers:

• If, then predict 1

• Otherwise predict 0

is a real number that is called the threshold (see below).

For each example with which it is presented, the learner applies the following update rule:

• If an example is correctly classified, do nothing.

• is set to 0 (demotion step).

• multiplied by (promotion step).

A typical value for is 2.

There are many variations to this basic approach. Winnow2 is similar except that in the demotion step the weights are divided by instead of being set to 0. Balanced Winnow maintains two sets of weights, and thus two hyperplanes. This can then be generalized for multi-label classification.

Mistake bounds

In certain circumstances, it can be shown that the number of mistakes Winnow makes as it learns has an upper bound.

References