On the Product Rule for Classification Problems
This provides theoretical insights into a common method in supervised learning, but it is incremental as it builds on existing classifier combination techniques.
The paper analyzes the product rule for classifier combination, showing it arises from MAP classification with certain assumptions and is equivalent to minimizing weighted squared distances under specific conditions.
We discuss theoretical aspects of the product rule for classification problems in supervised machine learning for the case of combining classifiers. We show that (1) the product rule arises from the MAP classifier supposing equivalent priors and conditional independence given a class; (2) under some conditions, the product rule is equivalent to minimizing the sum of the squared distances to the respective centers of the classes related with different features, such distances being weighted by the spread of the classes; (3) observing some hypothesis, the product rule is equivalent to concatenating the vectors of features.