Bayes optimal instance-based learning

In this paper we present a probabilistic formalization of the instance-based learning approach. In our Bayesian framework, moving from the construction of an explicit hypothesis to a data-driven instancebased learning approach, is equivalent to averaging over all the (possibly infinitely many) individual models. The general Bayesian instance-based learning framework described in this paper can be applied with any set of assumptions defining a parametric model family, and to any discrete prediction task where the number of simultaneously predicted attributes is small, which includes for example all classification tasks prevalent in the machine learning literature. To illustrate the use of the suggested general framework in practice, we show how the approach can be implemented in the special case with the strong independence assumptions underlying the so called Naive Bayes classifier. The resulting Bayesian instance-based classifier is validated empirically with public domain data sets and the results are compared to the performance of the traditional Naive Bayes classifier. The results suggest that the Bayesian instancebased learning approach yields better results than the traditional Naive Bayes classifier, especially in cases where the amount of the training data is small.