Fast NML Computation for Naive Bayes Models

The Minimum Description Length (MDL) is an informationtheoretic principle that can be used for model selection and other statistical inference tasks. One way to implement this principle in practice is to compute the Normalized Maximum Likelihood (NML) distribution for a given parametric model class. Unfortunately this is a computationally infeasible task for many model classes of practical importance. In this paper we present a fast algorithm for computing the NML for the Naive Bayes model class, which is frequently used in classification and clustering tasks. The algorithm is based on a relationship between powers of generating functions and discrete convolution. The resulting algorithm has the time complexity of O(n), where n is the size of the data.