Naive Bayes Classifiers and One-hot Encoding of Categorical Variables

This paper investigates the consequences of encoding a K-valued categorical variable incorrectly as K bits via one-hot encoding, when using a Na"ive Bayes classifier. This gives rise to a product-of-Bernoullis (PoB) assumption, rather than the correct categorical Na"ive Bayes classifier. The differences between the two classifiers are analysed mathematically and experimentally. In our experiments using probability vectors drawn from a Dirichlet distribution, the two classifiers are found to agree on the maximum a posteriori class label for most cases, although the posterior probabilities are usually greater for the PoB case.