Classification problems have a long history in the machine learning literature. One of the simplest, and yet most consistently well performing set of classifiers is the Nave Bayes models. However, an inherent problem with these classifiers is the assumption that all attributes used to describe an instance are conditionally independent given the class of that instance. When this assumption is violated (which is often the case in practice) it can reduce classification accuracy due to "information double-counting" and interaction omission.

this paper we show, how this supervised learning problem can be solved e#ciently. We introduce an alternative parametrization in which the supervised likelihood becomes concave. From this result it follows that there can be at most one maximum, easily found by local optimization methods. We present test results that show this is feasible and highly beneficial