  Classifiers based on probabilistic graphical models are very effective. In
continuous domains, maximum likelihood is usually used to assess the
predictions of those classifiers. When data is scarce, this can easily lead to
overfitting. In any probabilistic setting, Bayesian averaging (BA) provides
theoretically optimal predictions and is known to be robust to overfitting. In
this work we introduce Bayesian Conditional Gaussian Network Classifiers, which
efficiently perform exact Bayesian averaging over the parameters. We evaluate
the proposed classifiers against the maximum likelihood alternatives proposed
so far over standard UCI datasets, concluding that performing BA improves the
quality of the assessed probabilities (conditional log likelihood) whilst
maintaining the error rate.
  Overfitting is more likely to occur in domains where the number of data items
is small and the number of variables is large. These two conditions are met in
the realm of bioinformatics, where the early diagnosis of cancer from mass
spectra is a relevant task. We provide an application of our classification
framework to that problem, comparing it with the standard maximum likelihood
alternative, where the improvement of quality in the assessed probabilities is
confirmed.
