Marginal and simultaneous predictive classification using stratified graphical models

Supervised classification is one of the most common tasks considered in machine learning and statistics (Bishop, 2007; Duda et al., 2000; Hastie et al., 2009; Ripley, 1996), with a wide variety of applications over practically all fields of science and engineering. Today, there exists a myriad of different classification methods, out of which those based on probabilistic models are widely accepted as the most sensible way to solve classification problems. Probabilistic methods are often themselves classified as either generative or discriminative, depending on whether one directly models the class posterior distribution (discriminative classifiers) or first the joint distribution of observed features (variables) conditional on class training data and then the posterior distribution of labels is obtained through Bayes' rule. There has been a debate around which of these approaches should be preferred in a particular application, see Ripley (1996), Hastie et al. (2009), Bishop (2007), and Pernkopf and Bilmes (2005), however, both classes of methods continue to be supported and further developed. One of the popular methods of probabilistic classification is based on encoding feature dependencies with Bayesian networks (Friedman et al., 1997). Such models can often represent data structures more faithfully than the naive Bayes classifier, which has been shown to yield dramatic improvements in classification accuracy in some cases. Numerous variants and extensions of the original framework introduced by Friedman et al. (1997) have been considered over the years, e.g.