Some of the assumptions of the BIM can be removed. For example, we can remove the assumption that terms are independent. This assumption is very far from true in practice. A case that particularly violates this assumption is term pairs like Hong and Kong, which are strongly dependent. But dependencies can occur in various complex configurations, such as between the set of terms New, York, England, City, Stock, Exchange, and University. van Rijsbergen (1979) proposed a simple, plausible model which allowed a tree structure of term dependencies, as in Figure 11.1 . In this model each term can be directly dependent on only one other term, giving a tree structure of dependencies. When it was invented in the 1970s, estimation problems held back the practical success of this model, but the idea was reinvented as the Tree Augmented Naive Bayes model by Friedman and Goldszmidt (1996), who used it with some success on various machine learning data sets.
