Notes on hierarchical ensemble methods for DAG-structured taxonomies

Hierarchical classification problems are characterized by taxonomies structured according to a predefined hierarchy. Examples in the context of the gene or protein function prediction include trees or directed acyclic graphs [30], where functional classes are connected according to a tree (FunCat, Functional Categories [27]) or a DAG (GO, Gene Ontology [30]). Extensive experimental studies showed that flat prediction, i.e. predictions for each class made independently of the other classes, introduce significant inconsistencies in the classification, due to the violation of the true path rule, that governs the hierarchical relationships between classes [25, 13]. According to this rule, positive predictions for a given term must be transferred to its "ancestor" terms and negative predictions to its descendants. In their more general form hierarchical ensemble methods adopt a two-steps learning strategy [23, 14, 10, 28]: 1. In the first step each base learner separately or interacting with connected base learners learns the protein functional category on a per-term basis. In most cases this yields a set of independent classification problems, where each base learning machine is trained to learn a specific functional term, independently of the other base learners.