The Generalization Paradox of Ensembles

Ensemble models—built by methods such as bagging, boosting, and Bayesian model averaging—appear dauntingly complex, yet tend to strongly outperform their component models on new data. Doesn’t this violate “Occam’s razor”—the widespread belief that “the simpler of competing alternatives is preferred”? We argue no: if complexity is measured by function rather than form—for example, according to generalized degrees of freedom (GDF)—the razor’s role is restored. On a two-dimensional decision tree problem, bagging several trees is shown to actually have less GDF complexity than a single component tree, removing the generalization paradox of ensembles.