  We propose a novel hybrid loss for multiclass and structured prediction
problems that is a convex combination of log loss for Conditional Random Fields
(CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We
provide a sufficient condition for when the hybrid loss is Fisher consistent
for classification. This condition depends on a measure of dominance between
labels - specifically, the gap in per observation probabilities between the
most likely labels. We also prove Fisher consistency is necessary for
parametric consistency when learning models such as CRFs.
  We demonstrate empirically that the hybrid loss typically performs as least
as well as - and often better than - both of its constituent losses on variety
of tasks. In doing so we also provide an empirical comparison of the efficacy
of probabilistic and margin based approaches to multiclass and structured
prediction and the effects of label dominance on these results.
