On the Consistency of Ordinal Regression Methods

Many of the ordinal regression algorithms that have been proposed can be viewed as methods that minimize a convex surrogate of the zeroone, absolute, or squared errors. We provide a theoretical analysis of the risk consistency properties of a rich family of surrogate loss functions, including proportional odds and support vector ordinal regression. For all the surrogates considered, we either prove consistency or provide suf€cient conditions under which these approaches are consistent. Finally, we illustrate our €ndings on 8 di‚erent datasets.