Generalization Bounds for Some Ordinal Regression Algorithms

The problem of ordinal regression, in which the goal is to learn a rule to predict labels from a discrete but ordered set, has gained considerable attention in machine learning in recent years. We study generalization properties of algorithms for this problem. We start with the most basic algorithms that work by learning a real-valued function in a regression framework and then rounding off a predicted real value to the closest discrete label; our most basic bounds for such algorithms are derived by relating the ordinal regression error of the resulting prediction rule to the regression error of the learned real-valued function. We end with a margin-based bound for the state-of-the-art ordinal regression algorithm of Chu & Keerthi (2007).