 
Summary: Generalization Bounds for Some Ordinal Regression
Algorithms
Shivani Agarwal
Massachusetts Institute of Technology, Cambridge MA 02139, USA
shivani@mit.edu
Abstract. 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 atten
tion 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 realvalued 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 realvalued function. We end
with a marginbased bound for the stateoftheart ordinal regression algorithm
of Chu & Keerthi (2007).
1 Introduction
In addition to the classical problems of classification and regression, several new types
of learning problems have emerged in recent years. Among these is the problem of or
dinal regression, in which the goal is to learn a rule to predict labels of an ordinal scale,
i.e., labels from a discrete but ordered set. Ordinal regression is common in the social
