In this letter, we propose two new support vector approaches for ordinal regression, which optimize multiple thresholds to define parallel discriminant hyperplanes for the ordinal scales. Both approaches guarantee that the thresholds are properly ordered at the optimal solution. The size of these optimization problems is linear in the number of training samples. The sequential minimal optimization algorithm is adapted for the resulting optimization problems; it is extremely easy to implement and scales efficiently as a quadratic function of the number of examples. The results of numerical experiments on some benchmark and real-world data sets, including applications of ordinal regression to information retrieval, verify the usefulness of these approaches.
This letter describes Bayesian techniques for support vector classification. In particular, we propose a novel differentiable loss function, called the trigonometric loss function, which has the desirable characteristic of natural normalization in the likelihood function, and then follow standard gaussian processes techniques to set up a Bayesian framework. In this framework, Bayesian inference is used to implement model adaptation, while keeping the merits of support vector classifier, such as sparseness and convex programming. This differs from standard gaussian processes for classification. Moreover, we put forward class probability in making predictions. Experimental results on benchmark data sets indicate the usefulness of this approach.