There exists a family {Bα}α<ω1 of sets of countable ordinals such that (1) maxBα = α, (2) if α ∈ Bβ then Bα ⊆ Bβ , (3) if λ ≤ α and λ is a limit ordinal then Bα ∩ λ is not in the ideal generated by the Bβ , β < α, and by the bounded subsets of λ, (4) there is a partition {An}n=0 of ω1 such that for every α and every n, Bα∩An is finite.

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 optimizat...

Article history: Received 25 October 2010 Accepted 31 March 2011 Available online 8 April 2011

We consider the problem of regression analysis with imprecise data. By imprecise data we mean imprecise observations of precise quantities in the form of sets of values. In this paper, we explore a recently introduced likelihood-based approach to regression with such data. The approach is very general, since it covers all kinds of imprecise data (i.e. not only intervals) and it is not restricte...

Many applied studies collect one or more ordered categorical predictors, which do not fit neatly within classic regression frameworks. In most cases, ordinal predictors are treated as either nominal (unordered) variables or metric (continuous) variables in regression models, which is theoretically and/or computationally undesirable. In this paper, we discuss the benefit of taking a smoothing sp...