BACKGROUND Log-linear association models have been extensively used to investigate the pattern of agreement between ordinal ratings. In 2007, log-linear non-uniform association models were introduced to estimate, from a cross-classification of two independent raters using an ordinal scale, varying degrees of distinguishability between distant and adjacent categories of the scale. METHODS In t...

Threshold models are one of the most common approaches for ordinal regression, based on projecting patterns to the real line and dividing this real line in consecutive intervals, one interval for each class. However, finding such one-dimensional projection can be too harsh an imposition for some datasets. This paper proposes a multidimensional latent space representation with the purpose of rel...

Ordinal regression problem arises in situations where examples are rated in an ordinal scale. In practice, labeled ordinal data are difficult to obtain while unlabeled ordinal data are available in abundance. Designing a probabilistic semi-supervised classifier to perform ordinal regression is challenging. In this work, we propose a novel approach for semi-supervised ordinal regression using Ga...

We investigated the acquisition and integration of temporal and ordinal sequence information in an incidental learning model of motor skill acquisition (the serial reaction time task). Human participants were exposed to a stimulus-response sequence that had temporal structure, ordinal structure, or both. By changing the temporal or ordinal structure, or both, we were able to ask two questions: ...

Let λH be the term calculus of Howard’s system of constructive ordinals. I use this to name iteration gadgets (generalized ordinal notations). I isolate a family of higher order ordinal functions which give a partial semantics of λH. I indicate how λH provides an intrinsic measure of each ordinal below the Howard ordinal.1

The notion of ordinal computability is defined by generalising standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. The fundamental theorem on ordinal computability states that a set x of ordinals is ordinal computable from ordinal parameters if and only if x is an element of the constructible universe L. In this paper we present a new proof o...

A method is proposed for classification to ordinal categories by applying the search partition analysis (SPAN) approach. It is suggested that SPAN be repeatedly applied to binary outcomes formed by collapsing adjacent categories of the ordinal scale. By a simple device, whereby successive binary partitions are constrained to be nested, a partition for classification to the ordinal states is obt...

Let us observe that there exists an ordinal number which is non empty and natural. Let a be a natural ordinal number. Note that succa is natural. The scheme Omega Ind concerns a unary predicate P , and states that: For every natural ordinal number a holds P [a] provided the following conditions are met: • P [ / 0], and • For every natural ordinal number a such that P [a] holds P [succa]. Let a,...