We study sets of reals computable by ordinal Turing machines with a tape of length the ordinals that are steered by a standard Turing program. The machines halt at some ordinal time or diverge. We construct tree representations for ordinal semidecidable sets of reals from ordinal computations. The aim is to generalize uniformization results to classes of sets which are semi-decidable by computa...

Ordinal logistic regression is a statistical analysis method that can be used to model the relationship between an ordinal response variable and one or more explanatory variables. An ordinal variable is a categorical variable for which there is a clear ordering of the category levels. The explanatory variables may be either continuous or categorical. Estimating ordinal logistic regression model...

When measuring health inequality using ordinal data, analysts typically must choose between indices specifically based upon ordinal data and more standard indices using ordinal data, which has been transformed into cardinal data. This paper compares inequality rankings across a number of different approaches and finds considerable sensitivity to the choice between ordinal- and cardinal-based in...

We introduce the principle of robust ordinal regression to group decision. We consider the main multiple criteria decision methods to which robust ordinal regression has been applied, i.e., UTA and GRIP methods, dealing with choice and ranking problems, UTADIS , dealing with sorting (ordinal classification) problems, and ELECTRE , being an outranking method applying robust ordinal regression to...

Recently, ordinal regression, which predicts categories of ordinal scale, has received considerable attention. In this paper, we propose a new approach to solve ordinal regression problems within the learning vector quantization framework. It extends the previous approach termed ordinal generalized matrix learning vector quantization with a more suitable and natural cost function, leading to mo...

In this paper, we address the Multi-Instance-Learning (MIL) problem when bag labels are naturally represented as ordinal variables (Multi–Instance–Ordinal Regression). Moreover, we consider the case where bags are temporal sequences of ordinal instances. To model this, we propose the novel Multi-Instance Dynamic Ordinal Random Fields (MI-DORF). In this model, we treat instance-labels inside the...

We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor-Bendixson ranks (of trees). We prove the following results: 1) The ordinal height of any automatic wellfounded partial order is bounded by ω; 2) The ordinal heights of automatic well-founded r...

§0. The ordinal numbers were Georg Cantor’s deepest contribution to mathematics. After the natural numbers 0, 1, . . . , n, . . . comes the first infinite ordinal number ù, followed by ù + 1, ù + 2, . . . , ù + ù, . . . and so forth. ù is the first limit ordinal as it is neither 0 nor a successor ordinal. We follow the von Neumann convention, according to which each ordinal number α is identifi...