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Ordinal regression

About: Ordinal regression is a research topic. Over the lifetime, 1879 publications have been published within this topic receiving 65431 citations.


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TL;DR: The results show that the k-interactivity is an efficient way to reduce the complexity of capacities while preserving their expressiveness and representation ability, and that optimal capacities can be found by standard mathematical programming techniques.
Abstract: This paper addresses a methodology for decision support under multiple and correlated decision criteria. Nonadditive robust ordinal regression (NAROR) aims to build capacities that fit the decision makers’ explicit preferences and pairwise rankings of some alternatives. The capacities provide great flexibility to model decision problems accounting for interactions among the decision criteria. The feasible set of capacities helps identifying all the necessary and possible dominance relations among all the decision alternatives. In this paper we enhance the NAROR method by identifying optimal capacities through entropy maximisation. We formulate suitable optimisation problems and provide avenues for capacity simplification based on k-interactivity. We also consider the situation of large number of sparse constraints, for which we formulate a linear program based on Renyi entropy. We deal with preferences inconsistency by using multiple goal linear programming technique. The results show that the k-interactivity is an efficient way to reduce the complexity of capacities while preserving their expressiveness and representation ability, and that optimal capacities can be found by standard mathematical programming techniques.

8 citations

DOI
01 Dec 2014
TL;DR: Results based on simulated and real data suggest that predictor rankings can be improved by using new permutation VIMs that explicitly use the ordering in the response levels in combination with the ordinal regression trees suggested by Hothorn et al.
Abstract: The random forest method is a commonly used tool for classification with high-dimensional data that is able to rank candidate predictors through its inbuilt variable importance measures (VIMs). It can be applied to various kinds of regression problems including nominal, metric and survival response variables. While classification and regression problems using random forest methodology have been extensively investigated in the past, there seems to be a lack of literature on handling ordinal regression problems, that is if response categories have an inherent ordering. The classical random forest version of Breiman ignores the ordering in the levels and implements standard classification trees. Or if the variable is treated like a metric variable, regression trees are used which, however, are not appropriate for ordinal response data. Further compounding the difficulties the currently existing VIMs for nominal or metric responses have not proven to be appropriate for ordinal response. The random forest version of Hothorn et al. utilizes a permutation test framework that is applicable to problems where both predictors and response are measured on arbitrary scales. It is therefore a promising tool for handling ordinal regression problems. However, for this random forest version there is also no specific VIM for ordinal response variables and the appropriateness of the error rate based VIM computed by default in the case of ordinal responses has to date not been investigated in the literature. We performed simulation studies using random forest based on conditional inference trees to explore whether incorporating the ordering information yields any improvement in prediction performance or variable selection. We present two novel permutation VIMs that are reasonable alternatives to the currently implemented VIM which was developed for nominal response and makes no use of the ordering in the levels of an ordinal response variable. Results based on simulated and real data suggest that predictor rankings can be improved by using our new permutation VIMs that explicitly use the ordering in the response levels in combination with the ordinal regression trees suggested by Hothorn et al. With respect to prediction accuracy in our studies, the performance of ordinal regression trees was similar to and in most settings even slightly better than that of classification trees. An explanation for the greater performance is that in ordinal regression trees there is a higher probability of selecting relevant variables for a split. The codes implementing our studies and our novel permutation VIMs for the statistical software R are available at http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/070_drittmittel/janitza/index.html.

8 citations

Proceedings Article
24 May 2019
TL;DR: This paper proposed a generalization of the logistic loss that incorporates a metric or cost between classes, which results in unconstrained convex objective functions, supports infinite (or very large) class spaces, and naturally defines a geometric generalisation of the softmax operator.
Abstract: Building upon recent advances in entropy-regularized optimal transport, and upon Fenchel duality between measures and continuous functions , we propose a generalization of the logistic loss that incorporates a metric or cost between classes. Unlike previous attempts to use optimal transport distances for learning, our loss results in unconstrained convex objective functions, supports infinite (or very large) class spaces, and naturally defines a geometric generalization of the softmax operator. The geometric properties of this loss make it suitable for predicting sparse and singular distributions, for instance supported on curves or hyper-surfaces. We study the theoretical properties of our loss and show-case its effectiveness on two applications: ordinal regression and drawing generation.

8 citations

01 Jan 2010
TL;DR: This Conference Proceeding is brought to you for free and open access by the Northeastern Educational Research Association (NERA) Annual Conference at DigitalCommons@UConn.edu.
Abstract: This Conference Proceeding is brought to you for free and open access by the Northeastern Educational Research Association (NERA) AnnualConference at DigitalCommons@UConn. It has been accepted for inclusion in NERA Conference Proceedings 2010 by an authorized administratorof DigitalCommons@UConn. For more information, please contact digitalcommons@uconn.edu.

8 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023102
2022191
202188
202093
201979
201873