Ordinal regression

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

Distance metric learning for ordinal classification based on triplet constraints

Abstract: Ordinal classification is a problem setting in-between nominal classification and metric regression, where the goal is to predict classes of an ordinal scale. Usually, there is a clear ordering of the classes, but the absolute distances between them are unknown. Disregarding the ordering information, this kind of problems is commonly treated as multi-class classification problems, however, it often results in a significant loss of performance. Exploring such ordering information can help to improve the effectiveness of classifiers. In this paper, we propose a distance metric learning approach for ordinal classification by incorporating local triplet constraints containing the ordering information into a conventional large-margin distance metric learning approach. Specifically, our approach tries to preserve, for each training example, the ordinal relationship as well as the local geometry structure of its neighbors, which is suitable for use in local distance-based algorithms such as k-nearest-neighbor (k-NN) classification. Different from previous works that usually learn distance metrics by weighing the distances between training examples according to their class label differences, the proposed approach can directly satisfy the ordinal relationships where no assumptions about the distances between classes are made.

Min and Max Scorings for Two-Sample Ordinal Data

Abstract: To analyze two-sample ordinal data, one must often assign some increasing numerical scores to the ordinal categories. The choice of appropriate scores in these types of analyses is often problematic. This article presents a new approach for reporting the results of such analyses. Using techniques of order-restricted inference, we obtain the minimum and maximum of standard two-sample test statistics over all possible assignments of increasing scores. If the range of the min and max values does not include the critical value for the test statistics, then we can immediately conclude that the result of the analysis remains the same no matter what choice of increasing scores is used. On the other hand, if the range includes a critical value, the choice of scores used in the analysis must be carefully justified. Numerous examples are given to clarify our approach.

How to test for goodness of fit in ordinal logistic regression models

Abstract: Ordinal regression models are used to describe the relationship between an ordered categorical response variable and one or more explanatory variables. Several ordinal logistic models are available in Stata, such as the proportional odds, adjacent-category, and constrained continuation-ratio models. In this article, we present a command (ologitgof) that calculates four goodness-of-fit tests for assessing the overall adequacy of these models. These tests include an ordinal version of the Hosmer–Lemeshow test, the Pulkstenis–Robinson chi-squared and deviance tests, and the Lipsitz likelihood-ratio test. Together, these tests can detect several different types of lack of fit, including wrongly specified continuous terms, omission of different types of interaction terms, and an unordered response variable.

Learning Transformation Models for Ranking and Survival Analysis

Abstract: This paper studies the task of learning transformation models for ranking problems, ordinal regression and survival analysis The present contribution describes a machine learning approach termed MINLIP The key insight is to relate ranking criteria as the Area Under the Curve to monotone transformation functions Consequently, the notion of a Lipschitz smoothness constant is found to be useful for complexity control for learning transformation models, much in a similar vein as the 'margin' is for Support Vector Machines for classification The use of this model structure in the context of high dimensional data, as well as for estimating non-linear, and additive models based on primal-dual kernel machines, and for sparse models is indicated Given n observations, the present method solves a quadratic program existing of O(n) constraints and O(n) unknowns, where most existing risk minimization approaches to ranking problems typically result in algorithms with O(n2) constraints or unknowns We specify the MINLIP method for three different cases: the first one concerns the preference learning problem Secondly it is specified how to adapt the method to ordinal regression with a finite set of ordered outcomes Finally, it is shown how the method can be used in the context of survival analysis where one models failure times, typically subject to censoring The current approach is found to be particularly useful in this context as it can handle, in contrast with the standard statistical model for analyzing survival data, all types of censoring in a straightforward way, and because of the explicit relation with the Proportional Hazard and Accelerated Failure Time models The advantage of the current method is illustrated on different benchmark data sets, as well as for estimating a model for cancer survival based on different micro-array and clinical data sets

Deep Ordinal Regression Based on Data Relationship for Small Datasets

Abstract: Ordinal regression aims to classify instances into ordinal categories. As with other supervised learning problems, learning an effective deep ordinal model from a small dataset is challenging. This paper proposes a new approach which transforms the ordinal regression problem to binary classification problems and uses triplets with instances from different categories to train deep neural networks such that high-level features describing their ordinal relationship can be extracted automatically. In the testing phase, triplets are formed by a testing instance and other instances with known ranks. A decoder is designed to estimate the rank of the testing instance based on the outputs of the network. Because of the data argumentation by permutation, deep learning can work for ordinal regression even on small datasets. Experimental results on the historical color image benchmark and MSRA image search datasets demonstrate that the proposed algorithm outperforms the traditional deep learning approach and is comparable with other state-ofthe-art methods, which are highly based on prior knowledge to design effective features.