CART (Classification and Regression Trees) is a non-parametric tree-structured recursive partitioning method, introduced by Breiman et al. (1984), to predict a response variable $Y$ on the basis of $p$ predictors: $X_1,\ldots,X_p$ observed on a learning sample of $N$ units. In this paper the case where the response $Y$ is an ordered categorical variable with $k$ levels $y_1\prec \ldots\prec y_k$ is considered. The aim of the classification tree is thus to predict the level of $Y$ on the basis of the vector $\mathbf{X}$ of the $p$ explanatory variables. Instead of accommodating existing algorithm to the ordinal classification task, some papers have faced directly the problem of identifying a suitable rule to grow ordinal classification trees. We will consider these papers into details and propose some improvements based on a known decomposition result regarding Gini's mean difference.

Borroni, C., Radaelli, P., Zenga, M. (2012). Predicting ordinal classes via classification trees. In Proceedings of the 58th ISI World Statistics Congress (pp.5197-5203).

Predicting ordinal classes via classification trees

BORRONI, CLAUDIO GIOVANNI
Primo
;
ZENGA, MARIANGELA
2012

Abstract

CART (Classification and Regression Trees) is a non-parametric tree-structured recursive partitioning method, introduced by Breiman et al. (1984), to predict a response variable $Y$ on the basis of $p$ predictors: $X_1,\ldots,X_p$ observed on a learning sample of $N$ units. In this paper the case where the response $Y$ is an ordered categorical variable with $k$ levels $y_1\prec \ldots\prec y_k$ is considered. The aim of the classification tree is thus to predict the level of $Y$ on the basis of the vector $\mathbf{X}$ of the $p$ explanatory variables. Instead of accommodating existing algorithm to the ordinal classification task, some papers have faced directly the problem of identifying a suitable rule to grow ordinal classification trees. We will consider these papers into details and propose some improvements based on a known decomposition result regarding Gini's mean difference.
paper
CARTs, Ordinal categorical variables, Gini's mean difference
English
58th ISI World Statistics Congress
2011
Proceedings of the 58th ISI World Statistics Congress
978-90-73592-33-9
2012
5197
5203
CPS053
http://2011.isiproceedings.org/papers/951041.pdf
none
Borroni, C., Radaelli, P., Zenga, M. (2012). Predicting ordinal classes via classification trees. In Proceedings of the 58th ISI World Statistics Congress (pp.5197-5203).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/67253
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