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'''Preference learning''' is a subfield of [[machine learning]] that focuses on modeling and predicting preferences based on observed preference information.<ref>{{Cite Mehryar Afshin Ameet 2012}}</ref> Preference learning typically involves [[supervised learning]] using datasets of pairwise preference comparisons, rankings, or other preference information.
==Tasks==
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In label ranking, the model has an instance space <math>X=\{x_i\}\,\!</math> and a finite set of labels <math>Y=\{y_i|i=1,2,\cdots,k\}\,\!</math>. The preference information is given in the form <math>y_i \succ_{x} y_j\,\!</math> indicating instance <math>x\,\!</math> shows preference in <math>y_i\,\!</math> rather than <math>y_j\,\!</math>. A set of preference information is used as training data in the model. The task of this model is to find a preference ranking among the labels for any instance.
It was observed that some conventional [[Classification in machine learning|classification]] problems can be generalized in the framework of label ranking problem:<ref name="HARP03" /> if a training instance <math>x\,\!</math> is labeled as class <math>y_i\,\!</math>, it implies that <math>\forall j \neq i, y_i \succ_{x} y_j\,\!</math>. In the [[Multi-label classification|multi-label]] case, <math>x\,\!</math> is associated with a set of labels <math>L \subseteq Y\,\!</math> and thus the model can extract a set of preference information <math>\{y_i \succ_{x} y_j | y_i \in L, y_j \in Y\backslash L\}\,\!</math>. Training a preference model on this preference information and the classification result of an instance is just the corresponding top ranking label.
===Instance ranking===
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The binary representation of preference information is called preference relation. For each pair of alternatives (instances or labels), a binary predicate can be learned by conventional supervising learning approach. Fürnkranz and Hüllermeier proposed this approach in label ranking problem.<ref name="FURN03" /> For object ranking, there is an early approach by Cohen et al.<ref name="COHE98" />
Using preference relations to predict the ranking will not be so intuitive. Since observed preference
==Uses==
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