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16
Label Ranking by Learning Pairwise Preferences
"... Preference learning is an emerging topic that appears in different guises in the recent literature. This work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning s ..."
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Cited by 87 (20 self)
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Preference learning is an emerging topic that appears in different guises in the recent literature. This work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a mapping, called ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data using a natural extension of pairwise classification. A ranking is then derived from the preference relation thus obtained by means of a ranking procedure, whereby different ranking methods can be used for minimizing different loss functions. In particular, we show that a simple (weighted) voting strategy minimizes risk with respect to the wellknown Spearman rank correlation. We compare RPC to existing label ranking methods, which are based on scoring individual labels instead of comparing pairs of labels. Both empirically and theoretically, it is shown that RPC is superior in terms of computational efficiency, and at least competitive in terms of accuracy.
Learning label preferences: Ranking error versus position error
 In Advances in Intelligent Data Analysis: Proceedings of the 6th International Symposium (IDA05
, 2005
"... Abstract. We consider the problem of learning a ranking function, that is a mapping from instances to rankings over a finite number of labels. Our learning method, referred to as ranking by pairwise comparison (RPC), first induces pairwise order relations from suitable training data, using a natural ..."
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Cited by 13 (10 self)
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Abstract. We consider the problem of learning a ranking function, that is a mapping from instances to rankings over a finite number of labels. Our learning method, referred to as ranking by pairwise comparison (RPC), first induces pairwise order relations from suitable training data, using a natural extension of socalled pairwise classification. A ranking is then derived from a set of such relations by means of a ranking procedure. This paper elaborates on a key advantage of such a decomposition, namely the fact that our learner can be adapted to different loss functions by using different ranking procedures on the same underlying order relations. In particular, the Spearman rank correlation is minimized by using a simple weighted voting procedure. Moreover, we discuss a loss function suitable for settings where candidate labels must be tested successively until a target label is found, and propose a ranking procedure for minimizing the corresponding risk. 1
Combining Predictions in Pairwise Classification: An Optimal Adaptive Voting Strategy and Its Relation to Weighted Voting
 TO APPEAR IN PATTERN RECOGNITION
, 2009
"... Weighted voting is the commonly used strategy for combining predictions in pairwise classification. Even though it shows good classification performance in practice, it is often criticized for lacking a sound theoretical justification. In this paper, we study the problem of combining predictions wit ..."
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Cited by 12 (0 self)
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Weighted voting is the commonly used strategy for combining predictions in pairwise classification. Even though it shows good classification performance in practice, it is often criticized for lacking a sound theoretical justification. In this paper, we study the problem of combining predictions within a formal framework of label ranking and, under some model assumptions, derive a generalized voting strategy in which predictions are properly adapted according to the strengths of the corresponding base classifiers. We call this strategy adaptive voting and show that it is optimal in the sense of yielding a MAP prediction of the class label of a test instance. Moreover, we offer a theoretical justification for weighted voting by showing that it yields a good approximation of the optimal adaptive voting prediction. This result is further corroborated by empirical evidence from experiments with real and synthetic data sets showing that, even though adaptive voting is sometimes able to achieve consistent improvements, weighted voting is in general quite competitive, all the more in cases where the aforementioned model assumptions underlying adaptive voting are not met. In this sense, weighted voting appears to be a more robust aggregation strategy.
Label Ranking by Learning Pairwise Preferences
, 2005
"... Preference learning is a challenging problem that involves the prediction of complex structures, such as weak or partial order relations, rather than single values. In the recent literature, the problem appears in many different guises, which we will first put into a coherent framework. This work th ..."
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Cited by 5 (3 self)
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Preference learning is a challenging problem that involves the prediction of complex structures, such as weak or partial order relations, rather than single values. In the recent literature, the problem appears in many different guises, which we will first put into a coherent framework. This work then focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a ranking function, ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data using a natural extension of pairwise classification. A ranking is then derived from the learned relation relation by means of a ranking procedure, whereby different ranking functions can be used for minimizing different loss functions. In particular, we show that weighted voting minimizes the Spearman rank correlation. Finally, we compare RPC to constraint classification, an alternative approach to label ranking, and show empirically and theoretically that RPC is computationally more efficient.
Preference learning using the Choquet integral: The case of multipartite ranking
 IEEE Transactions on Fuzzy Systems
"... We propose a novel method for preference learning or, more specifically, learning to rank, where the task is to learn a ranking model that takes a subset of alternatives as input and produces a ranking of these alternatives as output. Just like in the case of conventional classifier learning, traini ..."
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Cited by 3 (1 self)
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We propose a novel method for preference learning or, more specifically, learning to rank, where the task is to learn a ranking model that takes a subset of alternatives as input and produces a ranking of these alternatives as output. Just like in the case of conventional classifier learning, training information is provided in the form of a set of labeled instances, with labels or, say, preference degrees taken from an ordered categorical scale. This setting is known as multipartite ranking in the literature. Our approach is based on the idea of using the (discrete) Choquet integral as an underlying model for representing ranking functions. Being an established aggregation function in fields such as multiple criteria decision making and information fusion, the Choquet integral offers a number of interesting properties that make it attractive from a machine learning perspective, too. The learning problem itself comes down to properly specifying the fuzzy measure on which the Choquet integral is defined. This problem is formalized as a margin maximization problem and solved by means of a cutting plane algorithm. The performance of our method is tested on a number of benchmark datasets.
Efficient Prediction Algorithms for Binary Decomposition Techniques
"... Binary decomposition methods transform multiclass learning problems into a series of twoclass learning problems that can be solved with simpler learning algorithms. As the number of such binary learning problems often grows superlinearly with the number of classes, we need efficient methods for c ..."
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Cited by 2 (2 self)
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Binary decomposition methods transform multiclass learning problems into a series of twoclass learning problems that can be solved with simpler learning algorithms. As the number of such binary learning problems often grows superlinearly with the number of classes, we need efficient methods for computing the predictions. In this paper, we discuss an efficient algorithm that queries only a dynamically determined subset of the trained classifiers, but still predicts the same classes that would have been predicted if all classifiers had been queried. The algorithm is first derived for the simple case of pairwise classification, and then generalized to arbitrary pairwise decompositions of the learning problem in the form of ternary errorcorrecting output codes under a variety of different code designs and decoding strategies.
Efficient pairwise classification and ranking
"... Pairwise classification is a class binarization procedure that converts a multiclass problem into a series of twoclass problems, one problem for each pair of classes. While it can be shown that for training, this procedure is more efficient than the more commonly used oneagainstall approach, it ..."
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Cited by 1 (1 self)
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Pairwise classification is a class binarization procedure that converts a multiclass problem into a series of twoclass problems, one problem for each pair of classes. While it can be shown that for training, this procedure is more efficient than the more commonly used oneagainstall approach, it still has to evaluate a quadratic number of classifiers when computing the predicted class for a given example. In this paper, we propose a method that allows a faster computation of the predicted class when weighted or unweighted voting are used for combining the predictions of the individual classifiers. While its worstcase complexity is still quadratic in the number of classes, we show that even in the case of completely random base classifiers, our method still outperforms the conventional pairwise classifier. For the more practical case of welltrained base classifiers, its asymptotic computational complexity seems to be almost linear. We also propose a method for approximating the full class ranking, based on the Swiss System, a common scheme for conducting multiround chess tournaments. Our results indicate that this adaptive scheme offers a better tradeoff between approximation quality and number of performed comparisons than alternative, fixed schemes for ordering the evaluation of the pairwise classifiers.
Learning Preference Models from Data: On the Problem of Label Ranking and Its Variants
, 2005
"... The term “preference learning” refers to the application of machine learning methods for inducing preference models from empirical data. In the recent literature, corresponding problems appear in various guises. After a brief overview of the field, this work focuses on a particular learning scenari ..."
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The term “preference learning” refers to the application of machine learning methods for inducing preference models from empirical data. In the recent literature, corresponding problems appear in various guises. After a brief overview of the field, this work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a ranking function, called ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data, using a natural extension of pairwise classification. A ranking is then derived from this relation by means of a ranking procedure. This paper elaborates on a key advantage of such an approach, namely the fact that our learner can be adapted to different loss functions by using different ranking procedures on the same underlying order relations. In particular, the Spearman rank correlation is minimized by using a simple weighted voting procedure. Moreover, we discuss a loss function suitable for settings where candidate labels must be tested successively until a target label is found. In this context, we propose the idea of “empirical conditioning” of class probabilities. A related ranking procedure, called “ranking through iterated choice”, is investigated experimentally.
On Position Error and Label Ranking through Iterated Choice
"... We consider the problem of learning a ranking function, that is a mapping from instances to rankings over a finite number of labels. Our learning method, referred to as ranking by pairwise comparison (RPC), first induces pairwise order relations from suitable training data, using a natural ext ..."
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We consider the problem of learning a ranking function, that is a mapping from instances to rankings over a finite number of labels. Our learning method, referred to as ranking by pairwise comparison (RPC), first induces pairwise order relations from suitable training data, using a natural extension of socalled pairwise classification. A ranking is
A Spectral Approach to Collaborative Ranking
"... Knowing your customers and their needs is mandatory when conducting business. In an ecommerce environment, where one often knows much less about individual customers than in a facetoface business, questionnaires besides historical transaction data and basic information like names and geographic ..."
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Knowing your customers and their needs is mandatory when conducting business. In an ecommerce environment, where one often knows much less about individual customers than in a facetoface business, questionnaires besides historical transaction data and basic information like names and geographic location are popular means to get to know customers. Here we report on an approach to analyze preference data that consumers provide in stated choice experiments which can be conducted on a company’s web site. Naturally, the information one captures with web based questionnaires tends to be sparse and noisy. Nevertheless, our results show that if one collects data from enough consumers one can learn about different segments and their needs. The results are obtained with a spectral collaborative ranking algorithm that can be applied to stated choice data, especially, choice based conjoint analysis data.