Bayesian inference for Plackett-Luce ranking models

Guiver, John; Snelson, Edward

doi:10.1145/1553374.1553423

Cited by 120 publications

(94 citation statements)

References 8 publications

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Order By: Relevance

“…As shown in Guiver and Snelson (2009), given two sets of labels A and B, B ⊂ A, the probability of a particular ordering of labels in B, marginalized over all possible unknown positions of the labels in A \ B, is exactly the same as the Plackett-Luce probability of ordering labels from B independently from A. Thus, the probability of a particular ordering of labels does not depend on the subset from which the labels are assumed to be drawn (Hunter 2004).…”

Section: Ranking Modelsmentioning

confidence: 91%

Supervised clustering of label ranking data using label preference information

et al. 2013

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This paper studies supervised clustering in the context of label ranking data. The goal is to partition the feature space into K clusters, such that they are compact in both the feature and label ranking space. This type of clustering has many potential applications. For example, in target marketing we might want to come up with K different offers or marketing strategies for our target audience. Thus, we aim at clustering the customers' feature space into K clusters by leveraging the revealed or stated, potentially incomplete customer preferences over products, such that the preferences of customers within one cluster are more similar to each other than to those of customers in other clusters. We establish several baseline algorithms and propose two principled algorithms for supervised clustering. In the first baseline, the clusters are created in an unsupervised manner, followed by assigning a representative label ranking to each cluster. In the second baseline, the label ranking space is clustered first, followed by partitioning the feature space based on the central rankings. In the third baseline, clustering is applied on a new feature space consisting of both features and label rankings, followed by mapping back to the original feature and ranking space. The RankTree principled approach is based on a Ranking Tree algorithm previously proposed for label ranking prediction. Our modification starts with K random label rankings and iteratively splits the feature space to minimize the ranking loss, followed by re-calculation of the K rankings based on cluster assignments. The MM-PL approach is a Learn (2013) 93:191-225 multi-prototype supervised clustering algorithm based on the Plackett-Luce (PL) probabilistic ranking model. It represents each cluster with a union of Voronoi cells that are defined by a set of prototypes, and assign each cluster with a set of PL label scores that determine the cluster central ranking. Cluster membership and ranking prediction for a new instance are determined by cluster membership of its nearest prototype. The unknown cluster PL parameters and prototype positions are learned by minimizing the ranking loss, based on two variants of the expectation-maximization algorithm. Evaluation of the proposed algorithms was conducted on synthetic and real-life label ranking data by considering several measures of cluster goodness: (1) cluster compactness in feature space, (2) cluster compactness in label ranking space and (3) label ranking prediction loss. Experimental results demonstrate that the proposed MM-PL and RankTree models are superior to the baseline models. Further, MM-PL is has shown to be much better than other algorithms at handling situations with significant fraction of missing label preferences.

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Section: Ranking Modelsmentioning

confidence: 91%

Supervised clustering of label ranking data using label preference information

et al. 2013

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“…as in (Gormley and Murphy, 2009;Guiver and Snelson, 2009) then we can maximize the resulting log-posterior using the EM algorithm which proceeds as follows at iteration t:…”

Section: Bradley-terry Modelmentioning

confidence: 99%

“…Recently several authors have proposed to perform Bayesian inference for (generalized) BradleyTerry models (Adams, 2005;Gormley and Murphy, 2009;Görür et al, 2006;Guiver and Snelson, 2009). The resulting posterior density is typically not tractable and needs to be approximated.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting posterior density is typically not tractable and needs to be approximated. An Expectation-Propagation method is developed in (Guiver and Snelson, 2009); this yields an approximation of the posterior which can be computed quickly and might be suitable for very large scale applications. However, it relies on a functional approximation of the posterior and the convergence properties of this algorithm are not well-understood.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Bayesian Inference for Generalized Bradley–Terry Models

Caron

Doucet

2012

Journal of Computational and Graphical Statistics

125

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Abstract:The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess ranking and multiclass classification. Numerous extensions of the basic model have also been proposed in the literature including models with ties, multiple comparisons, group comparisons and random graphs. From a computational point of view, Hunter (2004) has proposed efficient iterative MM (minorization-maximization) algorithms to perform maximum likelihood estimation for these generalized Bradley-Terry models whereas Bayesian inference is typically performed using MCMC (Markov chain Monte Carlo) algorithms based on tailored Metropolis-Hastings (M-H) proposals. We show here that these MM algorithms can be reinterpreted as special instances of Expectation-Maximization (EM) algorithms associated to suitable sets of latent variables and propose some original extensions. These latent variables allow us to derive simple Gibbs samplers for Bayesian inference. We demonstrate experimentally the efficiency of these algorithms on a variety of applications.

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“…. , σ (t) are ordered [8], rankings of subsets A of Λ where only labels in A are ordered [22], rankings over a partition of Λ (or bucket orders) [21]. Pairwise preferences are even more general, as most of the previous models cannot model a unique preference λ i λ j [7].…”

Section: Fig 1 Pairwise Decomposition Of Rankingsmentioning

confidence: 99%

A Pairwise Label Ranking Method with Imprecise Scores and Partial Predictions

Destercke

2013

Advanced Information Systems Engineering

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Abstract. In this paper, we are interested in the label ranking problem. We are more specifically interested in the recent trend consisting in predicting partial but more accurate (i.e., making less incorrect statements) orders rather than complete ones. To do so, we propose a ranking method based on pairwise imprecise scores obtained from likelihood functions. We discuss how such imprecise scores can be aggregated to produce interval orders, which are specific types of partial orders. We then analyse the performances of the method as well as its sensitivity to missing data and parameter values.

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Bayesian inference for Plackett-Luce ranking models

Cited by 120 publications

References 8 publications

Supervised clustering of label ranking data using label preference information

Supervised clustering of label ranking data using label preference information

Efficient Bayesian Inference for Generalized Bradley–Terry Models

A Pairwise Label Ranking Method with Imprecise Scores and Partial Predictions

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