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27
Preference Functions That Score Rankings and Maximum Likelihood Estimation
"... A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging ..."
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Cited by 39 (14 self)
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A preference function (PF) takes a set of votes (linear orders over a set of alternatives) as input, and produces one or more rankings (also linear orders over the alternatives) as output. Such functions have many applications, for example, aggregating the preferences of multiple agents, or merging rankings (of, say, webpages) into a single ranking. The key issue is choosing a PF to use. One natural and previously studied approach is to assume that there is an unobserved “correct ” ranking, and the votes are noisy estimates of this. Then, we can use the PF that always chooses the maximum likelihood estimate (MLE) of the correct ranking. In this paper, we define simple ranking scoring functions (SRSFs) and show that the class of neutral SRSFs is exactly the class of neutral PFs that are MLEs for some noise model. We also define extended ranking scoring functions (ERSFs) and show a condition under which these coincide with SRSFs. We study key properties such as consistency and continuity, and consider some example PFs. In particular, we study Single Transferable Vote (STV), a commonly used PF, showing that it is an ERSF but not an SRSF, thereby clarifying the extent to which it is an MLE function. This also gives a new perspective on how ties should be broken under STV. We leave some open questions. 1
Fourier Theoretic Probabilistic Inference over Permutations
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2009
"... Permutations are ubiquitous in many realworld problems, such as voting, ranking, and data association. Representing uncertainty over permutations is challenging, since there are n! possibilities, and typical compact and factorized probability distribution representations, such as graphical models, ..."
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Cited by 20 (8 self)
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Permutations are ubiquitous in many realworld problems, such as voting, ranking, and data association. Representing uncertainty over permutations is challenging, since there are n! possibilities, and typical compact and factorized probability distribution representations, such as graphical models, cannot capture the mutual exclusivity constraints associated with permutations. In this paper, we use the “lowfrequency” terms of a Fourier decomposition to represent distributions over permutations compactly. We present Kronecker conditioning, a novel approach for maintaining and updating these distributions directly in the Fourier domain, allowing for polynomial time bandlimited approximations. Low order Fourierbased approximations, however, may lead to functions that do not correspond to valid distributions. To address this problem, we present a quadratic program defined directly in the Fourier domain for projecting the approximation onto a relaxation of the polytope of legal marginal distributions. We demonstrate the effectiveness of our approach on a real camerabased multiperson tracking scenario.
Global models of document structure using latent permutations
 In NAACL’09
, 2009
"... We present a novel Bayesian topic model for learning discourselevel document structure. Our model leverages insights from discourse theory to constrain latent topic assignments in a way that reflects the underlying organization of document topics. We propose a global model in which both topic selec ..."
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Cited by 18 (4 self)
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We present a novel Bayesian topic model for learning discourselevel document structure. Our model leverages insights from discourse theory to constrain latent topic assignments in a way that reflects the underlying organization of document topics. We propose a global model in which both topic selection and ordering are biased to be similar across a collection of related documents. We show that this space of orderings can be elegantly represented using a distribution over permutations called the generalized Mallows model. Our structureaware approach substantially outperforms alternative approaches for crossdocument comparison and singledocument segmentation. 1 1
Riffled Independence for Ranked Data
"... Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence ..."
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Cited by 9 (3 self)
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Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of n objects scales factorially in n. One recent way that has been used to reduce storage complexity has been to exploit probabilistic independence, but as we argue, full independence assumptions impose strong sparsity constraints on distributions and are unsuitable for modeling rankings. We identify a novel class of independence structures, called riffled independence, which encompasses a more expressive family of distributions while retaining many of the properties necessary for performing efficient inference and reducing sample complexity. In riffled independence, one draws two permutations independently, then performs the riffle shuffle, common in card games, to combine the two permutations to form a single permutation. In ranking, riffled independence corresponds to ranking disjoint sets of objects independently, then interleaving those rankings. We provide a formal introduction and present algorithms for using riffled independence within Fouriertheoretic frameworks which have been explored by a number of recent papers. 1
Content Modeling Using Latent Permutations
"... We present a novel Bayesian topic model for learning discourselevel document structure. Our model leverages insights from discourse theory to constrain latent topic assignments in a way that reflects the underlying organization of document topics. We propose a global model in which both topic selec ..."
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Cited by 8 (5 self)
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We present a novel Bayesian topic model for learning discourselevel document structure. Our model leverages insights from discourse theory to constrain latent topic assignments in a way that reflects the underlying organization of document topics. We propose a global model in which both topic selection and ordering are biased to be similar across a collection of related documents. We show that this space of orderings can be effectively represented using a distribution over permutations called the Generalized Mallows Model. We apply our method to three complementary discourselevel tasks: crossdocument alignment, document segmentation, and information ordering. Our experiments show that incorporating our permutationbased model in these applications yields substantial improvements in performance over previously proposed methods. 1 1.
Dirichlet Process Mixtures of Generalized Mallows Models
"... We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several ..."
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Cited by 8 (1 self)
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We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several cluster parameters by taking advantage of approximations to the conditional posteriors. We empirically demonstrate (1) the effectiveness of this approximation for improving convergence, (2) the benefits of the Dirichlet process model over alternative clustering techniques for ranked data, and (3) the applicability of the approach to exploring large realworld ranking datasets. 1
Ranking vs. Regression in Machine Translation Evaluation
"... Automatic evaluation of machine translation (MT) systems is an important research topic for the advancement of MT technology. Most automatic evaluation methods proposed to date are scorebased: they compute scores that represent translation quality, and MT systems are compared on the basis of these ..."
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Cited by 7 (0 self)
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Automatic evaluation of machine translation (MT) systems is an important research topic for the advancement of MT technology. Most automatic evaluation methods proposed to date are scorebased: they compute scores that represent translation quality, and MT systems are compared on the basis of these scores. We advocate an alternative perspective of automatic MT evaluation based on ranking. Instead of producing scores, we directly produce a ranking over the set of MT systems to be compared. This perspective is often simpler when the evaluation goal is system comparison. We argue that it is easier to elicit human judgments of ranking and develop a machine learning approach to train on rank data. We compare this ranking method to a scorebased regression method on WMT07 data. Results indicate that ranking achieves higher correlation to human judgments, especially in cases where rankingspecific features are used. 1
Estimation and Clustering with Infinite Rankings
"... This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the Exponent ..."
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Cited by 5 (3 self)
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This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its properties and give procedures to estimate it from data. For estimation of multimodal distributions we introduce the ExponentialBlurringMeanShift nonparametric clustering algorithm. The experiments highlight the properties of the new model and demonstrate that infinite models can be simple, elegant and practical. 1
Comparing multiagent systems research in combinatorial auctions and voting
 Annals of Mathematics and Artificial Intelligence
"... In a combinatorial auction, a set of items is for sale, and agents can bid on subsets of these items. In a voting setting, the agents decide among a set of alternatives by having each agent rank all the alternatives. Many of the key research issues in these two domains are similar. The aim of this p ..."
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Cited by 4 (2 self)
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In a combinatorial auction, a set of items is for sale, and agents can bid on subsets of these items. In a voting setting, the agents decide among a set of alternatives by having each agent rank all the alternatives. Many of the key research issues in these two domains are similar. The aim of this paper is to give a convenient sidebyside comparison that will clarify the relation between the domains, and serve as a guide to future research. 1
A Flexible Generative Model for Preference Aggregation
"... Many areas of study, such as information retrieval, collaborative filtering, and social choice face the preference aggregation problem, in which multiple preferences over objects must be combined into a consensus ranking. Preferences over items can be expressed in a variety of forms, which makes the ..."
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Cited by 2 (0 self)
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Many areas of study, such as information retrieval, collaborative filtering, and social choice face the preference aggregation problem, in which multiple preferences over objects must be combined into a consensus ranking. Preferences over items can be expressed in a variety of forms, which makes the aggregation problem difficult. In this work we formulate a flexible probabilistic model over pairwise comparisons that can accommodate all these forms. Inference in the model is very fast, making it applicable to problems with hundreds of thousands of preferences. Experiments on benchmark datasets demonstrate superior performance to existing methods.