The auction algorithm: a distributed relaxation method for the assignment problem
Annals of Operations Research - Special Issue: Parallel Optimization on Novel Computer Architectures
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
On the algorithmic implementation of multiclass kernel-based vector machines
The Journal of Machine Learning Research
An efficient boosting algorithm for combining preferences
The Journal of Machine Learning Research
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Generalization Bounds for the Area Under the ROC Curve
The Journal of Machine Learning Research
Efficient Learning of Label Ranking by Soft Projections onto Polyhedra
The Journal of Machine Learning Research
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Parimutuel Betting on Permutations
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Margin-based Ranking and an Equivalence between AdaBoost and RankBoost
The Journal of Machine Learning Research
The P-Norm Push: A Simple Convex Ranking Algorithm that Concentrates at the Top of the List
The Journal of Machine Learning Research
Distributed random access algorithm: scheduling and congestion control
IEEE Transactions on Information Theory
Max-Product for Maximum Weight Matching: Convergence, Correctness, and LP Duality
IEEE Transactions on Information Theory
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The need to rank items based on user input arises in many practical applications such as elections, group decision making and recommendation systems. The primary challenge in such scenarios is to decide on a global ranking based on partial preferences provided by users. The standard approach to address this challenge is to ask users to provide explicit numerical ratings (cardinal information) of a subset of the items. The main appeal of such an approach is the ease of aggregation. However, the rating scale as well as the individual ratings are often arbitrary and may not be consistent from one user to another. A more natural alternative to numerical ratings requires users to compare pairs of items (ordinal information). On the one hand, such comparisons provide an "absolute" indicator of the user's preference. On the other hand, it is often hard to combine or aggregate these comparisons to obtain a consistent global ranking. In this work, we provide a tractable framework for utilizing comparison data as well as first-order marginal information (see Section 2) for the purpose of ranking. We treat the available information as partial samples from an unknown distribution over permutations. We then reduce ranking problems of interest to performing inference on this distribution. Specifically, we consider the problems of (a) finding an aggregate ranking of n items, (b) learning the mode of the distribution, and (c) identifying the top k items. For many of these problems, we provide efficient algorithms to infer the ranking directly from the data without the need to estimate the underlying distribution. In other cases, we use the Principle of Maximum Entropy to devise a concise parameterization of a distribution consistent with observations using only O(n2) parameters, where n is the number of items in question. We propose a distributed, iterative algorithm for estimating the parameters of the distribution. We establish the correctness of the algorithm and identify its rate of convergence explicitly.