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Efficient Ranking from Pairwise Comparisons
"... The ranking of n objects based on pairwise comparisons is a core machine learning problem, arising in recommender systems, ad placement, player ranking, biological applications and others. In many practical situations the true pairwise comparisons cannot be actively measured, but a subset of all n(n ..."
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The ranking of n objects based on pairwise comparisons is a core machine learning problem, arising in recommender systems, ad placement, player ranking, biological applications and others. In many practical situations the true pairwise comparisons cannot be actively measured, but a subset of all n(n−1)/2 comparisons is passively and noisily observed. Optimization algorithms (e.g., the SVM) could be used to predict a ranking with fixed expected Kendall tau distance, while achieving an Ω(n) lower bound on the corresponding sample complexity. However, due to their centralized structure they are difficult to extend to online or distributed settings. In this paper we show that much simpler algorithms can match the same Ω(n) lower bound in expectation. Furthermore, if an average of O(n log(n)) binary comparisons are measured, then one algorithm recovers the true ranking in a uniform sense, while the other predicts the ranking more accurately near the top than the bottom. We discuss extensions to online and distributed ranking, with benefits over traditional alternatives. 1.
Probabilistic and utilitytheoretic models in social choice: Challenges for learning, elicitation, and manipulation
 In IJCAI Workshop on Social Choice and Artificial Intelligence
, 2011
"... The abundance of inexpensive preference data facilitated by online commerce, search, recommender systems, and social networks has the potential to stretch the boundaries of social choice. Specifically, concepts and models usually applied to ..."
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The abundance of inexpensive preference data facilitated by online commerce, search, recommender systems, and social networks has the potential to stretch the boundaries of social choice. Specifically, concepts and models usually applied to
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"... Address email This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this problem do not have theoretical guarantees an ..."
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Address email This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this problem do not have theoretical guarantees and can get stuck in bad local optima. We present the first polynomial time algorithm which provably learns the parameters of a mixture of two Mallows models. A key component of our algorithm is a novel use of tensor decomposition techniques to learn the topk prefix in both the rankings. Before this work, even the question of identifiability in the case of a mixture of two Mallows models was unresolved. 1
Learning from Subsampled Data: Active and Randomized Strategies
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