Results 1 
2 of
2
Preference completion: Largescale collaborative ranking from pairwise comparison
 In ICML
, 2015
"... Abstract In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between d possible items; from these we need to predict each users preferences for items they have not yet seen. We do so by fitting a rank r score matrix to th ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between d possible items; from these we need to predict each users preferences for items they have not yet seen. We do so by fitting a rank r score matrix to the pairwise data, and provide two main contributions: (a) we show that an algorithm based on convex optimization provides good generalization guarantees once each user provides as few as O(r log 2 d) pairwise comparisons essentially matching the sample complexity required in the related matrix completion setting (which uses actual numerical as opposed to pairwise information), and (b) we develop a largescale nonconvex implementation, which we call AltSVM, that trains a factored form of the matrix via alternating minimization (which we show reduces to alternating SVM problems), and scales and parallelizes very well to large problem settings. It also outperforms common baselines on many moderately large popular collaborative filtering datasets in both NDCG and in other measures of ranking performance.
Datadriven Rank Breaking for Efficient Rank Aggregation
, 2016
"... Abstract Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. Rankbreaking is a common practice to reduce the computational complexity of learning the global ranking. The individual preferences are broken into pair ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. Rankbreaking is a common practice to reduce the computational complexity of learning the global ranking. The individual preferences are broken into pairwise comparisons and applied to efficient algorithms tailored for independent paired comparisons. However, due to the ignored dependencies in the data, naive rankbreaking approaches can result in inconsistent estimates. The key idea to produce accurate and consistent estimates is to treat the pairwise comparisons unequally, depending on the topology of the collected data. In this paper, we provide the optimal rankbreaking estimator, which not only achieves consistency but also achieves the best error bound. This allows us to characterize the fundamental tradeoff between accuracy and complexity. Further, the analysis identifies how the accuracy depends on the spectral gap of a corresponding comparison graph.