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Individualized rank aggregation using nuclear norm regularization

De Sahand Neghaban

Apparaît dans la collection : Meeting in mathematical statistics: new procedures for new data / Rencontre de statistiques mathématiques : nouvelles procédures pour de nouvelles données

In recent years rank aggregation has received significant attention from the machine learning community. The goal of such a problem is to combine the (partially revealed) preferences over objects of a large population into a single, relatively consistent ordering of those objects. However, in many cases, we might not want a single ranking and instead opt for individual rankings. We study a version of the problem known as collaborative ranking. In this problem we assume that individual users provide us with pairwise preferences (for example purchasing one item over another). From those preferences we wish to obtain rankings on items that the users have not had an opportunity to explore. The results here have a very interesting connection to the standard matrix completion problem. We provide a theoretical justification for a nuclear norm regularized optimization procedure, and provide high-dimensional scaling results that show how the error in estimating user preferences behaves as the number of observations increase.

rank aggregation - nuclear norm - rank centrality - convex optimization - regularized $M$-estimation - matrix completion - collaborative filtering

Informations sur la vidéo

Date de captation 16/12/2014
Date de publication 08/01/2015
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18659403
Citer cette vidéo Neghaban, Sahand (16/12/2014). Individualized rank aggregation using nuclear norm regularization. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18659403
URL https://dx.doi.org/10.24350/CIRM.V.18659403

Domaine(s)

Bibliographie

Candès, E.J., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational mathematics, 9(6), 717-772 - http://dx.doi.org/10.1007/s10208-009-9045-5
Lu, Y., & Negahban, S. (2014). Individualized rank aggregation using nuclear norm regularization. <arXiv:1410.0860> - http://arxiv.org/abs/1410.0860
Negahban, S., Ravikumar, P., Wainwright, M.J., & Yu, B. (2012). A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers. Statistical Science, 27(4), 538-557 - http://dx.doi.org/10.1214/12-STS400
Negahban, S., Oh, S., & Shah, D. (2014) Iterative ranking from pair-wise comparisons. <arXiv:1209.1688> - http://arxiv.org/abs/1209.1688
Negahban, S., & Wainwright, M.J. (2012). Restricted strong convexity and weighted matrix completion: optimal bounds with noise. Journal of Machine Learning Research, 13, 1665-1697 - http://www.jmlr.org/papers/v13/negahban12a.html
Yi, J., Jin, R., Jain, S., & Jain, A. (2013). Inferring users' preferences from crowdsourced pairwise comparisons: a matrix completion approach. In B. Hartmann, & E. Horvitz (Eds.), Proceedings of the first AAAI Conference on Human Computation and Crowdsourcing (pp. 207-215) - http://www.aaai.org/ocs/index.php/HCOMP/HCOMP13/paper/viewFile/7536/7421

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