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H 1 Individualized rank aggregation using nuclear norm regularization

Auteurs : Neghaban, Sahand (Auteur de la Conférence)
CIRM (Editeur )

Résumé : 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

Codes MSC :
62H12 - Multivariate estimation
68T05 - Learning and adaptive systems

 Informations sur la Vidéo Langue : Anglais Date de publication : 08/01/15 Date de captation : 16/12/14 Collection : Research talks ; Computer Science ; Probability and Statistics Format : quicktime ; audio/x-aac Durée : 00:25:10 Domaine : Computer Science ; Probability & Statistics Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2014-12-16_Neghaban.mp4 Informations sur la rencontre Nom de la rencontre : Meeting in mathematical statistics: new procedures for new data / Rencontre de statistiques mathématiques : nouvelles procédures pour de nouvelles donnéesOrganisateurs de la rencontre : Pouet, Christophe ; Reiss, Markus ; Rigollet, PhilippeDates : 15/12/14 - 19/12/14 Année de la rencontre : 2014 Citation Data DOI : 10.24350/CIRM.V.18659403 Cite this video as: Neghaban, Sahand (2014). Individualized rank aggregation using nuclear norm regularization. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18659403 URI : http://dx.doi.org/10.24350/CIRM.V.18659403

Bibliographie

1. 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

2. Lu, Y., & Negahban, S. (2014). Individualized rank aggregation using nuclear norm regularization. - http://arxiv.org/abs/1410.0860

3. 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

4. Negahban, S., Oh, S., & Shah, D. (2014) Iterative ranking from pair-wise comparisons. - http://arxiv.org/abs/1209.1688

5. 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

6. 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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