MRA-based Statistical Learning from Incomplete Rankings

Eric Sibony, Stéphan Clemençon, Jérémie Jakubowicz
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1432-1441, 2015.

Abstract

Statistical analysis of rank data describing preferences over small and variable subsets of a potentially large ensemble of items 1, ..., n is a very challenging problem. It is motivated by a wide variety of modern applications, such as recommender systems or search engines. However, very few inference methods have been documented in the literature to learn a ranking model from such incomplete rank data. The goal of this paper is twofold: it develops a rigorous mathematical framework for the problem of learning a ranking model from incomplete rankings and introduces a novel general statistical method to address it. Based on an original concept of multi-resolution analysis (MRA) of incomplete rankings, it finely adapts to any observation setting, leading to a statistical accuracy and an algorithmic complexity that depend directly on the complexity of the observed data. Beyond theoretical guarantees, we also provide experimental results that show its statistical performance.

Cite this Paper


BibTeX
@InProceedings{pmlr-v37-sibony15, title = {MRA-based Statistical Learning from Incomplete Rankings}, author = {Sibony, Eric and Clemençon, Stéphan and Jakubowicz, Jérémie}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1432--1441}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/sibony15.pdf}, url = { http://proceedings.mlr.press/v37/sibony15.html }, abstract = {Statistical analysis of rank data describing preferences over small and variable subsets of a potentially large ensemble of items 1, ..., n is a very challenging problem. It is motivated by a wide variety of modern applications, such as recommender systems or search engines. However, very few inference methods have been documented in the literature to learn a ranking model from such incomplete rank data. The goal of this paper is twofold: it develops a rigorous mathematical framework for the problem of learning a ranking model from incomplete rankings and introduces a novel general statistical method to address it. Based on an original concept of multi-resolution analysis (MRA) of incomplete rankings, it finely adapts to any observation setting, leading to a statistical accuracy and an algorithmic complexity that depend directly on the complexity of the observed data. Beyond theoretical guarantees, we also provide experimental results that show its statistical performance.} }
Endnote
%0 Conference Paper %T MRA-based Statistical Learning from Incomplete Rankings %A Eric Sibony %A Stéphan Clemençon %A Jérémie Jakubowicz %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-sibony15 %I PMLR %P 1432--1441 %U http://proceedings.mlr.press/v37/sibony15.html %V 37 %X Statistical analysis of rank data describing preferences over small and variable subsets of a potentially large ensemble of items 1, ..., n is a very challenging problem. It is motivated by a wide variety of modern applications, such as recommender systems or search engines. However, very few inference methods have been documented in the literature to learn a ranking model from such incomplete rank data. The goal of this paper is twofold: it develops a rigorous mathematical framework for the problem of learning a ranking model from incomplete rankings and introduces a novel general statistical method to address it. Based on an original concept of multi-resolution analysis (MRA) of incomplete rankings, it finely adapts to any observation setting, leading to a statistical accuracy and an algorithmic complexity that depend directly on the complexity of the observed data. Beyond theoretical guarantees, we also provide experimental results that show its statistical performance.
RIS
TY - CPAPER TI - MRA-based Statistical Learning from Incomplete Rankings AU - Eric Sibony AU - Stéphan Clemençon AU - Jérémie Jakubowicz BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-sibony15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1432 EP - 1441 L1 - http://proceedings.mlr.press/v37/sibony15.pdf UR - http://proceedings.mlr.press/v37/sibony15.html AB - Statistical analysis of rank data describing preferences over small and variable subsets of a potentially large ensemble of items 1, ..., n is a very challenging problem. It is motivated by a wide variety of modern applications, such as recommender systems or search engines. However, very few inference methods have been documented in the literature to learn a ranking model from such incomplete rank data. The goal of this paper is twofold: it develops a rigorous mathematical framework for the problem of learning a ranking model from incomplete rankings and introduces a novel general statistical method to address it. Based on an original concept of multi-resolution analysis (MRA) of incomplete rankings, it finely adapts to any observation setting, leading to a statistical accuracy and an algorithmic complexity that depend directly on the complexity of the observed data. Beyond theoretical guarantees, we also provide experimental results that show its statistical performance. ER -
APA
Sibony, E., Clemençon, S. & Jakubowicz, J.. (2015). MRA-based Statistical Learning from Incomplete Rankings. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1432-1441 Available from http://proceedings.mlr.press/v37/sibony15.html .

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