Active multiple matrix completion with adaptive confidence sets

Andrea Locatelli, Alexandra Carpentier, Michal Valko
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1783-1791, 2019.

Abstract

We address the problem of an active setting for a matrix completion, where the learner can choose, from which matrix, it receives a sample (drawn uniformly at random). Our main practical motivation is the market segmentation, where the matrices are different regions with different preferences of the customers. The challenge in this setting is that each of the matrices can be of a different size and also of a different rank. We provide and analyze a new algorithm, MAlocate that is able to adapt to the ranks of the different matrices. We also prove a lower-bound showing that our strategy is minimax-optimal, and we demonstrate its performance with synthetic experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-locatelli19a, title = {Active multiple matrix completion with adaptive confidence sets}, author = {Locatelli, Andrea and Carpentier, Alexandra and Valko, Michal}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1783--1791}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/locatelli19a/locatelli19a.pdf}, url = {https://proceedings.mlr.press/v89/locatelli19a.html}, abstract = {We address the problem of an active setting for a matrix completion, where the learner can choose, from which matrix, it receives a sample (drawn uniformly at random). Our main practical motivation is the market segmentation, where the matrices are different regions with different preferences of the customers. The challenge in this setting is that each of the matrices can be of a different size and also of a different rank. We provide and analyze a new algorithm, MAlocate that is able to adapt to the ranks of the different matrices. We also prove a lower-bound showing that our strategy is minimax-optimal, and we demonstrate its performance with synthetic experiments.} }
Endnote
%0 Conference Paper %T Active multiple matrix completion with adaptive confidence sets %A Andrea Locatelli %A Alexandra Carpentier %A Michal Valko %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-locatelli19a %I PMLR %P 1783--1791 %U https://proceedings.mlr.press/v89/locatelli19a.html %V 89 %X We address the problem of an active setting for a matrix completion, where the learner can choose, from which matrix, it receives a sample (drawn uniformly at random). Our main practical motivation is the market segmentation, where the matrices are different regions with different preferences of the customers. The challenge in this setting is that each of the matrices can be of a different size and also of a different rank. We provide and analyze a new algorithm, MAlocate that is able to adapt to the ranks of the different matrices. We also prove a lower-bound showing that our strategy is minimax-optimal, and we demonstrate its performance with synthetic experiments.
APA
Locatelli, A., Carpentier, A. & Valko, M.. (2019). Active multiple matrix completion with adaptive confidence sets. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1783-1791 Available from https://proceedings.mlr.press/v89/locatelli19a.html.

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