Thy friend is my friend: Iterative collaborative filtering for sparse matrix estimation
Name
7057-thy-friend-is-my-friend-iterative-collaborative-filtering-for-sparse-matrix-estimation.pdf
Description
Published version
Size
290.5 KB
Format
Adobe PDF
Checksum (MD5)
e46cc7012ec12250ef6c460043e18ca3
Author(s)
Shah, Devavrat
Lee, Christina E.
Date Issued
2017
Citation
Shah, Devavrat and Lee, Christina E. 2017. "Thy friend is my friend: Iterative collaborative filtering for sparse matrix estimation."
Version
Final published version
Abstract
© 2017 Neural information processing systems foundation. All rights reserved. The sparse matrix estimation problem consists of estimating the distribution of an n x n matrix Y, from a sparsely observed single instance of this matrix where the entries of Y are independent random variables. This captures a wide array of problems; special instances include matrix completion in the context of recommendation systems, graphon estimation, and community detection in (mixed membership) stochastic block models. Inspired by classical collaborative filtering for recommendation systems, we propose a novel iterative, collaborative filteringstyle algorithm for matrix estimation in this generic setting. We show that the mean squared error (MSE) of our estimator converges to 0 at the rate of O(d2 (pn)-2/5) as long as ω(d5n) random entries from a total of n2 entries of Y are observed (uniformly sampled), E[Y] has rank d, and the entries of Y have bounded support. The maximum squared error across all entries converges to 0 with high probability as long as we observe a little more, Ω(d5nln (n)) entries. Our results are the best known sample complexity results in this generality.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Statistics and Data Science Center (Massachusetts Institute of Technology)
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://papers.nips.cc/paper/7057-thy-friend-is-my-friend-iterative-collaborative-filtering-for-sparse-matrix-estimation
