Iterative Collaborative Filtering for Sparse Matrix Estimation
Name
1712.00710.pdf
Description
Accepted version
Size
598.55 KB
Format
Adobe PDF
Checksum (MD5)
7f37f981f2107e0cec0cd07be8b470aa
Author(s)
Borgs, Christian
Chayes, Jennifer T
Shah, Devavrat
Yu, Christina Lee
Date Issued
2021
Journal
Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Borgs, Christian, Chayes, Jennifer T, Shah, Devavrat and Yu, Christina Lee. 2021. "Iterative Collaborative Filtering for Sparse Matrix Estimation." Operations Research.
Version
Author's final manuscript
Abstract
Matrix estimation or completion has served as a canonical mathematical model for recommendation systems. More recently, it has emerged as a fundamental building block for data analysis as a first step to denoise the observations and predict missing values. Since the dawn of e-commerce, similarity-based collaborative filtering has been used as a heuristic for matrix etimation. At its core, it encodes typical human behavior: you ask your friends to recommend what you may like or dislike. Algorithmically, friends are similar “rows” or “columns” of the underlying matrix. The traditional heuristic for computing similarities between rows has costly requirements on the density of observed entries. In “Iterative Collaborative Filtering for Sparse Matrix Estimation” by Christian Borgs, Jennifer T. Chayes, Devavrat Shah, and Christina Lee Yu, the authors introduce an algorithm that computes similarities in sparse datasets by comparing expanded local neighborhoods in the associated data graph: in effect, you ask friends of your friends to recommend what you may like or dislike. This work provides bounds on the max entry-wise error of their estimate for low rank and approximately low rank matrices, which is stronger than the aggregate mean squared error bounds found in classical works. The algorithm is also interpretable, scalable, and amenable to distributed implementation.
MIT Department
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Statistics and Data Science Center (Massachusetts Institute of Technology)
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1287/OPRE.2021.2193
