Recommendation on a Budget: Column Space Recovery from Partially Observed Entries with Random or Active Sampling
Abstract
We analyze alternating minimization for column space recovery of a partially observed, approximately low rank matrix with a growing number of columns and a fixed budget of observations per column. We prove that if the budget is greater than the rank of the matrix, column space recovery succeeds – as the number of columns grows, the estimate from alternating minimization converges to the true column space with probability tending to one. From our proof techniques, we naturally formulate an active sampling strategy for choosing entries of a column that is theoretically and empirically (on synthetic and real data) better than the commonly studied uniformly random sampling strategy.
Cite
Text
Kim and Bayati. "Recommendation on a Budget: Column Space Recovery from Partially Observed Entries with Random or Active Sampling." Artificial Intelligence and Statistics, 2020.Markdown
[Kim and Bayati. "Recommendation on a Budget: Column Space Recovery from Partially Observed Entries with Random or Active Sampling." Artificial Intelligence and Statistics, 2020.](https://mlanthology.org/aistats/2020/kim2020aistats-recommendation/)BibTeX
@inproceedings{kim2020aistats-recommendation,
title = {{Recommendation on a Budget: Column Space Recovery from Partially Observed Entries with Random or Active Sampling}},
author = {Kim, Carolyn and Bayati, Mohsen},
booktitle = {Artificial Intelligence and Statistics},
year = {2020},
pages = {445-455},
volume = {108},
url = {https://mlanthology.org/aistats/2020/kim2020aistats-recommendation/}
}