Summary of Online Matrix Completion: a Collaborative Approach with Hott Items, by Dheeraj Baby and Soumyabrata Pal
Online Matrix Completion: A Collaborative Approach with Hott Items
by Dheeraj Baby, Soumyabrata Pal
First submitted to arxiv on: 11 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Information Retrieval (cs.IR); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates the low rank matrix completion problem in an online setting, with a focus on recommending items to users based on noisy rewards. The authors propose two computationally efficient algorithms, PhasedClusterElim and DeterminantElim, which analyze the benign “hott items” assumption. The first algorithm achieves a near-optimal per-user regret of O(NM(-1)(Δ(-1)+Δ_{hott}^(-2))) under additional incoherence/smoothness assumptions on the reward matrix R. The second algorithm introduces PhasedClusterElim, with a simplified setting and milder assumptions, yielding a regret guarantee of O(NM(-1/r)Δ_{det}(-1)). Both algorithms leverage collaboration among users to eliminate sub-optimal items for groups of users in phases. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about recommending things people like online. It’s trying to figure out how to do this when we don’t know what people will like ahead of time and we can only ask them a few times. The authors came up with two new ways to solve this problem that are fast and efficient. One way works well even if the people who like certain things have some weird patterns, while the other way is simpler and works okay even if there’s not much information. Both methods use the ideas of what different groups of people like to help figure out what individual people will like. |
