Summary of In-depth Analysis Of Low-rank Matrix Factorisation in a Federated Setting, by Constantin Philippenko et al.
In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting
by Constantin Philippenko, Kevin Scaman, Laurent Massoulié
First submitted to arxiv on: 13 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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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 The paper presents a distributed algorithm for computing low-rank matrix factorizations on multiple clients, each holding local datasets. The goal is to minimize the squared Frobenius norm between the local datasets and their approximations using a common set of factors. The authors use a power initialization for one of the factors and rewrite the non-convex problem as a strongly-convex one, which they solve using parallel Nesterov gradient descent. They prove a linear rate of convergence for the excess loss, improving previous results. Experiments are provided on both synthetic and real data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about a new way to do math problems that involves lots of computers working together. The goal is to make a good guess at what a big matrix should look like by combining smaller pieces of information from many different places. The authors come up with a clever trick to help the computers work together better and show that this trick makes their method much faster than previous methods. They test their idea on some fake data and some real data, and it seems to work really well. |
Keywords
» Artificial intelligence » Gradient descent
