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In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting

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Τίτλος: In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting
Συγγραφείς: Philippenko, Constantin, Scaman, Kevin, Massoulié, Laurent
Συνεισφορές: Philippenko, Constantin
Πηγή: Proceedings of the AAAI Conference on Artificial Intelligence. 39:19904-19912
Publication Status: Preprint
Στοιχεία εκδότη: Association for the Advancement of Artificial Intelligence (AAAI), 2025.
Έτος έκδοσης: 2025
Θεματικοί όροι: Optimization, Matrix factorisation, Machine Learning, FOS: Computer and information sciences, Optimization and Control (math.OC), Optimization and Control, Federated learning, FOS: Mathematics, [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG)
Περιγραφή: This work presents a novel approach to low-rank matrix factorization in a federated learning context, where multiple clients collaboratively solve a matrix decomposition problem without sharing their local data. The algorithm introduces a power initialization technique for the global factorization matrix and combines it with local gradient descent updates to achieve strong theoretical and practical guarantees. Considering this power initialization, we rewrite the previous smooth non-convex problem into a smooth strongly-convex problem that we solve using a parallel Nesterov gradient descent potentially requiring a single step of communication at the initialization step. We provide a linear rate of convergence of the excess loss, our results improve the rates of convergence given in the literature. We provide an upper bound on the Frobenius-norm error of reconstruction under the power initialization strategy. We complete our analysis with experiments on both synthetic and real data.
Τύπος εγγράφου: Article
Conference object
Περιγραφή αρχείου: application/pdf
ISSN: 2374-3468
2159-5399
DOI: 10.1609/aaai.v39i19.34192
DOI: 10.48550/arxiv.2409.08771
Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2409.08771
https://hal.science/hal-04893622v2
Rights: CC BY
Αριθμός Καταχώρησης: edsair.doi.dedup.....43f1eae6b3e8dfb7e16e7bd3ff8606d2
Βάση Δεδομένων: OpenAIRE
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  Data: In-depth Analysis of Low-rank Matrix Factorisation in a Federated Setting
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  Data: This work presents a novel approach to low-rank matrix factorization in a federated learning context, where multiple clients collaboratively solve a matrix decomposition problem without sharing their local data. The algorithm introduces a power initialization technique for the global factorization matrix and combines it with local gradient descent updates to achieve strong theoretical and practical guarantees. Considering this power initialization, we rewrite the previous smooth non-convex problem into a smooth strongly-convex problem that we solve using a parallel Nesterov gradient descent potentially requiring a single step of communication at the initialization step. We provide a linear rate of convergence of the excess loss, our results improve the rates of convergence given in the literature. We provide an upper bound on the Frobenius-norm error of reconstruction under the power initialization strategy. We complete our analysis with experiments on both synthetic and real data.
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