Generalization analysis of deep nonlinear matrix completion

• Main Authors: LEDENT, Antoine, ALVES, Rodrigo
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2024
• Subjects: Matrix Completion; Schatten p Quasi Norms; Learning Theory; Databases and Information Systems
• Online Access: https://ink.library.smu.edu.sg/sis_research/9303; https://ink.library.smu.edu.sg/context/sis_research/article/10303/viewcontent/ledent24a.pdf
• Institution: Singapore Management University

We provide generalization bounds for matrix completion with Schatten $p$ quasi-norm constraints, which is equivalent to deep matrix factorization with Frobenius constraints. In the uniform sampling regime, the sample complexity scales like $\widetilde{O}\left( rn\right)$ where $n$ is the size of the...