TY - JOUR
AU - Ledent, Antoine
AU - Alves, Rodrigo
AU - Lei, Yunwen
AU - Guermeur, Yann
AU - Kloft, Marius
PY - 2023/06/26
Y2 - 2024/04/14
TI - Generalization Bounds for Inductive Matrix Completion in Low-Noise Settings
JF - Proceedings of the AAAI Conference on Artificial Intelligence
JA - AAAI
VL - 37
IS - 7
SE - AAAI Technical Track on Machine Learning II
DO - 10.1609/aaai.v37i7.26018
UR - https://ojs.aaai.org/index.php/AAAI/article/view/26018
SP - 8447-8455
AB - We study inductive matrix completion (matrix completion with side information) under an i.i.d. subgaussian noise assumption at a low noise regime, with uniform sampling of the entries. We obtain for the first time generalization bounds with the following three properties: (1) they scale like the standard deviation of the noise and in particular approach zero in the exact recovery case; (2) even in the presence of noise, they converge to zero when the sample size approaches infinity; and (3) for a fixed dimension of the side information, they only have a logarithmic dependence on the size of the matrix. Differently from many works in approximate recovery, we present results both for bounded Lipschitz losses and for the absolute loss, with the latter relying on Talagrand-type inequalities. The proofs create a bridge between two approaches to the theoretical analysis of matrix completion, since they consist in a combination of techniques from both the exact recovery literature and the approximate recovery literature.
ER -