Global Optimality in Inductive Matrix Completion

Inductive matrix completion (IMC) is a model for incorporating side information in form of "features" of the row and column entities of an unknown matrix in the matrix completion problem. As side information, features can substantially reduce the number of observed entries required for rec...

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Bibliographic Details
Published in2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 2226 - 2230
Main Authors Ghassemi, Mohsen, Sarwate, Anand, Goela, Naveen
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.04.2018
Subjects
Complexity theory
Convergence
Estimation
inductive matrix completion
Linear matrix inequalities
Linear programming
local minima
matrix recovery
Optimization
saddle points
Sensors
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Summary:Inductive matrix completion (IMC) is a model for incorporating side information in form of "features" of the row and column entities of an unknown matrix in the matrix completion problem. As side information, features can substantially reduce the number of observed entries required for reconstructing an unknown matrix from its given entries. The IMC problem can be formulated as a low-rank matrix recovery problem where the observed entries are seen as measurements of a smaller matrix that models the interaction between the column and row features. We take advantage of this property to study the optimization landscape of the factorized IMC problem. In particular, we show that the critical points of the objective function of this problem are either global minima that correspond to the true solution or are "escapable" saddle points. This result implies that any minimization algorithm with guaranteed convergence to a local minimum can be used for solving the factorized IMC problem.
ISSN:2379-190X
DOI:10.1109/ICASSP.2018.8462250