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Global Optimality in Inductive Matrix Completion

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Citation Author(s):
Mohsen Ghassemi, Anand D. Sarwate, Naveen goela
Submitted by:
Mohsen Ghassemi
Last updated:
1 May 2018 - 11:04pm
Document Type:
Presentation Slides
Document Year:
2018
Event:
Presenters Name:
Anand Sarwate
Paper Code:
1764

Abstract 

Abstract: 

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.

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ICASSP2018.pdf

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