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Global Optimality in Inductive Matrix Completion

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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Paper Details

Authors:
Mohsen Ghassemi, Anand D. Sarwate, Naveen goela
Submitted On:
1 May 2018 - 11:04pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Anand Sarwate
Paper Code:
1764
Document Year:
2018
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Document Files

ICASSP2018.pdf

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[1] Mohsen Ghassemi, Anand D. Sarwate, Naveen goela, "Global Optimality in Inductive Matrix Completion", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/3171. Accessed: Jul. 17, 2018.
@article{3171-18,
url = {http://sigport.org/3171},
author = {Mohsen Ghassemi; Anand D. Sarwate; Naveen goela },
publisher = {IEEE SigPort},
title = {Global Optimality in Inductive Matrix Completion},
year = {2018} }
TY - EJOUR
T1 - Global Optimality in Inductive Matrix Completion
AU - Mohsen Ghassemi; Anand D. Sarwate; Naveen goela
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/3171
ER -
Mohsen Ghassemi, Anand D. Sarwate, Naveen goela. (2018). Global Optimality in Inductive Matrix Completion. IEEE SigPort. http://sigport.org/3171
Mohsen Ghassemi, Anand D. Sarwate, Naveen goela, 2018. Global Optimality in Inductive Matrix Completion. Available at: http://sigport.org/3171.
Mohsen Ghassemi, Anand D. Sarwate, Naveen goela. (2018). "Global Optimality in Inductive Matrix Completion." Web.
1. Mohsen Ghassemi, Anand D. Sarwate, Naveen goela. Global Optimality in Inductive Matrix Completion [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/3171