Efficient Convex Completion of Coupled Tensors using Coupled Nuclear Norms

Kishan Wimalawarne; Hiroshi Mamitsuka

Efficient Convex Completion of Coupled Tensors using Coupled Nuclear Norms

Research output: Contribution to conference › Paper › Scientific › peer-review

Abstract

Coupled norms have emerged as a convex method to solve coupled tensor com-
pletion. A limitation with coupled norms is that they only induce low-rankness
using the multilinear rank of coupled tensors. In this paper, we introduce a new
set of coupled norms known as coupled nuclear norms by constraining the CP
rank of coupled tensors. We propose new coupled completion models using the
coupled nuclear norms as regularizers, which can be optimized using computa-
tionally efficient optimization methods. We derive excess risk bounds for pro-
posed coupled completion models and show that proposed norms lead to better
performance. Through simulation and real-data experiments, we demonstrate that
proposed norms achieve better performance for coupled completion compared to
existing coupled norms.

Original language	English
Pages	6902-6910
Number of pages	9
Publication status	Published - 2018
MoE publication type	Not Eligible
Event	Conference on Neural Information Processing Systems - Palais des Congrès de Montréal, Montréal, Canada Duration: 2 Dec 2018 → 8 Dec 2018 Conference number: 32 http://nips.cc

Conference

Conference	Conference on Neural Information Processing Systems
Abbreviated title	NeurIPS
Country	Canada
City	Montréal
Period	02/12/2018 → 08/12/2018
Internet address	http://nips.cc

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title = "Efficient Convex Completion of Coupled Tensors using Coupled Nuclear Norms",

abstract = "Coupled norms have emerged as a convex method to solve coupled tensor com-pletion. A limitation with coupled norms is that they only induce low-ranknessusing the multilinear rank of coupled tensors. In this paper, we introduce a newset of coupled norms known as coupled nuclear norms by constraining the CPrank of coupled tensors. We propose new coupled completion models using thecoupled nuclear norms as regularizers, which can be optimized using computa-tionally efficient optimization methods. We derive excess risk bounds for pro-posed coupled completion models and show that proposed norms lead to betterperformance. Through simulation and real-data experiments, we demonstrate thatproposed norms achieve better performance for coupled completion compared toexisting coupled norms.",

author = "Kishan Wimalawarne and Hiroshi Mamitsuka",

year = "2018",

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note = "Conference on Neural Information Processing Systems, NeurIPS ; Conference date: 02-12-2018 Through 08-12-2018",

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T1 - Efficient Convex Completion of Coupled Tensors using Coupled Nuclear Norms

AU - Wimalawarne, Kishan

AU - Mamitsuka, Hiroshi

N1 - Conference code: 32

PY - 2018

Y1 - 2018

N2 - Coupled norms have emerged as a convex method to solve coupled tensor com-pletion. A limitation with coupled norms is that they only induce low-ranknessusing the multilinear rank of coupled tensors. In this paper, we introduce a newset of coupled norms known as coupled nuclear norms by constraining the CPrank of coupled tensors. We propose new coupled completion models using thecoupled nuclear norms as regularizers, which can be optimized using computa-tionally efficient optimization methods. We derive excess risk bounds for pro-posed coupled completion models and show that proposed norms lead to betterperformance. Through simulation and real-data experiments, we demonstrate thatproposed norms achieve better performance for coupled completion compared toexisting coupled norms.

AB - Coupled norms have emerged as a convex method to solve coupled tensor com-pletion. A limitation with coupled norms is that they only induce low-ranknessusing the multilinear rank of coupled tensors. In this paper, we introduce a newset of coupled norms known as coupled nuclear norms by constraining the CPrank of coupled tensors. We propose new coupled completion models using thecoupled nuclear norms as regularizers, which can be optimized using computa-tionally efficient optimization methods. We derive excess risk bounds for pro-posed coupled completion models and show that proposed norms lead to betterperformance. Through simulation and real-data experiments, we demonstrate thatproposed norms achieve better performance for coupled completion compared toexisting coupled norms.

M3 - Paper

SP - 6902

EP - 6910

T2 - Conference on Neural Information Processing Systems

Y2 - 2 December 2018 through 8 December 2018

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