Fused multiple graphical lasso

Sen Yang, Zhaosong Lu, Xiaotong Shen, Peter Wonka, Jieping Ye

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to estimate a brain network for the normal controls (NC), a brain network for the patients with mild cognitive impairment (MCI), and a brain network for Alzheimer's patients (AD). We expect the two brain networks for NC and MCI to share common structures but not to be identical to each other; similarly for the two brain networks for MCI and AD. The proposed formulation can be solved using a second-order method. Our key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which decomposes the large graphs into small subgraphs and allows an efficient estimation of multiple independent (small) subgraphs, dramatically reducing the computational cost. We perform experiments on both synthetic and real data; our results demonstrate the effectiveness and efficiency of the proposed approach.

Original languageEnglish (US)
Pages (from-to)916-943
Number of pages28
JournalSIAM Journal on Optimization
Volume25
Issue number2
DOIs
StatePublished - 2015

Fingerprint

Lasso
Brain
Subgraph
Graph in graph theory
Neuroimaging
Alzheimer's Disease
Efficient Estimation
Multiple Models
Graphical Models
Decomposable
Screening
Penalty
Graphics
Computational Cost
Adjacent
Necessary Conditions
Decompose
Formulation
Sufficient Conditions
Estimate

Keywords

  • Fused multiple graphical lasso
  • Screening
  • Second-order method

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science

Cite this

Yang, S., Lu, Z., Shen, X., Wonka, P., & Ye, J. (2015). Fused multiple graphical lasso. SIAM Journal on Optimization, 25(2), 916-943. https://doi.org/10.1137/130936397

Fused multiple graphical lasso. / Yang, Sen; Lu, Zhaosong; Shen, Xiaotong; Wonka, Peter; Ye, Jieping.

In: SIAM Journal on Optimization, Vol. 25, No. 2, 2015, p. 916-943.

Research output: Contribution to journalArticle

Yang, S, Lu, Z, Shen, X, Wonka, P & Ye, J 2015, 'Fused multiple graphical lasso', SIAM Journal on Optimization, vol. 25, no. 2, pp. 916-943. https://doi.org/10.1137/130936397
Yang S, Lu Z, Shen X, Wonka P, Ye J. Fused multiple graphical lasso. SIAM Journal on Optimization. 2015;25(2):916-943. https://doi.org/10.1137/130936397
Yang, Sen ; Lu, Zhaosong ; Shen, Xiaotong ; Wonka, Peter ; Ye, Jieping. / Fused multiple graphical lasso. In: SIAM Journal on Optimization. 2015 ; Vol. 25, No. 2. pp. 916-943.
@article{7c820b4afd2d4eb19a716cc824f8ba9a,
title = "Fused multiple graphical lasso",
abstract = "In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to estimate a brain network for the normal controls (NC), a brain network for the patients with mild cognitive impairment (MCI), and a brain network for Alzheimer's patients (AD). We expect the two brain networks for NC and MCI to share common structures but not to be identical to each other; similarly for the two brain networks for MCI and AD. The proposed formulation can be solved using a second-order method. Our key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which decomposes the large graphs into small subgraphs and allows an efficient estimation of multiple independent (small) subgraphs, dramatically reducing the computational cost. We perform experiments on both synthetic and real data; our results demonstrate the effectiveness and efficiency of the proposed approach.",
keywords = "Fused multiple graphical lasso, Screening, Second-order method",
author = "Sen Yang and Zhaosong Lu and Xiaotong Shen and Peter Wonka and Jieping Ye",
year = "2015",
doi = "10.1137/130936397",
language = "English (US)",
volume = "25",
pages = "916--943",
journal = "SIAM Journal on Optimization",
issn = "1052-6234",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",

}

TY - JOUR

T1 - Fused multiple graphical lasso

AU - Yang, Sen

AU - Lu, Zhaosong

AU - Shen, Xiaotong

AU - Wonka, Peter

AU - Ye, Jieping

PY - 2015

Y1 - 2015

N2 - In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to estimate a brain network for the normal controls (NC), a brain network for the patients with mild cognitive impairment (MCI), and a brain network for Alzheimer's patients (AD). We expect the two brain networks for NC and MCI to share common structures but not to be identical to each other; similarly for the two brain networks for MCI and AD. The proposed formulation can be solved using a second-order method. Our key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which decomposes the large graphs into small subgraphs and allows an efficient estimation of multiple independent (small) subgraphs, dramatically reducing the computational cost. We perform experiments on both synthetic and real data; our results demonstrate the effectiveness and efficiency of the proposed approach.

AB - In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to estimate a brain network for the normal controls (NC), a brain network for the patients with mild cognitive impairment (MCI), and a brain network for Alzheimer's patients (AD). We expect the two brain networks for NC and MCI to share common structures but not to be identical to each other; similarly for the two brain networks for MCI and AD. The proposed formulation can be solved using a second-order method. Our key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which decomposes the large graphs into small subgraphs and allows an efficient estimation of multiple independent (small) subgraphs, dramatically reducing the computational cost. We perform experiments on both synthetic and real data; our results demonstrate the effectiveness and efficiency of the proposed approach.

KW - Fused multiple graphical lasso

KW - Screening

KW - Second-order method

UR - http://www.scopus.com/inward/record.url?scp=84940386483&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940386483&partnerID=8YFLogxK

U2 - 10.1137/130936397

DO - 10.1137/130936397

M3 - Article

VL - 25

SP - 916

EP - 943

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

SN - 1052-6234

IS - 2

ER -