Latent Variable Graphical Model Selection Using Harmonic Analysis

Applications to the Human Connectome Project (HCP)

Won Hwa Kim, Hyun Woo Kim, Nagesh Adluru, Vikas Singh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

A major goal of imaging studies such as the (ongoing) Human Connectome Project (HCP) is to characterize the structural network map of the human brain and identify its associations with covariates such as genotype, risk factors, and so on that correspond to an individual. But the set of image derived measures and the set of covariates are both large, so we must first estimate a 'parsimonious' set of relations between the measurements. For instance, a Gaussian graphical model will show conditional independences between the random variables, which can then be used to setup specific downstream analyses. But most such data involve a large list of 'latent' variables that remain unobserved, yet affect the 'observed' variables sustantially. Accounting for such latent variables is not directly addressed by standard precision matrix estimation, and is tackled via highly specialized optimization methods. This paper offers a unique harmonic analysis view of this problem. By casting the estimation of the precision matrix in terms of a composition of low-frequency latent variables and high-frequency sparse terms, we show how the problem can be formulated using a new wavelet-type expansion in non-Euclidean spaces. Our formulation poses the estimation problem in the frequency space and shows how it can be solved by a simple sub-gradient scheme. We provide a set of scientific results on 500 scans from the recently released HCP data where our algorithm recovers highly interpretable and sparse conditional dependencies between brain connectivity pathways and well-known covariates.

Original languageEnglish
Title of host publicationProceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
PublisherIEEE Computer Society
Pages2443-2451
Number of pages9
ISBN (Electronic)9781467388504
DOIs
Publication statusPublished - 2016 Dec 9
Externally publishedYes
Event29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 - Las Vegas, United States
Duration: 2016 Jun 262016 Jul 1

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume2016-December
ISSN (Print)1063-6919

Conference

Conference29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016
CountryUnited States
CityLas Vegas
Period16/6/2616/7/1

Fingerprint

Harmonic analysis
Brain
Random variables
Casting
Imaging techniques
Chemical analysis

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this

Kim, W. H., Kim, H. W., Adluru, N., & Singh, V. (2016). Latent Variable Graphical Model Selection Using Harmonic Analysis: Applications to the Human Connectome Project (HCP). In Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 (pp. 2443-2451). [7780637] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 2016-December). IEEE Computer Society. https://doi.org/10.1109/CVPR.2016.268

Latent Variable Graphical Model Selection Using Harmonic Analysis : Applications to the Human Connectome Project (HCP). / Kim, Won Hwa; Kim, Hyun Woo; Adluru, Nagesh; Singh, Vikas.

Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016. IEEE Computer Society, 2016. p. 2443-2451 7780637 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 2016-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kim, WH, Kim, HW, Adluru, N & Singh, V 2016, Latent Variable Graphical Model Selection Using Harmonic Analysis: Applications to the Human Connectome Project (HCP). in Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016., 7780637, Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2016-December, IEEE Computer Society, pp. 2443-2451, 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, Las Vegas, United States, 16/6/26. https://doi.org/10.1109/CVPR.2016.268
Kim WH, Kim HW, Adluru N, Singh V. Latent Variable Graphical Model Selection Using Harmonic Analysis: Applications to the Human Connectome Project (HCP). In Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016. IEEE Computer Society. 2016. p. 2443-2451. 7780637. (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2016.268
Kim, Won Hwa ; Kim, Hyun Woo ; Adluru, Nagesh ; Singh, Vikas. / Latent Variable Graphical Model Selection Using Harmonic Analysis : Applications to the Human Connectome Project (HCP). Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016. IEEE Computer Society, 2016. pp. 2443-2451 (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition).
@inproceedings{27a368dd695c49d998a9d615856cc311,
title = "Latent Variable Graphical Model Selection Using Harmonic Analysis: Applications to the Human Connectome Project (HCP)",
abstract = "A major goal of imaging studies such as the (ongoing) Human Connectome Project (HCP) is to characterize the structural network map of the human brain and identify its associations with covariates such as genotype, risk factors, and so on that correspond to an individual. But the set of image derived measures and the set of covariates are both large, so we must first estimate a 'parsimonious' set of relations between the measurements. For instance, a Gaussian graphical model will show conditional independences between the random variables, which can then be used to setup specific downstream analyses. But most such data involve a large list of 'latent' variables that remain unobserved, yet affect the 'observed' variables sustantially. Accounting for such latent variables is not directly addressed by standard precision matrix estimation, and is tackled via highly specialized optimization methods. This paper offers a unique harmonic analysis view of this problem. By casting the estimation of the precision matrix in terms of a composition of low-frequency latent variables and high-frequency sparse terms, we show how the problem can be formulated using a new wavelet-type expansion in non-Euclidean spaces. Our formulation poses the estimation problem in the frequency space and shows how it can be solved by a simple sub-gradient scheme. We provide a set of scientific results on 500 scans from the recently released HCP data where our algorithm recovers highly interpretable and sparse conditional dependencies between brain connectivity pathways and well-known covariates.",
author = "Kim, {Won Hwa} and Kim, {Hyun Woo} and Nagesh Adluru and Vikas Singh",
year = "2016",
month = "12",
day = "9",
doi = "10.1109/CVPR.2016.268",
language = "English",
series = "Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition",
publisher = "IEEE Computer Society",
pages = "2443--2451",
booktitle = "Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016",

}

TY - GEN

T1 - Latent Variable Graphical Model Selection Using Harmonic Analysis

T2 - Applications to the Human Connectome Project (HCP)

AU - Kim, Won Hwa

AU - Kim, Hyun Woo

AU - Adluru, Nagesh

AU - Singh, Vikas

PY - 2016/12/9

Y1 - 2016/12/9

N2 - A major goal of imaging studies such as the (ongoing) Human Connectome Project (HCP) is to characterize the structural network map of the human brain and identify its associations with covariates such as genotype, risk factors, and so on that correspond to an individual. But the set of image derived measures and the set of covariates are both large, so we must first estimate a 'parsimonious' set of relations between the measurements. For instance, a Gaussian graphical model will show conditional independences between the random variables, which can then be used to setup specific downstream analyses. But most such data involve a large list of 'latent' variables that remain unobserved, yet affect the 'observed' variables sustantially. Accounting for such latent variables is not directly addressed by standard precision matrix estimation, and is tackled via highly specialized optimization methods. This paper offers a unique harmonic analysis view of this problem. By casting the estimation of the precision matrix in terms of a composition of low-frequency latent variables and high-frequency sparse terms, we show how the problem can be formulated using a new wavelet-type expansion in non-Euclidean spaces. Our formulation poses the estimation problem in the frequency space and shows how it can be solved by a simple sub-gradient scheme. We provide a set of scientific results on 500 scans from the recently released HCP data where our algorithm recovers highly interpretable and sparse conditional dependencies between brain connectivity pathways and well-known covariates.

AB - A major goal of imaging studies such as the (ongoing) Human Connectome Project (HCP) is to characterize the structural network map of the human brain and identify its associations with covariates such as genotype, risk factors, and so on that correspond to an individual. But the set of image derived measures and the set of covariates are both large, so we must first estimate a 'parsimonious' set of relations between the measurements. For instance, a Gaussian graphical model will show conditional independences between the random variables, which can then be used to setup specific downstream analyses. But most such data involve a large list of 'latent' variables that remain unobserved, yet affect the 'observed' variables sustantially. Accounting for such latent variables is not directly addressed by standard precision matrix estimation, and is tackled via highly specialized optimization methods. This paper offers a unique harmonic analysis view of this problem. By casting the estimation of the precision matrix in terms of a composition of low-frequency latent variables and high-frequency sparse terms, we show how the problem can be formulated using a new wavelet-type expansion in non-Euclidean spaces. Our formulation poses the estimation problem in the frequency space and shows how it can be solved by a simple sub-gradient scheme. We provide a set of scientific results on 500 scans from the recently released HCP data where our algorithm recovers highly interpretable and sparse conditional dependencies between brain connectivity pathways and well-known covariates.

UR - http://www.scopus.com/inward/record.url?scp=84986252340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84986252340&partnerID=8YFLogxK

U2 - 10.1109/CVPR.2016.268

DO - 10.1109/CVPR.2016.268

M3 - Conference contribution

T3 - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

SP - 2443

EP - 2451

BT - Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016

PB - IEEE Computer Society

ER -