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 language | English |
|---|---|
| Title of host publication | Proceedings - 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 |
| Publisher | IEEE Computer Society |
| Pages | 2443-2451 |
| Number of pages | 9 |
| ISBN (Electronic) | 9781467388504 |
| DOIs | |
| Publication status | Published - 2016 Dec 9 |
| Externally published | Yes |
| Event | 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 - Las Vegas, United States Duration: 2016 Jun 26 → 2016 Jul 1 |
Publication series
| Name | Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition |
|---|---|
| Volume | 2016-December |
| ISSN (Print) | 1063-6919 |
Conference
| Conference | 29th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016 |
|---|---|
| Country | United States |
| City | Las Vegas |
| Period | 16/6/26 → 16/7/1 |
Fingerprint
ASJC Scopus subject areas
- Software
- Computer Vision and Pattern Recognition
Cite this
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 proceeding › Conference contribution
}
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.
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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 -