Latent Variable Graphical Model Selection Using Harmonic Analysis: Applications to the Human Connectome Project (HCP)

Won Hwa Kim, Hyunwoo J. Kim, Nagesh Adluru, Vikas Singh; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016, pp. 2443-2451

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 hypothesis based analyses downstream. 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 falls outside the scope of standard inverse covariance 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 formalization poses the estimation problem entirely in the frequency space and shows how it can be solved by a simple sub-gradient scheme (involving a single variable). We provide a compelling 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.

Related Material


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[bibtex]
@InProceedings{Kim_2016_CVPR,
author = {Hwa Kim, Won and Kim, Hyunwoo J. and Adluru, Nagesh and Singh, Vikas},
title = {Latent Variable Graphical Model Selection Using Harmonic Analysis: Applications to the Human Connectome Project (HCP)},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2016}
}