ㅇ 제목 : Multi-resolution Analysis for Inverse Covariance Matrix Estimation

ㅇ 장소 : ETRI 12연구동 608호

A major goal of medical imaging studies 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 among the measurements. For instance, a Gaussian graphical model will show conditional independences between 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 substantially. Accounting for such latent variables is not directly addressed by standard precision matrix estimation, and is tackled via highly specialized optimization methods. This work 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 wavelet-type expansion in non-Euclidean spaces. This formulation poses the estimation problem in the frequency space and shows how it can be solved by a simple sub-gradient scheme. When the proposed method is applied on Human Connectome Project (HCP) data, it recovers highly interpretable sparse conditional dependencies between brain connectivity pathways and well-known covariates.