Fused Multiple Graphical Lasso

Abstract

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.

Unified and Contrasting Graphical Lasso for Brain Network Discovery

“…For ADNI dataset, as can be seen from Fig. 6, the major differences between AD patients and normal people are located in parietal lobe and temporal lobe, which is consistent with previous studies [9,16]. Strong decrease of connectivity in these lobes have been detected for AD patients before, which explains the symptoms such as memory loss, mental confusion etc.…”

“…Previous studies [14] sometimes exclude the frontal lobe in analysis since it is thought to be unrelated to AD. However, recent works show there exists increased connectivity in the frontal lobe of AD patients [16]. CGLasso also reveals such pattern in the frontal lobe.…”

“…We adopt the approach in [16] with some modifications to generate the synthetic precision matrices. To simulate subjects in single collection, we generate p separate sparse precision matrices of size m × m with similar structure.…”

Joint sparse canonical correlation analysis for detecting differential imaging genetics modules

“…Our main results in this paper presented an extension of sparse CCA to discover differential association modules from different disease statuses. Inspired by the idea of a joint sparse model (Baron et al, 2005) and fused graphical lasso (Danaher et al, 2014;Yang et al, 2015), we proposed an JSCCA method and verified its performance in a schizophrenia dataset. The dataset consists of fMRI data and SNP data with 116 healthy controls and 92 schizophrenia patients.…”

“…We also apply a fused lasso penalty on the K canonical vectors for genetic data to encourage them to share a similar (but not the same) structure. The fused lasso penalty is chosen because it has been successfully applied to jointly estimate multiple graphical models to find differential dependency networks (Danaher et al, 2014;Tian et al, 2014;Yang et al, 2015). Inspired by the optimization framework for penalized CCA in , we design an efficient algorithm based on block coordinate descent for solving JSCCA.…”