Fused Multiple Graphical Lasso

Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity

Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for comparing these estimated GGMs. Our goal is to identify differences in GGMs known to have similar structure. We characterize the uncertainty of differences with conf...

Supplementary Web Materials For “Fused Lasso with the Adaptation of Parameter Ordering in Combining Multiple Studies with Repeated Measurements”

On the Complexity of the Weighted Fussed Lasso

The solution path of the 1D fused lasso for an ndimensional input is piecewise linear with O(n) segments [1], [2]. However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the weighted fused lasso is a special case, allow Ω(3) segments [3]. In this paper, we prove that the number of segments in the solution pa...

The group fused Lasso for multiple change-point detection

We present the group fused Lasso for detection of multiple change-points shared by a set of cooccurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are proposed to solve the resulting optimization problems, either exactly or appro...

Exact Hybrid Covariance Thresholding for Joint Graphical Lasso

This paper studies precision matrix estimation for multiple related Gaussian graphical models from a dataset consisting of different classes, based upon the formulation of this problem as group graphical lasso. In particular, this paper proposes a novel hybrid covariance thresholding algorithm that can effectively identify zero entries in the precision matrices and split a large joint graphical...