Efficient Graph Laplacian Estimation by Proximal Newton

arXiv:2302.06434v3 Announce Type: replace
Abstract: The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood estimation (MLE) of the precision matrix, subject to Laplacian structural constraints, with a sparsity-inducing penalty term. This paper aims to solve this learning problem accurately and efficiently. First, since the commonly used $\ell_1$-norm penalty is inappropriate in this setting and may …

abstract arxiv constraints cs.lg data graph graph learning likelihood markov math.oc matrix maximum likelihood estimation mle multivariate precision random sparsity statistical type