A Block Coordinate Descent Algorithm for Sparse Gaussian Graphical Model Inference with Laplacian Constraints

We consider the problem of inferring sparse Gaussian graphical models with Laplacian constraints, which can also be viewed as learning a graph Laplacian such that the observed graph signals are smooth with respect to it. A block coordinate descent algorithm is proposed for the resulting linearly constrained log-determinant maximum likelihood estimation problem with sparse regularization. Simulation results on synthetic data show the efficiency of our proposed algorithm.

[1]  N. Meinshausen,et al.  High-dimensional graphs and variable selection with the Lasso , 2006, math/0608017.

[2]  Mihailo R. Jovanovic,et al.  Topology identification of undirected consensus networks via sparse inverse covariance estimation , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[3]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[4]  Licheng Zhao,et al.  Optimization Algorithms for Graph Laplacian Estimation via ADMM and MM , 2019, IEEE Transactions on Signal Processing.

[5]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

[6]  Pascal Frossard,et al.  Learning Laplacian Matrix in Smooth Graph Signal Representations , 2014, IEEE Transactions on Signal Processing.

[7]  Sandeep Kumar,et al.  A Unified Framework for Structured Graph Learning via Spectral Constraints , 2019, J. Mach. Learn. Res..

[8]  J. Bunch,et al.  Rank-one modification of the symmetric eigenproblem , 1978 .

[9]  Joshua B. Tenenbaum,et al.  Discovering Structure by Learning Sparse Graphs , 2010 .

[10]  Antonio Ortega,et al.  Graph Learning From Data Under Laplacian and Structural Constraints , 2016, IEEE Journal of Selected Topics in Signal Processing.

[11]  Alexandre d'Aspremont,et al.  Model Selection Through Sparse Maximum Likelihood Estimation , 2007, ArXiv.

[12]  Santiago Segarra,et al.  Connecting the Dots: Identifying Network Structure via Graph Signal Processing , 2018, IEEE Signal Processing Magazine.

[13]  Michael G. Rabbat.  Inferring sparse graphs from smooth signals with theoretical guarantees , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[14]  Yang Yang,et al.  A Unified Successive Pseudoconvex Approximation Framework , 2015, IEEE Transactions on Signal Processing.

[15]  Antonio Ortega,et al.  Generalized Laplacian precision matrix estimation for graph signal processing , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[16]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[17]  Pradeep Ravikumar,et al.  Sparse inverse covariance matrix estimation using quadratic approximation , 2011, MLSLP.

[18]  Ren-Cang Li.  Solving secular equations stably and efficiently , 1993 .

[19]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[20]  M. Yuan,et al.  Model selection and estimation in the Gaussian graphical model , 2007 .