# Technical Program

## Paper Detail

 Paper ID SPTM-16.5 Paper Title A Graph Learning Algorithm Based on Gaussian Markov Random Fields and Minimax Concave Penalty Authors Tatsuya Koyakumaru, Masahiro Yukawa, Keio University, Japan; Eduardo Pavez, Antonio Ortega, University of Southern California, United States Session SPTM-16: Graph Topology Inference Location Gather.Town Session Time: Thursday, 10 June, 14:00 - 14:45 Presentation Time: Thursday, 10 June, 14:00 - 14:45 Presentation Poster Topic Signal Processing Theory and Methods: [SIPG] Signal and Information Processing over Graphs IEEE Xplore Open Preview Click here to view in IEEE Xplore Virtual Presentation Click here to watch in the Virtual Conference Abstract This paper presents a graph learning framework to produce sparse and accurate graphs from network data. While our formulation is inspired by the graphical lasso, a key difference is the use of a nonconvex alternative of the $\ell_1$ norm as well as a quadratic term to ensure overall convexity. Specifically, the weakly-convex minimax concave penalty (MCP) is used, which is given by subtracting the Huber function from the $\ell_1$ norm, inducing a less-biased sparse solution than $\ell_1$. In our framework, the graph Laplacian is represented by a linear transform of the vector corresponding to its upper triangular part. Via a reformulation relying on the Moreau decomposition, the problem can be solved by the primal-dual splitting method. An admissible choice of parameters for provable convergence is presented. Numerical examples show that the proposed method significantly outperforms its $\ell_1$-based counterpart for sparse grid graphs.