A graph learning algorithm based on gaussian markov random fields and minimax concave penalty

Tatsuya Koyakumaru, Masahiro Yukawa, Eduardo Pavez, Antonio Ortega

Research output: Contribution to journalConference articlepeer-review

5 Citations (Scopus)


This paper presents a graph learning framework to produce sparse and accurate graphs from network data. While our formulation is in- spired by the graphical lasso, a key difference is the use of a noncon- vex alternative of the ℓ1 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 func- tion from the ℓ1 norm, inducing a less-biased sparse solution than ℓ1. In our framework, the graph Laplacian is represented by a lin- ear transform of the vector corresponding to its upper triangular part. Via a reformulation relying on the Moreau decomposition, the prob- lem can be solved by the primal-dual splitting method. An admis- sible choice of parameters for provable convergence is presented. Numerical examples show that the proposed method significantly outperforms its ℓ1-based counterpart for sparse grid graphs.

Original languageEnglish
Pages (from-to)5410-5414
Number of pages5
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Publication statusPublished - 2021
Event2021 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2021 - Virtual, Toronto, Canada
Duration: 2021 Jun 62021 Jun 11


  • Graph learning
  • Graph signal processing
  • Graph- ical lasso
  • Minimax concave penalty
  • Primal-dual splitting method
  • Proximity operator

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering


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