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Efficient Proximal Gradient Algorithms for Joint Graphical Lasso.

Jie Chen1, Ryosuke Shimmura1, Joe Suzuki1

  • 1Graduate School of Engineering Science, Osaka University, Osaka 560-0043, Japan.

Entropy (Basel, Switzerland)
|December 24, 2021
PubMed
Summary

We introduce new proximal gradient algorithms for joint graphical lasso (JGL) from sparse data. These methods offer competitive accuracy and efficiency compared to existing joint graphical lasso techniques.

Keywords:
Gaussian graphical modeljoint graphical lassoproximal gradient descent method

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Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Network Inference

Background:

  • Learning undirected graphical models from sparse data is crucial in many fields.
  • Existing methods for joint graphical lasso (JGL) often rely on the alternating direction method of multipliers (ADMM).

Purpose of the Study:

  • To develop novel, efficient algorithms for the joint graphical lasso (JGL) problem.
  • To address limitations of current ADMM-based approaches for JGL.

Main Methods:

  • Proposed proximal gradient procedures for JGL, with and without a backtracking option.
  • These are first-order methods designed for efficient closed-form subproblem solutions.
  • Demonstrated boundedness of the JGL solution and algorithm iterates.

Main Results:

  • The proposed algorithms achieve high accuracy and precision in graphical model recovery.
  • Numerical results show competitive efficiency against state-of-the-art JGL algorithms.
  • The methods are shown to be theoretically sound with proven boundedness properties.

Conclusions:

  • The developed proximal gradient algorithms provide effective and efficient solutions for joint graphical lasso.
  • These new methods offer a valuable alternative to ADMM-based approaches for learning graphical structures from sparse data.