mlsanityData to 7 Oct 2026

Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity

arXiv 2112.01939 ↗First posted 3 Dec 2021cs.LGcited by 8

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Abstract (arXiv)

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two (MTP2). The precision matrix in such a distribution is an M-matrix. This problem can be formulated as a sign-constrained log-determinant program. Current algorithms are designed using the block coordinate descent method or the proximal point algorithm, which becomes computationally challenging in high-dimensional cases due to the requirement to solve numerous nonnegative quadratic programs or large-scale linear systems. To address this issue, we propose a novel algorithm based on the two-metric projection method, incorporating a carefully designed search direction and variable partitioning scheme. Our algorithm substantially reduces computational complexity, and its theoretical convergence is established. Experimental results on synthetic and real-world datasets demonstrate that our proposed algorithm provides a significant improvement in computational efficiency compared to the state-of-the-art methods.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 13 of its 63 references that are in the map. First posted on arXiv 3 Dec 2021.

Builds on

13 of 63 references.

References · 13

  1. 2019A Unified Framework for Structured Graph Learning via Spectral Constraintscited by 53
  2. 2019Learning Some Popular Gaussian Graphical Models without Condition Number Boundscited by 20
  3. 2019Structured Graph Learning Via Laplacian Spectral Constraintscited by 20
  4. 2014Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov Random fieldscited by 19
  5. 2015Large-scale Log-determinant Computation through Stochastic Chebyshev Expansionscited by 17
  6. 2017Maximum likelihood estimation in Gaussian models under total positivitycited by 14
  7. 2017Learning Graphs with Monotone Topology Properties and Multiple Connected Componentscited by 13
  8. 2019Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameterscited by 9
  9. 2019Covariance Matrix Estimation under Total Positivity for Portfolio Selectioncited by 8
  10. 2013Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systemscited by 7
  11. 2017Speeding Up Latent Variable Gaussian Graphical Model Estimation via Nonconvex Optimizationscited by 4
  12. 2019Total positivity in exponential families with application to binary variablescited by 4
1 more
  1. 2013A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversionscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 3; 2024: 0; 2025: 1; 2026: 2.

8 papers.

  1. 2022Learning Graphical Factor Models with Riemannian Optimizationcited by 8
  2. 2023Learning Large-Scale MTP2 Gaussian Graphical Models via Bridge-Block Decompositioncited by 5
  3. 2023Network Topology Inference with Sparsity and Laplacian Constraintscited by 4
  4. 2022Adaptive Estimation of Graphical Models under Total Positivitycited by 2
  5. 2023Graph Learning Across Data Siloscited by 1
  6. 2025Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learningcited by 1
  7. 2026Learning Gaussian Graphical Models under Total Positivity via Spectral Graph Sparsificationcited by 1
  8. 2026Spectral Sparsification of Laplacian-Constrained Gaussian and H"usler-Reiss Graphical Modelscited by 0