mlsanityData to 14 Oct 2026

Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation

arXiv 2411.15624 ↗First posted 23 Nov 2024stat.ML cs.LG stat.MEcited by 2

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Abstract (arXiv)

Precision matrix estimation is essential in various fields; yet it is challenging when samples for the target study are limited. Transfer learning can enhance estimation accuracy by leveraging data from related source studies. We propose Trans-Glasso, a two-step transfer learning method for precision matrix estimation. First, we obtain initial estimators using a multi-task learning objective that captures shared and unique features across studies. Then, we refine these estimators through differential network estimation to adjust for structural differences between the target and source precision matrices. Under the assumption that most entries of the target precision matrix are shared with source matrices, we derive non-asymptotic error bounds and show that Trans-Glasso achieves minimax optimality under certain conditions. Extensive simulations demonstrate Trans Glasso's superior performance compared to baseline methods, particularly in small-sample settings. We further validate Trans-Glasso in applications to gene networks across brain tissues and protein networks for various cancer subtypes, showcasing its effectiveness in biological contexts. Additionally, we derive the minimax optimal rate for differential network estimation, representing the first such guarantee in this area. The Python implementation of Trans-Glasso, along with code to reproduce all experiments in this paper, is publicly available at https://github.com/boxinz17/transglasso-experiments.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 25 of its 65 references that are in the map. First posted on arXiv 23 Nov 2024.

Builds on

25 of 65 references.

References · 25

  1. 2020Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimalitycited by 90
  2. 2021Transfer Learning under High-dimensional Generalized Linear Modelscited by 70
  3. 2019Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifiercited by 65
  4. 2020On the Value of Target Data in Transfer Learningcited by 65
  5. 2022Optimally tackling covariate shift in RKHS-based nonparametric regressioncited by 54
  6. 2020Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Controlcited by 38
  7. 2022A new similarity measure for covariate shift with applications to nonparametric regressioncited by 33
  8. 2020A No-Free-Lunch Theorem for MultiTask Learningcited by 28
  9. 2013Node-Based Learning of Multiple Gaussian Graphical Modelscited by 26
  10. 2022Transfer Learning for Contextual Multi-armed Banditscited by 24
  11. 2023Pseudo-Labeling for Kernel Ridge Regression under Covariate Shiftcited by 17
  12. 2023Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shiftcited by 15
13 more
  1. 2013Asymptotic normality and optimalities in estimation of large Gaussian graphical modelscited by 12
  2. 2024TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regressioncited by 11
  3. 2015Differential Network Analysis via the Lasso Penalized D-Trace Losscited by 10
  4. 2018Bayesian multi-domain learning for cancer subtype discovery from next-generation sequencing count datacited by 10
  5. 2021Joint Gaussian Graphical Model Estimation: A Surveycited by 10
  6. 2019Direct Estimation of Differential Functional Graphical Modelscited by 8
  7. 2020FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Settingcited by 7
  8. 2021High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approachcited by 7
  9. 2016Joint Estimation of Precision Matrices in Heterogeneous Populationscited by 5
  10. 2013Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimationcited by 3
  11. 2022Latent Multimodal Functional Graphical Model Estimationcited by 3
  12. 2023Unified Transfer Learning Models in High-Dimensional Linear Regressioncited by 3
  13. 2016Generalized Direct Change Estimation in Ising Model Structurecited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Transfer Learning for Matrix Completioncited by 0
  2. 2026Transfer Learning in High-dimensional Ising Modelscited by 0