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

arXiv: https://arxiv.org/abs/2411.15624 · HTML: https://mlsanity.com/paper/2411.15624/

## 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 (most cited first, 25 of 25)

- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [On the Value of Target Data in Transfer Learning](https://mlsanity.com/paper/2002.04747/) (2020)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control](https://mlsanity.com/paper/2010.11037/) (2020)
- [A new similarity measure for covariate shift with applications to nonparametric regression](https://mlsanity.com/paper/2202.02837/) (2022)
- [A No-Free-Lunch Theorem for MultiTask Learning](https://mlsanity.com/paper/2006.15785/) (2020)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Transfer Learning for Contextual Multi-armed Bandits](https://mlsanity.com/paper/2211.12612/) (2022)
- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shift](https://mlsanity.com/paper/2311.15961/) (2023)
- [Asymptotic normality and optimalities in estimation of large Gaussian graphical models](https://mlsanity.com/paper/1309.6024/) (2013)
- [TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression](https://mlsanity.com/paper/2404.01153/) (2024)
- [Differential Network Analysis via the Lasso Penalized D-Trace Loss](https://mlsanity.com/paper/1511.09188/) (2015)
- [Bayesian multi-domain learning for cancer subtype discovery from next-generation sequencing count data](https://mlsanity.com/paper/1810.09433/) (2018)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Direct Estimation of Differential Functional Graphical Models](https://mlsanity.com/paper/1910.09701/) (2019)
- [FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting](https://mlsanity.com/paper/2003.05402/) (2020)
- [High-dimensional Functional Graphical Model Structure Learning via Neighborhood Selection Approach](https://mlsanity.com/paper/2105.02487/) (2021)
- [Joint Estimation of Precision Matrices in Heterogeneous Populations](https://mlsanity.com/paper/1601.00142/) (2016)
- [Direct Learning of Sparse Changes in Markov Networks by Density Ratio Estimation](https://mlsanity.com/paper/1304.6803/) (2013)
- [Latent Multimodal Functional Graphical Model Estimation](https://mlsanity.com/paper/2210.17237/) (2022)
- [Unified Transfer Learning Models in High-Dimensional Linear Regression](https://mlsanity.com/paper/2307.00238/) (2023)
- [Generalized Direct Change Estimation in Ising Model Structure](https://mlsanity.com/paper/1606.05302/) (2016)

## Built on by (most cited first, 2 of 2)

- [Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2507.02248/) (2025)
- [Transfer Learning in High-dimensional Ising Models](https://mlsanity.com/paper/2607.03005/) (2026)

## 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.