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

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.

💡 Research Summary

The paper introduces TransGlasso, a novel two‑step transfer‑learning framework for estimating high‑dimensional precision (inverse covariance) matrices when the target study has a limited sample size but related source studies are available. The authors assume a structural similarity: the target precision matrix Ω₀ and each source precision matrix Ω_k share a large common component Ω* (with s non‑zero entries) while each source has a sparse unique component Γ_k (with h non‑zero entries), where s ≫ h. This “shared‑plus‑sparse‑difference” model is motivated by Gaussian graphical models and is more interpretable than divergence‑based similarity assumptions used in prior work.

Step 1 – Multi‑Task Initialization (Trans‑MT‑Glasso).
All datasets (target plus K sources) are jointly fitted by minimizing a penalized negative log‑likelihood:
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