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

TL;DR

Trans-Glasso is a novel transfer learning method that improves precision matrix estimation by leveraging related data sources, with proven theoretical guarantees and demonstrated effectiveness in biological network applications.

Contribution

It introduces a two-step transfer learning approach for precision matrix estimation with minimax optimality and provides the first theoretical guarantees for differential network estimation.

Findings

Trans-Glasso outperforms baseline methods in small-sample simulations.

It achieves minimax optimal error bounds under shared structure assumptions.

The method is validated on gene and protein network data, showing practical effectiveness.

Abstract

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.