Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation
This addresses the problem of small-sample precision matrix estimation for researchers in fields like genomics, offering a novel transfer learning approach that is incremental but with theoretical guarantees.
The paper tackles precision matrix estimation with limited target samples by proposing Trans-Glasso, a transfer learning method that leverages related source data, achieving minimax optimality and superior performance in simulations and biological applications like gene and protein networks.
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.