2022/10/27 by Jiaxi Ying, Ying, Jiaxi, José Vinícius de Miranda Cardoso +3 · 1 citation
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Advanced Statistical Methods and Models #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2210.15471
We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two observations for M-matrices \citeplauritzen2019maximum,slawski2015estimation and even one observation for diagonally dominant M-matrices \citeptruell2021maximum. We propose an adaptive multiple-stage estimation method that refines the estimate by solving a weighted ℓ1-regularized problem at each stage. Furthermore, we develop a unified framework based on the gradient projection method to solve the regularized problem, incorporating distinct projections to handle the constraints of M-matrices and diagonally dominant M-matrices. A theoretical analysis of the estimation error is provided. Our method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification, as evidenced by synthetic and financial time-series data sets.