Abstract: We used the adaptive penalized likelihood method to solve the structure learning problem of Gaussian graphical models with latent variables. The simulation results show that the adaptive penalties are significantly superior to the non-adaptive penalties, which can effectively reduce the estimation bias and more accurately estimate the conditional independence relationships among observed variables given latent variables.

Key words: latent variable Gaussian graphical model, adaptive LASSO penalty, adaptive nuclear norm penalty, alternating direction method of multipliers