Long-tailed graphical model and frequentist inference of the model parameters for biological networks

Abstract

The biological organism is a complex structure regulated by interactions of genes and proteins. Various linear and nonlinear models can define activations of these interactions. In this study, we have aimed to improve the Gaussian graphical model (GGM), which is one of the well-known probabilistic and parametric models describing steady-state activations of biological systems, and its inference based on the graphical lasso, shortly Glasso, method. Because, GGM with Glasso can have low accuracy when the system has many genes and data are far from the normal distribution. Hereby, we construct the model like GGM, but, suggest the long-tailed symmetric distribution (LTS), rather than the normality, and use the modified maximum likelihood (MML) estimator, rather than Glasso, in inference. From the assessment of simulated and real data analyses, it is seen that LTS with MML has higher accuracy and less computational demand with explicit expressions than results of GGM with Glasso.