Robust Unified Graphical Lasso Based on t Distribution

Estimating networks among variables from multi-variate data is often important to clarify relationships among variables. Graphical Lasso (GL) is a useful tool for network exploration and is used in genetic data analysis. However, when dealing with genetic data, there are cases where multi-block data observed from several different databases for the same set of variables are handled. Unified Graphical Lasso (UGL) is a method to estimate the common network structure of each block data from such multi-block data. However, it is known that the presence of noise in such data can affect the results of network structure estimation using ordinary UGL. To solve such problems, we propose Robust Unified Graphical Lasso based on t-distribution (robust UGL). In robust UGL, we also developed an algorithm to estimate parameters based on the EM algorithm. We compared and evaluated the results of UGL and robust UGL on artificial and genetic data. Experimental results show that robust UGL performs better than UGL on both artificial and genetic data. These results suggest that robust UGL may be effective for noisy data such as biometric data.