Before revision:  To implement this multi-family EC analysis strategy, we use a set of  correlated multivariate Gaussian distributions to model the related families and then co-estimate the inverse covariance matrices of the Gaussian distributions subject to the constraint that these matrices shall have similar patternsto some degree.
After revision:  To implement this multi-family EC analysis strategy, we use a set of correlated multivariate Gaussian distributions to model the related families and then co-estimate the inverse covariance matrices of the Gaussian distributions subject to the constraint that the matrices shall share similar patterns. Finally we solve this optimization problem using Alternating Direction Method of Multipliers (ADMM).