Before revision:  Then we co-estimate the precision matrices by maximizing the occurring probability of all the involved sequences , subject to the constraint that the  matrices shall share similar patterns .
After revision:  Then we co-estimate the precision matrices by maximizing the occurring probability of all the involved sequences , subject to the constraint that the matrices shall share similar residue co-evolution patterns. To further improve the accuracy of the estimated precision matrices, we employ a supervised learning method to predict contact probability from a variety of evolutionary and non-evolutionary information and then incorporate the predicted probability as prior into our GGL framework .