Before revision:  The method incorporates in a very natural manner amino acid similarity in the calculation of covariance, and accounts for low number of observations by a regularization parameter that depends on the effective number of sequences in the alignment. Most importantly, inversion of the sample covariance matrix allows the computation of partial correlations between pairs of residues, thereby removing the effect of spurious transitive correlations.
After revision:  The basic assumption is that spatially proximal residues in a protein coevolve to maintain the physicochemical complementarity of the amino acids involved in the contact. Our regularized inversion of the sample covariance matrix allows the computation of partial correlations between pairs of residues, thereby removing the effect of spurious transitive correlations.