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We present a new method of estimating graphical models with the clear goal of providing models that minimize the mean squared error of certain parameters of interest to the researcher. The method is applicable to undirected as well as to mixed graphs containing both directed and undirected edges. Quadratic approximations to several well studied penalties deal with problems where the number of nodes is greater than the number of samples. Extensions of the current application include a dynamical image of graphs based on consecutive focus points and estimating graphs where information is borrowed among subjects.