With the increasing popularity of large-scale probabilistic graphical models, even "lightweight" approximate inference methods are becoming infeasible. Fortunately, often large parts of the model are of no immediate interest to the end user. Given the variable that the user actually cares about, we show how to quantify edge importance in graphical models and to significantly speed up inference by focusing computation on important parts of the model. Our algorithm empirically demonstrates convergence speedup by multiple times over state of the art