  Maximum likelihood estimation (MLE) is a fundamental computational problem in
statistics. In this paper, MLE for statistical models with discrete data is
studied from an algebraic statistics viewpoint. A reformulation of the MLE
problem in terms of dual varieties and conormal varieties will be given. With
this description, the dual likelihood equations and the dual MLE problem are
defined. We show that solving the dual MLE problem yields solutions to the MLE
problem, so we can solve the MLE problem without ever determining the defining
equations of the model.
