  A mixed-integer linear programming (MILP) formulation is presented for
parameter estimation of the Potts model. Two algorithms are developed; the
first method estimates the parameters such that the set of ground states
replicate the user-prescribed data set; the second method allows the user to
prescribe the ground states multiplicity. In both instances, the optimization
process ensures that the bandgap is maximized. Consequently, the model
parameter efficiently describes the user data for a broad range of
temperatures. This is useful in the development of energy-based graph models to
be simulated on Quantum annealing hardware where the exact simulation
temperature is unknown. Computationally, the memory requirement in this method
grows exponentially with the graph size. Therefore, this method can only be
practically applied to small graphs. Such applications include learning of
small generative classifiers and spin-lattice model with energy described by
Ising hamiltonian. Learning large data sets poses no extra cost to this method;
however, applications involving the learning of high dimensional data are out
of scope.
