Towards algebraic methods for maximum entropy estimation

Abstract: We show that various formulations (e.g., dual and Kullback-Csiszar iterations) of estimation of maximum entropy (ME) models can be transformed to solving systems of polynomial equations in several variables for which one can use celebrated Grobner bases methods. Posing of ME estimation as solving polynomial equations is possible, in the cases where feature functions (sufficient statistic) that provides the information about the underlying random variable in the form of expectations are integer valued.