ON THE COMPLEMENTARITY OF MAXIMUM LIKELIHOOD AND MiniMax ENTROPY

Marian Grendár – Marián Grendár

   The article 1) extends the notion of the exponential family into a general exponential form, 2) utilizes an analogy between Boltzmann’s deduction of equilibrium distribution of ideal gas in an external potential field and a probability density function, and consequently, based on it, 3) investigates a complementary relationship between Maximum Likelihood (ML) and Maximum Entropy (MaxEnt) methods. MiniMaximization of Entropy (MiniMax Ent), for the case of parametric inverse problem is proposed, and demonstrated to be complementary to ML on the general exponential form. The complementary relationship with ML method seems to be a specific property of Shannon’s entropy (mini)maximization.

Keywords: simple and general exponential form/potentials, ML task, ME task, MiniMax Entropy task, complemen-

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