Ill-posed inverse problems of the form y = Xp where y is J-dimensional vector of a data, p is m-dimensional probability vector which can not be measured directly and matrix X of observable variables is a known J x m matrix, J < m, are frequently solved by Shannon's entropy maximization (MaxEnt, ME). Several axiomatizations were proposed (see for instance as well as for a critique of some of them) to justify the MaxEnt method (also) in this context. The main aim of the presented work is two-fold: 1) to view the concept of complementarity of MaxEnt and Maximum Likelihood (ML) tasks introduced at from a geometric perspective, and consequently 2) to provide an intuitive and non-axiomatic answer to the 'Why MaxEnt?' question.
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