engleski

ALGORITHM FOR SOLVING MAXIMUM ENTROPY PROBLEM BASED ON FINITE BASIS FUNCTIONS

The Maximum Entropy (MaxEnt) principle is a versatile tool for statistical finding of the probability density function (pdf) from its moments as a least-biased estimation among all other possible pdf’s. The MaxEnt algorithm transforms the original constrained optimization problem to the unconstrained dual optimization problem using Lagrangian multipliers. The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities. These difficulties can be overcome by using orthogonal polynomials which enable roughly the same sensitivity for all Lagrangian multipliers. In this paper the Fup MaxEnt Algoritam (FMEA) that based on using finite basis functions Fup4(x) with compact support is presented. These basis functions can exactly describe algebraic polynomials up to the fourth order while polynomials of high orders describe approximately. FMEA solves the CMP finding an optimal pdf with better balanced Lagrangian multipliers. The algorithm is numerically very efficient due to localized properties of Fup4 basis functions implying a weaker dependence between Lagrangian multipliers and faster convergence. Application of Fup MaxEnt algoritam is demonstrated on continuous beta distribution as pdf example.

maximum entropy ; Shannon entropy ; Fup basis functions ; probability density function

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