Constructive approximations of the $q=1/2$ maximum entropy distribution from redundant and noisy data

TL;DR

This paper presents a new method for constructing the $q=1/2$ maximum entropy distribution from noisy, redundant data, involving a forward approach for parameter estimation and a backward approach for model reduction.

Contribution

It introduces a generalized forward approach for noisy data and a backward method for reducing distribution parameters, enhancing robustness in maximum entropy modeling.

Findings

Effective handling of noisy data in maximum entropy distribution construction

A combined forward and backward approach improves model accuracy

Method reduces parameters while maintaining distribution fidelity

Abstract

The problem of constructing the $q=1/2$ non-extensive maximum entropy distributions from redundant and noisy data is considered. A strategy is proposed, which evolves through the following steps: i)independent constraints are first pre-selected by recourse to a data-independent technique to be discussed here. ii)the data are a posteriori used to determine the parameters of the distribution by a previously introduced forward approach. iii) A backward approach is proposed for reducing the parameters of such distribution. The previously introduced forward approach is generalised here in order to make it suitable for dealing with very noisy data.