In this paper, the continuous optimal control theory is used to model and solve the maximum entropy problem for a continuous random variable. The maximum entropy principle provides a method to obtain least-biased probability density function (Pdf) estimation. In this paper, to find a closed form solution for the maximum entropy problem with any number of moment constraints, the entropy is consi...

This paper considers the problem of maximizing the entropy of two-dimensional (2D) Pickard Random Fields (PRF) subject to constraints. We consider binary Pickard Random Fields, which provides a 2D causal finite context model and use it to define stationary probabilities for 2x2 squares, thus allowing us to calculate the entropy of the field. All possible binary 2x2 constraints are considered an...

Autoencoders are widely used for dimensionality reduction and feature extraction. The backpropagation algorithm training the parameters of autoencoder model suffers from problems such as slow convergence. Therefore, researchers propose forward propagation algorithms. However, existing algorithms do not consider characteristics data itself. This paper proposes an based on relative entropy constr...

In this paper, we consider the determination methods of maximum entropy multivariate distributions with given prior under the constraints, that the marginal distributions or the marginals and covariance matrix are prescribed. Next, some numerical solutions are considered for the cases of unavailable closed form of solutions. Finally, these methods are illustrated via some numerical examples.

In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that on some e.g., dimension-eight term a single massless scalar field, Standard Model Effective Field Theory $SU(N)$ gauge bosonic operators, higher-derivative in Einstein-Maxwell generated by interactions between heavy light degrees freedom can be non...