In the present communication, the existing measures of fuzzy entropy are reviewed. A generalized parametric exponential fuzzy entropy is defined.Our study of the four essential and some other properties of the proposed measure, clearly establishes the validity of the measure as an entropy. Keywords—fuzzy sets, fuzzy entropy, exponential entropy, exponential fuzzy entropy.

In this paper, we suggest a framework to make use of mutual information as a regularization criterion to train Auto-Encoders (AEs). In the proposed framework, AEs are regularized by minimization of the mutual information between input and encoding variables of AEs during the training phase. In order to estimate the entropy of the encoding variables and the mutual information, we propose a non-p...

We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore useless as a distance measure in this case. We study basic properties of this quantity, and find interesting relationships between the TRE and the trace norm ...

A method, which we suggest to call the Empirical Maximum Entropy method, is implicitly present at Maximum Entropy Empirical Likelihood method, as its special, non-parametric case. From this vantage point the entropy-based empirical approach to estimation is surveyed.

In previous work, we described the geometry of Bayesian learning on a manifold. this paper, inspired by notion modified double contingency communications from sociologist Niklas Luhmann, take two manifolds in equal parts and potential function their product to set up mutual learning. Particularly, given parametric statistical model, consider between copies parameter space. Here, associate with ...

This technical report describes a cute idea of how to create new policy search approaches. It directly relates to the Natural Actor-Critic methods but allows the derivation of one shot solutions. Future work may include the application to interesting problems. 1 Problem Statement In reinforcement learning, we have an agent which is in a state s and draws actions a from a policy π. Upon an actio...

We show that the naive mean-field approximation correctly predicts leading term of logarithmic lower tail probabilities for number copies a given subgraph in G(n,p) and arithmetic progressions length random subsets integers entire range densities where is viable. Our main technical result provides sufficient conditions on maximum degrees uniform hypergraph H guarantee edges, induced by binomial...