scholarly journals Relating Relative Entropy, Optimal Transport and Fisher Information: A Quantum HWI Inequality

2020 ◽  
Vol 21 (7) ◽  
pp. 2115-2150 ◽  
Author(s):  
Nilanjana Datta ◽  
Cambyse Rouzé
Keyword(s):  
Relative Entropy ◽  
Fisher Information ◽  
Optimal Transport

Diffeomorphism learning via relative entropy constrained optimal transport

2016 ◽  
Author(s):  
Todd P. Coleman ◽  
Justin Tantiongloc ◽  
Alexis Allegra ◽  
Diego Mesa ◽  
Dae Kang ◽  
...  
Keyword(s):  
Relative Entropy ◽  
Optimal Transport

REMARKS ON THE FREE RELATIVE ENTROPY AND THE FREE FISHER INFORMATION DISTANCE

2010 ◽  
Vol 13 (02) ◽  
pp. 243-255
Author(s):  
HIROAKI YOSHIDA
Keyword(s):  
Relative Entropy ◽  
Fisher Information ◽  
Sobolev Inequality ◽  
Logarithmic Sobolev Inequality ◽  
Semicircle Law ◽  
Information Distance ◽  
Poisson Law ◽  
Free Relative ◽  
Free Fisher Information

In this paper, we shall introduce the free Fisher information distance which is inspired by the estimation-theoretic representation of the free relative entropy investigated by Verdú. We shall see the free analogue of the logarithmic Sobolev inequality with respect to a centered semicircle law and also the semicircular approximation of the free Poisson law.

scholarly journals Formulation and properties of a divergence used to compare probability measures without absolute continuity

2022 ◽  
Author(s):  
Paul Dupuis ◽  
Yixiang Mao
Keyword(s):  
Relative Entropy ◽  
Model Uncertainty ◽  
Absolute Continuity ◽  
Optimal Transport ◽  
Transport Cost ◽  
Probability Measures

This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and exploit a representation as an infimum convolution of optimal transport cost and relative entropy.  Also included are examples of computation and approximation of the divergence, and the demonstration of properties that are useful when one quantifies model uncertainty.

scholarly journals Entropy considerations in the noncommutative setting

2000 ◽  
Vol 24 (12) ◽  
pp. 807-819
Author(s):  
Patricia Giurgescu
Keyword(s):  
Probability Theory ◽  
Relative Entropy ◽  
Fisher Information ◽  
Information Entropy ◽  
Free Probability ◽  
Density Matrices ◽  
Free Probability Theory ◽  
Classical Link ◽  
Noncommutative Setting

An analogue of the classical link between the relative entropy and Fisher information entropy is presented in the context of free probability theory. Several generalizations of the relative entropy in terms of density matrices are also discussed.

scholarly journals Computations of Optimal Transport Distance with Fisher Information Regularization

2017 ◽  
Vol 75 (3) ◽  
pp. 1581-1595 ◽  
Author(s):  
Wuchen Li ◽  
Penghang Yin ◽  
Stanley Osher
Keyword(s):  
Fisher Information ◽  
Optimal Transport ◽  
Transport Distance

scholarly journals Strong convexity of sandwiched entropies and related optimization problems

2018 ◽  
Vol 30 (09) ◽  
pp. 1850014 ◽  
Author(s):  
Rajendra Bhatia ◽  
Tanvi Jain ◽  
Yongdo Lim
Keyword(s):  
Relative Entropy ◽  
Special Interest ◽  
Optimal Transport ◽  
Optimization Problems ◽  
Linear Convergence ◽  
Projection Algorithm ◽  
Strong Convexity ◽  
Gaussian Measures ◽  
Coupling Problem ◽  
Global Linear Convergence

We present several theorems on strict and strong convexity, and higher order differential formulae for sandwiched quasi-relative entropy (a parametrized version of the classical fidelity). These are crucial for establishing global linear convergence of the gradient projection algorithm for optimization problems for these functions. The case of the classical fidelity is of special interest for the multimarginal optimal transport problem (the [Formula: see text]-coupling problem) for Gaussian measures.

Efficient Steganography Algorithm Based On DCT And Entropy Thresholding Technique

2018 ◽  
Vol 8 (1) ◽  
pp. 45
Author(s):  
Satvir Singh
Keyword(s):  
Relative Entropy ◽  
Experimental Work ◽  
Random Function ◽  
Signal To Noise Ratio ◽  
Binary Sequence ◽  
Threshold Value ◽  
Absolute Difference ◽  
Secret Message ◽  
Signal To Noise ◽  
Confidential Information

Steganography is the special art of hidding important and confidential information in appropriate multimedia carrier. It also restrict the detection of  hidden messages. In this paper we proposes steganographic method based on dct and entropy thresholding technique. The steganographic algorithm uses random function in order to select block of the image where the elements of the binary sequence of a secret message will be inserted. Insertion takes place at the lower frequency  AC coefficients of the  block. Before we insert the secret  message. Image under goes dc transformations after insertion of the secret message we apply inverse dc transformations. Secret message will only be inserted into a particular block if  entropy value of that particular block is greater then threshold value of the entropy and if block is selected by the random function. In  Experimental work we calculated the peak signal to noise ratio(PSNR), Absolute difference , Relative entropy. Proposed algorithm give high value of PSNR  and low value of Absolute difference which clearly indicate level of distortion in image due to insertion of secret message is reduced. Also value of  relative entropy is close to zero which clearly indicate proposed algorithm is sufficiently secure. 

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