Diffeomorphism learning via relative entropy constrained optimal transport

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.

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Strong convexity of sandwiched entropies and related optimization problems

Reviews in Mathematical Physics ◽

10.1142/s0129055x18500149 ◽

2018 ◽

Vol 30 (09) ◽

pp. 1850014 ◽

Cited By ~ 5

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.

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Efficient Steganography Algorithm Based On DCT And Entropy Thresholding Technique

International Journal of Advanced Research in Computer Science and Software Engineering ◽

10.23956/ijarcsse.v8i1.483 ◽

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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Measuring information content from observations for data assimilation: relative entropy versus shannon entropy difference

Tellus A Dynamic Meteorology and Oceanography ◽

10.3402/tellusa.v59i2.14932 ◽

2007 ◽

Author(s):

Qin Xu

Keyword(s):

Data Assimilation ◽

Information Content ◽

Relative Entropy ◽

Shannon Entropy

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Complete monotonicity of entropy production in chemical reaction

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19810452 ◽

1981 ◽

Vol 46 (2) ◽

pp. 452-456

Author(s):

Milan Šolc

Keyword(s):

Entropy Production ◽

Equilibrium Constant ◽

Chemical Reaction ◽

Relative Entropy ◽

Order Reaction ◽

Complete Monotonicity ◽

First Order Reaction ◽

First Order ◽

Completely Monotonic ◽

Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

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A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-191374 ◽

2021 ◽

Vol 40 (1) ◽

pp. 235-250

Author(s):

Liuxin Chen ◽

Nanfang Luo ◽

Xiaoling Gou

Keyword(s):

Decision Making ◽

Relative Entropy ◽

Group Decision Making ◽

Shapley Value ◽

Group Decision ◽

Similarity Measures ◽

Entropy Measure ◽

Shapley Values ◽

Interactive Relationship ◽

The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

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Optimal transport and unitary orbits in C⁎-algebras

Journal of Functional Analysis ◽

10.1016/j.jfa.2021.109068 ◽

2021 ◽

Vol 281 (5) ◽

pp. 109068

Author(s):

Bhishan Jacelon ◽

Karen R. Strung ◽

Alessandro Vignati

Keyword(s):

Optimal Transport ◽

C Algebras

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Modeling Epidemic Spread among a Commuting Population Using Transport Schemes

Mathematics ◽

10.3390/math9161861 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1861

Author(s):

Daniela Calvetti ◽

Alexander P. Hoover ◽

Johnie Rose ◽

Erkki Somersalo

Keyword(s):

Network Model ◽

Transport Theory ◽

Optimal Transport ◽

State Level ◽

Compartment Model ◽

Census Bureau ◽

Mitigation Strategies ◽

Mitigation Measures ◽

Metapopulation Model ◽

Infection Dynamics

Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.

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