Fisher information under restriction of Shannon information in multi-terminal situations

1989 ◽  
Vol 41 (4) ◽  
pp. 623-648 ◽  
Author(s):  
Shun-ichi Amari
Keyword(s):  
Fisher Information ◽  
Shannon Information

Fisher information and Shannon entropy calculations for two-electron systems

2020 ◽  
Vol 98 (8) ◽  
pp. 784-789 ◽  
Author(s):  
Ibraheem Nasser ◽  
Afaf Abdel-Hady
Keyword(s):  
Fisher Information ◽  
Yukawa Potential ◽  
Shannon Information ◽  
Electron Systems ◽  
Charge Densities ◽  
Screening Parameter ◽  
Information Products ◽  
Physical Features ◽  
First Time

Fisher information is calculated for the ground state of He-isoelectronic series, in position ([Formula: see text]) space. The results are given and discussed as a function of the nuclear charge (Z) and the screening parameter (λ) in the case study of Yukawa potential. Simple and explicit one-, two-, and three-correlated terms of Hylleraas wave function are used to focus on extracting the most characteristic physical features of the results. The numerical values of Fisher information are given in 1- and 2-electron charge densities, and their ratio of 2- to 1-electron densities results are defined and analyzed. To enable a comparison with others, the Fisher–Shannon information products, which measure the electron–electron correlation strength, are calculated in 1-electron density. The calculations of Fisher information, the ratio, and the Shannon-information products for two-electron systems in the presence of Yukawa potential are carried out for the first time in this study.

scholarly journals Understanding VAEs in Fisher-Shannon Plane

2019 ◽  
Vol 33 ◽  
pp. 5917-5924 ◽  
Author(s):  
Huangjie Zheng ◽  
Jiangchao Yao ◽  
Ya Zhang ◽  
Ivor W. Tsang ◽  
Jia Wang
Keyword(s):  
Fisher Information ◽  
Likelihood Estimation ◽  
Representation Learning ◽  
Shannon Information ◽  
Reconstruction Accuracy ◽  
Qualitative And Quantitative ◽  
Shannon Information Entropy ◽  
Log Likelihood ◽  
High Resolution Reconstruction ◽  
The Relationship

In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These two quantities are complementary and are jointly applied to information behavior analysis in most cases. The uncertainty property in information asserts a fundamental trade-off between Fisher information and Shannon information, which enlightens us the relationship between the encoder and the decoder in variational auto-encoders (VAEs). In this paper, we investigate VAEs in the Fisher-Shannon plane, and demonstrate that the representation learning and the log-likelihood estimation are intrinsically related to these two information quantities. Through extensive qualitative and quantitative experiments, we provide with a better comprehension of VAEs in tasks such as high-resolution reconstruction, and representation learning in the perspective of Fisher information and Shannon information. We further propose a variant of VAEs, termed as Fisher auto-encoder (FAE), for practical needs to balance Fisher information and Shannon information. Our experimental results have demonstrated its promise in improving the reconstruction accuracy and avoiding the noninformative latent code as occurred in previous works.

scholarly journals Fisher information regularization schemes for Wasserstein gradient flows

2020 ◽  
Vol 416 ◽  
pp. 109449 ◽  
Author(s):  
Wuchen Li ◽  
Jianfeng Lu ◽  
Li Wang
Keyword(s):  
Fisher Information ◽  
Gradient Flows ◽  
Wasserstein Gradient Flows

scholarly journals Information-Efficient, Off-Center Sampling Results in Improved Precision in 3D Single-Particle Tracking Microscopy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 498
Author(s):  
Chen Zhang ◽  
Kevin Welsher
Keyword(s):  
Fisher Information ◽  
Particle Tracking ◽  
Single Particle ◽  
Biological Samples ◽  
Tracking System ◽  
Single Particle Tracking ◽  
Uniform Sampling ◽  
Single Dimension ◽  
3D Localization ◽  
Particle Localization

In this work, we present a 3D single-particle tracking system that can apply tailored sampling patterns to selectively extract photons that yield the most information for particle localization. We demonstrate that off-center sampling at locations predicted by Fisher information utilizes photons most efficiently. When performing localization in a single dimension, optimized off-center sampling patterns gave doubled precision compared to uniform sampling. A ~20% increase in precision compared to uniform sampling can be achieved when a similar off-center pattern is used in 3D localization. Here, we systematically investigated the photon efficiency of different emission patterns in a diffraction-limited system and achieved higher precision than uniform sampling. The ability to maximize information from the limited number of photons demonstrated here is critical for particle tracking applications in biological samples, where photons may be limited.

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