scholarly journals Sandwiched Rényi divergence satisfies data processing inequality

2013 ◽  
Vol 54 (12) ◽  
pp. 122202 ◽  
Author(s):  
Salman Beigi
Keyword(s):  
Data Processing ◽  
Rényi Divergence ◽  
Data Processing Inequality

scholarly journals Two Measures of Dependence

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 778 ◽  
Author(s):  
Amos Lapidoth ◽  
Christoph Pfister
Keyword(s):  
Mutual Information ◽  
Data Processing ◽  
Optimal Error ◽  
Error Exponents ◽  
Rényi Divergence ◽  
Measures Of Dependence ◽  
Data Processing Inequality ◽  
Two Measures ◽  
Task Encoding ◽  
Dependence Measures

Two families of dependence measures between random variables are introduced. They are based on the Rényi divergence of order α and the relative α -entropy, respectively, and both dependence measures reduce to Shannon’s mutual information when their order α is one. The first measure shares many properties with the mutual information, including the data-processing inequality, and can be related to the optimal error exponents in composite hypothesis testing. The second measure does not satisfy the data-processing inequality, but appears naturally in the context of distributed task encoding.

scholarly journals Disentangling environmental effects in microbial association networks

Microbiome ◽  
2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Ina Maria Deutschmann ◽  
Gipsi Lima-Mendez ◽  
Anders K. Krabberød ◽  
Jeroen Raes ◽  
Sergio M. Vallina ◽  
...  
Keyword(s):  
Data Processing ◽  
Simulated Data ◽  
Potential Interaction ◽  
Microbial Interactions ◽  
Ecological Interactions ◽  
Sign Pattern ◽  
Interaction Information ◽  
Microbial Association ◽  
Environmental Selection ◽  
Data Processing Inequality

Abstract Background Ecological interactions among microorganisms are fundamental for ecosystem function, yet they are mostly unknown or poorly understood. High-throughput-omics can indicate microbial interactions through associations across time and space, which can be represented as association networks. Associations could result from either ecological interactions between microorganisms, or from environmental selection, where the association is environmentally driven. Therefore, before downstream analysis and interpretation, we need to distinguish the nature of the association, particularly if it is due to environmental selection or not. Results We present EnDED (environmentally driven edge detection), an implementation of four approaches as well as their combination to predict which links between microorganisms in an association network are environmentally driven. The four approaches are sign pattern, overlap, interaction information, and data processing inequality. We tested EnDED on networks from simulated data of 50 microorganisms. The networks contained on average 50 nodes and 1087 edges, of which 60 were true interactions but 1026 false associations (i.e., environmentally driven or due to chance). Applying each method individually, we detected a moderate to high number of environmentally driven edges—87% sign pattern and overlap, 67% interaction information, and 44% data processing inequality. Combining these methods in an intersection approach resulted in retaining more interactions, both true and false (32% of environmentally driven associations). After validation with the simulated datasets, we applied EnDED on a marine microbial network inferred from 10 years of monthly observations of microbial-plankton abundance. The intersection combination predicted that 8.3% of the associations were environmentally driven, while individual methods predicted 24.8% (data processing inequality), 25.7% (interaction information), and up to 84.6% (sign pattern as well as overlap). The fraction of environmentally driven edges among negative microbial associations in the real network increased rapidly with the number of environmental factors. Conclusions To reach accurate hypotheses about ecological interactions, it is important to determine, quantify, and remove environmentally driven associations in marine microbial association networks. For that, EnDED offers up to four individual methods as well as their combination. However, especially for the intersection combination, we suggest using EnDED with other strategies to reduce the number of false associations and consequently the number of potential interaction hypotheses.

scholarly journals A strengthened data processing inequality for the Belavkin–Staszewski relative entropy

2019 ◽  
Vol 32 (02) ◽  
pp. 2050005 ◽  
Author(s):  
Andreas Bluhm ◽  
Ángela Capel
Keyword(s):  
Data Processing ◽  
Relative Entropy ◽  
Quantum Channels ◽  
Equality Case ◽  
Standard Formula ◽  
Conditional Expectations ◽  
Data Processing Inequality ◽  
Equivalent Conditions ◽  
Arbitrary Quantum

In this work, we provide a strengthening of the data processing inequality for the relative entropy introduced by Belavkin and Staszewski (BS-entropy). This extends previous results by Carlen and Vershynina for the relative entropy and other standard [Formula: see text]-divergences. To this end, we provide two new equivalent conditions for the equality case of the data processing inequality for the BS-entropy. Subsequently, we extend our result to a larger class of maximal [Formula: see text]-divergences. Here, we first focus on quantum channels which are conditional expectations onto subalgebras and use the Stinespring dilation to lift our results to arbitrary quantum channels.

scholarly journals Tsirelson's bound from a generalized data processing inequality

2012 ◽  
Vol 14 (6) ◽  
pp. 063024 ◽  
Author(s):  
Oscar C O Dahlsten ◽  
Daniel Lercher ◽  
Renato Renner
Keyword(s):  
Data Processing ◽  
Data Processing Inequality

Data processing inequality and stochastic resonance

2003 ◽  
Author(s):  
Mark D. McDonnell ◽  
Nigel G. Stocks ◽  
Charles E. M. Pearce ◽  
Derek Abbott
Keyword(s):  
Data Processing ◽  
Stochastic Resonance ◽  
Data Processing Inequality

Strong data processing inequality in neural networks with noisy neurons and its implications

2021 ◽  
Author(s):  
Chuteng Zhou ◽  
Quntao Zhuang ◽  
Matthew Mattina ◽  
Paul N. Whatmough
Keyword(s):  
Neural Networks ◽  
Data Processing ◽  
Data Processing Inequality
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