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Extended Divergence on a Foliation by Deformed Probability Simplexes
1Faculty of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Miyagi, Japan.
Entropy (Basel, Switzerland)
|December 23, 2022
Summary
This study introduces a new divergence decomposition for deformed probability simplexes, specifically q-escort distributions. This theorem helps understand the proximity of distributions with varying q-parameters in information geometry.
Area of Science:
- Information Geometry
- Probability Theory
- Differential Geometry
Background:
- The study builds upon existing concepts in information geometry and divergence measures.
- It addresses the complexity of analyzing probability distributions using deformed simplexes and q-escort distributions.
Purpose of the Study:
- To introduce a novel decomposition of extended divergence on foliations of deformed probability simplexes.
- To analyze the properties of q-escort distributions within this framework.
- To propose a new divergence decomposition theorem and compare it with existing theorems.
Main Methods:
- Utilizing the framework of information geometry.
- Decomposing extended divergence on foliations of deformed probability simplexes.
- Defining q-parameters and α-parameters for dualistic structures on foliation leaves.
- Proposing and comparing divergence decomposition theorems.
Main Results:
- A new divergence decomposition theorem is proposed for foliations of deformed probability simplexes.
- The theorem provides insights into the proximity of q-escort distributions with different q-parameters.
- The new theorem is compared to the standard divergence theorem on Hessian manifolds.
Conclusions:
- The proposed divergence decomposition theorem offers a new perspective on analyzing q-escort distributions.
- This work extends the understanding of divergence measures in information geometry.
- The findings facilitate the comparison of distribution proximity across different parameter spaces.
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