التفاصيل البيبلوغرافية
| العنوان: |
Dynamical Systems over Lie Groups Associated with Statistical Transformation Models |
| المؤلفون: |
Daisuke Tarama, Jean-Pierre Françoise |
| المصدر: |
Physical Sciences Forum; Volume 5; Issue 1; Pages: 21 |
| بيانات النشر: |
Multidisciplinary Digital Publishing Institute |
| سنة النشر: |
2022 |
| المجموعة: |
MDPI Open Access Publishing |
| مصطلحات موضوعية: |
information geometry, statistical transformation model, Fisher–Rao semi-definite metric, geodesic flow, Hamiltonian system, Lie group, Euler–Poincaré equation, Lie–Poisson equation |
| الوصف: |
A statistical transformation model consists of a smooth data manifold, on which a Lie group smoothly acts, together with a family of probability density functions on the data manifold parametrized by elements in the Lie group. For such a statistical transformation model, the Fisher–Rao semi-definite metric and the Amari–Chentsov cubic tensor are defined in the Lie group. If the family of probability density functions is invariant with respect to the Lie group action, the Fisher–Rao semi-definite metric and the Amari–Chentsov tensor are left-invariant, and hence we have a left-invariant structure of a statistical manifold. In the present work, the general framework of statistical transformation models is explained. Then, the left-invariant geodesic flow associated with the Fisher–Rao metric is considered for two specific families of probability density functions on the Lie group. The corresponding Euler–Poincaré and the Lie–Poisson equations are explicitly found in view of geometric mechanics. Related dynamical systems over Lie groups are also mentioned. A generalization in relation to the invariance of the family of probability density functions is further studied. |
| نوع الوثيقة: |
text |
| وصف الملف: |
application/pdf |
| اللغة: |
English |
| Relation: |
https://dx.doi.org/10.3390/psf2022005021 |
| DOI: |
10.3390/psf2022005021 |
| الاتاحة: |
https://doi.org/10.3390/psf2022005021 |
| Rights: |
https://creativecommons.org/licenses/by/4.0/ |
| رقم الانضمام: |
edsbas.EC97AC21 |
| قاعدة البيانات: |
BASE |