Direct Calculation Methods for Parameter Estimation in Statistical Manifolds of Finite Discrete Distributions
Summary :
From an information geometric viewpoint, we investigate a characteristic of the submanifold of a mixture or exponential family in the manifold of finite discrete distributions. Using the characteristic, we derive a direct calculation method for an em-geodesic in the submanifold. In this method, the value of the primal parameter on the geodesic can be obtained without iterations for a gradient system which represents the geodesic. We also derive the similar algorithms for both problems of parameter estimation and functional extension of the submanifold for a data in the ambient manifold. These theoretical approaches from geometric analysis will contribute to the development of an efficient algorithm in computational complexity.
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- IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.7 pp.1486-1492
- Publication Date
- 1998/07/25
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- General Fundamentals and Boundaries
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Yukio HAYASHI, "Direct Calculation Methods for Parameter Estimation in Statistical Manifolds of Finite Discrete Distributions" in IEICE TRANSACTIONS on Fundamentals,
vol. E81-A, no. 7, pp. 1486-1492, July 1998, doi: .
Abstract: From an information geometric viewpoint, we investigate a characteristic of the submanifold of a mixture or exponential family in the manifold of finite discrete distributions. Using the characteristic, we derive a direct calculation method for an em-geodesic in the submanifold. In this method, the value of the primal parameter on the geodesic can be obtained without iterations for a gradient system which represents the geodesic. We also derive the similar algorithms for both problems of parameter estimation and functional extension of the submanifold for a data in the ambient manifold. These theoretical approaches from geometric analysis will contribute to the development of an efficient algorithm in computational complexity.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_7_1486/_p
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@ARTICLE{e81-a_7_1486,
author={Yukio HAYASHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Direct Calculation Methods for Parameter Estimation in Statistical Manifolds of Finite Discrete Distributions},
year={1998},
volume={E81-A},
number={7},
pages={1486-1492},
abstract={From an information geometric viewpoint, we investigate a characteristic of the submanifold of a mixture or exponential family in the manifold of finite discrete distributions. Using the characteristic, we derive a direct calculation method for an em-geodesic in the submanifold. In this method, the value of the primal parameter on the geodesic can be obtained without iterations for a gradient system which represents the geodesic. We also derive the similar algorithms for both problems of parameter estimation and functional extension of the submanifold for a data in the ambient manifold. These theoretical approaches from geometric analysis will contribute to the development of an efficient algorithm in computational complexity.},
keywords={},
doi={},
ISSN={},
month={July},}
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TY - JOUR
TI - Direct Calculation Methods for Parameter Estimation in Statistical Manifolds of Finite Discrete Distributions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1486
EP - 1492
AU - Yukio HAYASHI
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 1998
AB - From an information geometric viewpoint, we investigate a characteristic of the submanifold of a mixture or exponential family in the manifold of finite discrete distributions. Using the characteristic, we derive a direct calculation method for an em-geodesic in the submanifold. In this method, the value of the primal parameter on the geodesic can be obtained without iterations for a gradient system which represents the geodesic. We also derive the similar algorithms for both problems of parameter estimation and functional extension of the submanifold for a data in the ambient manifold. These theoretical approaches from geometric analysis will contribute to the development of an efficient algorithm in computational complexity.
ER -
English
