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Direct Calculation Methods for Parameter Estimation in Statistical Manifolds of Finite Discrete Distributions
Yukio HAYASHI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E81-A No.7 pp.1486-1492
Publication Date: 1998/07/20
Online ISSN:
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: General Fundamentals and Boundaries
Keyword:
information geometry,
parameter estimation,
finite discrete distribution,
exponential family,
mixture family,
autoparallel submanifold,
gradient system,
Full Text: PDF
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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