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[Keyword] exponential family(1hit)

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  • Direct Calculation Methods for Parameter Estimation in Statistical Manifolds of Finite Discrete Distributions

    Yukio HAYASHI  

     
    PAPER-General Fundamentals and Boundaries

      Vol:
    E81-A No:7
      Page(s):
    1486-1492

    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.