Katsuyoshi Ohara
Properties and applications of Fisher distribution on the rotation group.
Wed, 10/05/2011 - 15:01 — SomNambulAuthors: Akimichi Takemura, Tomonari Sei, Nobuki Takayama, Katsuyoshi Ohara, Hiroki Shibata
Subjects: Methodology
AbstractWe study properties of Fisher distribution (von Mises-Fisher distribution,
matrix Langevin distribution) on the rotation group SO(3). In particular we
apply the holonomic gradient descent, introduced by Nakayama et al. (2011), and
a method of series expansion for evaluating the normalizing constant of the
distribution and for computing the maximum likelihood estimate. The rotation
group can be identified with the Stiefel manifold of two orthonormal vectors.
Therefore from the viewpoint of statistical modeling, it is of interest to
compare Fisher distributions on these manifolds.Holonomic Gradient Descent and its Application to Fisher-Bingham Integral.
Wed, 09/08/2010 - 15:01 — SomNambulAuthors: Akimichi Takemura, Tomonari Sei, Nobuki Takayama, Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara
Subjects: Symbolic Computation
AbstractWe give a new algorithm to find local maximum and minimum of a holonomic
function and apply it for the Fisher-Bingham integral on the sphere $S^n$,
which is used in the directional statistics. The method utilizes the theory and
algorithms of holonomic systems.
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