| Budget Amount *help |
¥3,890,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
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| Research Abstract |
In this research, we studied reproducing kernels from the viewpoint of differential geometry and studied information geometry related to the theory of reproducing kernels. A nonlinear map to the feature space in the theory of reproducing kernels can be regarded as a map to the tangent space of a high-dimensional manifold. We applied this idea to information geometry, and we obtained several results of geometry of affine distributions. A map to the feature space induces geometric structures on the sample space of a statistical model. In order to elucidate the theory of reproducing kernels and information geometry, we studied geometry of Tsallis statistics.
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