Geometry of reproducing kernels and information geometry with reproducing kernels

本研究从微分几何的角度研究再生核，并研究与再生核理论相关的信息几何。再生核理论中到特征空间的非线性映射可以视为到高维流形切空间的映射。我们将这一思想应用到信息几何中，得到了仿射分布几何的若干结果。到特征空间的映射在统计模型的样本空间上诱导几何结构。为了阐明再生核理论和信息几何，我们研究了Tsallis统计量的几何。

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.