Geometry of reproducing kernels and information geometry with reproducing kernels

点击翻译按钮获取中文摘要

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.