Information geometry

This thesis is devoted to building the connection of information geometry and optimal transport. In- formation geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. The modern theory of information…

Statistical machine learning algorithms deal with the problem of selecting an appropriate statistical model from a model space Θ based on a training set [special characters omitted] ⊂ X or [special characters omitted] ⊂ X × Y. In doing so they either implicitly or explicitly mak…