Information geometry of statistical inference - an overview

The present paper gives a short introduction to information geometry, by using a simple model of an exponential family which is a dually flat Riemannian space. The paper then overviews some of the applications of information geometry: 1) the higher-order asymptotic theory of estimation; 2) semiparametric estimation of the parameter of interest; 3) learning neural networks under the Riemannian structure; and 4) analysis of turbo codes, low density parity check codes and belief propagation algorithm.