Abstract:
Information Geometry is the application of differential geometry to the study of statistical manifolds. Probability distributions form Riemannian manifolds where a divergence measure (e.g. Kullback-Leibler) introduces a Non-Euclidian notion of 'distance'. It is an interesting concept which allows to gain deeper insight into various aspects (e.g. MLE as projection on statistical manifolds) or to devise improved learning algorithms such as Natural Gradients or Geometric MCMC methods that take into account the geometry of the underlying manifold.