Statistical inference with optimal transport

Optimal transportation (OT) theory provides a powerful toolbox for data analysis in nonlinear spaces, where nonlinearity appears as an inevitable consequence of complexity of objects of interest (e.g. medical images or meta-genomes). OT opens a new direction in creating complete package of statistical instruments which takes into account the underlying geometry of an observed data set. In this talk we introduce basics on statistical inference based on OT and present recent results.