I am looking for references (books/sites/articles) on the following three subjects: Large Deviation, Optimal Transport and Machine Learning References. I would like works which involve any of them individually, or jointly. My motivation for this is the following course description which used to be taught at my school:
Two mathematical frameworks: optimal transport and large deviation theory, can be combined to provide tools and methods of analysis for some central tasks in data science: classification, clustering and regression, dimensionality reduction, conditional probability estimation, prediction of rare events. Recurring themes will include the power of the composition of simple functions to capture complex behavior - as demonstrated by neural networks - and of the characterization of both the available observations of the system under study and the parameters tuned to model it in terms of underlying probability distributions.
If you know of any core books on either Large Deviation or Optimal Trasport that can be grasped at a beginning graduate level, I would much appreciate it!