Conformal predictive distributions with kernels

This paper reviews the checkered history of predictive distributions in statistics and discusses two developments, one from recent literature and the other new. The first development is bringing predictive distributions into machine learning, whose early development was so deeply influenced by two remarkable groups at the Institute of Automation and Remote Control. The second development is combining predictive distributions with kernel methods, which were originated by one of those groups, including Emmanuel Braverman. This paper has been prepared for the Proceedings of the Braverman Readings, held in Boston on 28–30 April 2017. Its version at http://alrw.net (Working Paper 20, first posted on 19 October 2017) is updated most often.