The future of machine learning will see data distributed across multiple devices. This project studies effective model learning when data is distributed, and communication bandwidth between devices is limited. We regard special importance to machine learning algorithms that minimize the central knowledge of participants in learning algorithms; examples of such settings are decentralized learning, and learning under local differential privacy. The first two projects have been on decentralized probabilistic inferen and differential privacy. We applied this to statistical contact tracing algorithms for virus pandemics like COVID19. Statistical contact tracing is a vital application where learning algorithms could provide utility, but privacy leaks could be harmful.