Section: New Results

Pointless learning

Participants : Florence Clerc, Fredrik Dahlqvist, Vincent Danos, Ilias Garnier [correspondant] .

Bayesian inversion is at the heart of probabilistic programming and more generally machine learning. Understanding inversion is made difficult by the pointful (kernel-centric) point of view usually taken in the literature. We develop in a pointless (kernel-free) approach to inver- sion. While doing so, we revisit some foundational objects of probability theory, unravel their category-theoretical underpinnings and show how pointless Bayesian inversion sits naturally at the centre of this construction.