Pointless learning (long version)

Florence Clerc (1) , Vincent Danos (2, 3) , Fredrik Dahlqvist (4) , Ilias Garnier (2)

1 School of Computer Science [Montréal]
2 School of Informatics [Edimbourg]
3 ANTIQUE - Analyse Statique par Interprétation Abstraite
4 UCL - University College of London [London]

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 a pointless (kernel-free) approach to inversion. 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 .

Domaines: Informatique [cs]; Mathématiques [math]

Florence Clerc, Vincent Danos, Fredrik Dahlqvist, Ilias Garnier. Pointless learning (long version). Proceedings of FoSSaCS 2017, 2017, Uppsala, Sweden. ⟨hal-01974692⟩