Probabilistic morphisms, stochastic processes, and Bayesian supervised learning

Abstract: Using a categorical approach to Markov kernels, and stochastic processes taking values in the space of probability measures on a label space, I propose a unifying model for Bayesian supervised learning. I show that batch learning equals online learning in Bayesian supervised learning. As a result, I derive a recursive formula for predictive distributions which reduces to the Kalman filter in Gaussian process regression. Finally, I shall discuss some related problems in mathematical machine learning.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.