In the last few years, a new perspective on probabilistic reasoning has been extensively developed with the help of tools from category theory. The idea is to shift focus from the measure-theoretic details to structural properties of information flow in the presence of uncertainty - independence, conditioning, nested uncertainty, etc. This shift allows one to reason without the need to specify a concrete model of uncertainty, be it discrete, continuous, Gaussian, possibilistic or one of many other instantiations. In this course I will present a high-level overview of the leading approach to categorical probability that is based on so-called Markov categories. We will focus on the diagrammatic language of Markov categories that can be understood without any knowledge of category theory. Using such diagrams, we can also express basic concepts that have been useful in proving a plethora of categorical versions of classical theorems - strong law of large numbers, de Finetti's theorem, d-separation criterion for Bayesian networks, ergodic decomposition theorem, zero/one laws and others.
Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo
Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact academic@perimeterinstitute.ca.
To request the Zoom link for online participation contact yying@perimeterinstitute.ca.