Talk by Paolo Perrone

The next talk of our seminar series will be given by Paolo Perrone (University of Oxford) via Teams (please, see details below) on Monday, March 18th, starting from 12:30 (Milan time). Here it is the title and abstract of his talk:

Title: Higher abstraction for probability and statistics

Abstract: Probability and statistics are at the heart of the modern world, from medicine, to finance, to the most recent advances in machine learning.
However, they are poorly understood by the general public, and even to scientists they often present an excessive degree of technicality.
When the complexity of a theory reaches such a state, it calls for an additional layer of abstraction.
We provide such an abstraction, called “categorical probability”, which aims to make probabilistic reasoning intuitive through the lens of abstract mathematics, in particular category theory.
The concepts of randomness, statistical independence, and conditioning have a very deep, conceptual nature, which our formalism makes explicit.
Moreover, the formalism allows to recover, and sometimes simplify, the core concepts and results of probability.

In this talk we introduce the formalism without assuming any background in either category theory or probability.
We then turn to the study of stochastic systems displaying invariance under symmetries, and show how our theory can provide systematic understanding, for example by giving a simple statement and proof of de Finetti’s theorem.
Given time and interest, we can also discuss the relevance of stochastic invariance in the context of generative AI. 

Relevant papers: arXiv:2212.11719, arXiv:2207.07353, arXiv:2207.05740.

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