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SUMMARY:Paolo Perrone: Markov categories: towards user-friendly probability
theory
DESCRIPTION:\nAbstract: Markov categories are a new mathematical framework
designed to deal with problems in probability and statistics\, using a hig
her abstraction layer. For an analogy\, high-level programming languages (
such as Python) allow the user to write code without worrying about lower-
level issues such as memory allocation. Similarly\, Markov categories allo
w the user to write rigorous mathematics\, possibly involving continuous s
ample spaces and singularities\, without having to know any measure theory
. Moreover\, they come equipped with a graphical formalism which faithfull
y reflects the information flow and the stochastic dependencies\, and so t
hey give a very general theory of graphical models.\nSeveral concepts of p
robability and statistics have already been incorporated into the formalis
m\, and sometimes restated and reproven in \na more general way. Among the
se we have conditioning\, filtering\, de Finetti’s theorem\, Blackwell
’s theorem on statistical experiments\, Shannon’s entropy and informat
ion inequalities\, and d-separation theorems. This is an active field of r
esearch\, and more and more results are added by the day.\nIn this talk I
will give an introduction to the part of this formalism which is already d
eveloped and ready to be used. I will assume no prerequisite knowledge of
category theory.\n
URL:https://www.imperial.ac.uk/events/177192/paolo-perrone-markov-categorie
s-towards-user-friendly-probability-theory/
DTSTART;TZID=Europe/London:20240514T140000
DTEND;TZID=Europe/London:20240514T150000
LOCATION:144\, Huxley Building\, South Kensington Campus\, Imperial College
London\, London\, SW7 2AZ\, United Kingdom
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