Serving the Quantitative Finance Community

 
user3203472
Topic Author
Posts: 7
Joined: January 3rd, 2019, 11:33 am

Markov/Kleisli categories / categorical approach to probability

September 21st, 2022, 9:01 am

Hello experts,

I was wondering what your thoughts were on the categorical approach to probability theory, as opposed to foundations based on Kolmogorov's axioms.

https://ncatlab.org/nlab/show/Markov+category

I think categorical probability does seem to have some successes, however, I am no expert in probability. Is this yet another algebraic geometry / category theory overreach / pointless fluffery ?
 
User avatar
Cuchulainn
Posts: 18065
Joined: July 16th, 2004, 7:38 am
Location: Lviv

Re: Markov/Kleisli categories / categorical approach to probability

September 22nd, 2022, 2:16 pm

Just out of curiosity, does it support negatve categorical probability theory?
вот мой дорогой двоюродный брат
 
user3203472
Topic Author
Posts: 7
Joined: January 3rd, 2019, 11:33 am

Re: Markov/Kleisli categories / categorical approach to probability

October 1st, 2022, 5:47 am

HI, in the categorical approach, signed measures etc are nothing more than a first-order model of the underlying theory, so for example if could be a first-order model for the theory underlying the category obtained by applying the Giry monad to suitable categories.
 
User avatar
katastrofa
Posts: 7024
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: Markov/Kleisli categories / categorical approach to probability

October 1st, 2022, 1:44 pm

Some success like Haskell?
 
User avatar
Cuchulainn
Posts: 18065
Joined: July 16th, 2004, 7:38 am
Location: Lviv

Re: Markov/Kleisli categories / categorical approach to probability

October 4th, 2022, 1:38 pm

Category Theory is as boring as hell.
вот мой дорогой двоюродный брат
 
user3203472
Topic Author
Posts: 7
Joined: January 3rd, 2019, 11:33 am

Re: Markov/Kleisli categories / categorical approach to probability

October 9th, 2022, 2:35 am

I hear you completely, however it does simplify things a great deal. For example the 0th K-group of a variety in algebraic geometry is the number of objects in the  full exceptional collection of the derived category for the variety, so it makes computing them really easy. https://ncatlab.org/nlab/show/K-theory#idea
 
User avatar
Cuchulainn
Posts: 18065
Joined: July 16th, 2004, 7:38 am
Location: Lviv

Re: Markov/Kleisli categories / categorical approach to probability

October 9th, 2022, 5:40 pm

Maybe developers/programmers should learn CT
https://bartoszmilewski.com/2020/08/05/ ... rogrammer/

esp. composition stuff, higher order functions, (Haskell) curry, partial function evaluation.
вот мой дорогой двоюродный брат
 
User avatar
Cuchulainn
Posts: 18065
Joined: July 16th, 2004, 7:38 am
Location: Lviv

Re: Markov/Kleisli categories / categorical approach to probability

October 9th, 2022, 7:15 pm

Can bounded quantificaton (C++ Concepts) be aligned with CT somehow?

https://en.wikipedia.org/wiki/Bounded_quantification
вот мой дорогой двоюродный брат