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Random connection to maths

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Random connection to maths

Postby shouldsee » July 26th, 2016, 7:36 pm

I am surprised by the structual homology between a Markov Random Field and a cellular automata. It really looks like a stochastic/probablistic automaton.
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Re: Random connection to maths

Postby shouldsee » November 9th, 2017, 1:14 pm

Belief propagation looks very much like a cellular automata. (see this ising example)
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Re: Random connection to maths

Postby shouldsee » February 28th, 2018, 1:44 pm

Anyone fancy implementing a "backpropagation through time“ (BPTT) using CA as substrate?
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Re: Random connection to maths

Postby BlinkerSpawn » February 28th, 2018, 11:04 pm

The temperature model (and possibly the belief propagation system too, although I don't know how that works) could probably be approximated on the VN neighborhood using states 1,2,...,n to represent temperatures of 1/n,2/n,etc., for some n.
Granted, you'd need a script to generate the necessary transitions and there'd be a lot of them, although you'd have access to the permute symmetry which would save some space.
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Re: Random connection to maths

Postby shouldsee » March 28th, 2018, 11:56 am

BlinkerSpawn wrote:The temperature model (and possibly the belief propagation system too, although I don't know how that works) could probably be approximated on the VN neighborhood using states 1,2,...,n to represent temperatures of 1/n,2/n,etc., for some n.
Granted, you'd need a script to generate the necessary transitions and there'd be a lot of them, although you'd have access to the permute symmetry which would save some space.


My interest lies in exploiting message-passing to make fast inference algorithm. A more recent analogue seems to be dynamic bayesian network (DBN), it is remarkably similar to CA and an oscillator in CA corresponds to something like a stable cycle in the DBN. The difference between DBN and MRF is that DBN is embedded in time whereas MRF isn't (though I supposes possible). Anyway it'd be interesting to see how much of the result of CA is transferable to DBN, please comments if you guys have any thought/reference.
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Re: Random connection to maths

Postby shouldsee » March 31st, 2018, 8:21 am

So excited that I dropped my jaw due to this paper by Cosma Shalizi [1].

accompanying blog

Reference
1. Shalizi, C. R., Haslinger, R., Rouquier, J., Klinkner, K. L. & Moore, C. Automatic filters for the detection of coherent structure in spatiotemporal systems. 1–16 (2006). doi:10.1103/PhysRevE.73.036104
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Re: Random connection to maths

Postby Bullet51 » March 31st, 2018, 9:33 am

shouldsee wrote:So excited that I dropped my jaw due to this paper by Cosma Shalizi [1].

accompanying blog

Reference
1. Shalizi, C. R., Haslinger, R., Rouquier, J., Klinkner, K. L. & Moore, C. Automatic filters for the detection of coherent structure in spatiotemporal systems. 1–16 (2006). doi:10.1103/PhysRevE.73.036104


I'm curious of how it works on the Turbulent phase cyclic cellular automata, where large-scale structure dominates.
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Re: Random connection to maths

Postby shouldsee » April 24th, 2018, 7:13 pm

This brain model looks very CA to me. https://www.youtube.com/watch?v=843G1WDnmAU
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