Hopfield Networks = Ising Models = Distributions over Causal models?
Given a joint probability distributions p(x1,...,xn) famously there might be many ‘Markov’ factorizations. Each corresponds with a different causal model.
Instead of choosing a particular one we might have a distribution of beliefs over these different causal models. This feels basically like a Hopfield Network/ Ising Model.
You have a distribution over nodes and an ‘interaction’ distribution over edges.
The distribution over nodes corresponds to the joint probability distribution while the distribution over edges corresponds to a mixture of causal models where a normal DAG graphical causal G model corresponds to the Ising model/ Hopfield network which assigns 1 to an edge x→y if the edge is in G and 0 otherwise.
Hopfield Networks = Ising Models = Distributions over Causal models?
Given a joint probability distributions p(x1,...,xn) famously there might be many ‘Markov’ factorizations. Each corresponds with a different causal model.
Instead of choosing a particular one we might have a distribution of beliefs over these different causal models. This feels basically like a Hopfield Network/ Ising Model.
You have a distribution over nodes and an ‘interaction’ distribution over edges.
The distribution over nodes corresponds to the joint probability distribution while the distribution over edges corresponds to a mixture of causal models where a normal DAG graphical causal G model corresponds to the Ising model/ Hopfield network which assigns 1 to an edge x→y if the edge is in G and 0 otherwise.