The linked paper introduces the key concept of factored spaced models / finite factored sets, structural independence, in a fully general setting using families of random elements. The key contribution is a general definition of the history object and a theorem that the history fully characterizes the semantic implications of the assumption that a family of random elements is independent. This is analogous to how d-separation precisely characterizes which nodal variables are independent given some nodal variables in any probability distribution which fulfills the markov property on the graph.

Abstract: Structural independence is the (conditional) independence

Formally, let _U = (U_i)_{i in I}_

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First published:

Source:

Linkpost URL:
https://arxiv.org/pdf/2412.00847

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