[Linkpost] “A Theory of Structural Independence” by Matthias G. Mayer

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

that arises from the structure rather than the precise

numerical values of a distribution.

We develop this concept and relate

it to d-separation and structural causal models.

Formally, let <span>_U = (U_i)_{i in I}_</span>

be an independent family of random elements

on a probability space <span>_(Omega, mathcal{A} [...]

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First published:

July 7th, 2025

Source:

https://www.lesswrong.com/posts/Xo8EFTd3YJbs7y5ay/a-theory-of-structural-independence

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

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