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Temporal Inference with Finite Factored Sets
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We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are sets expressed as Cartesian products. We show that finite factored sets are powerful tools for inferring temporal relations. We introduce an analog of d-separation for factored sets, conditional orthogonality, and we demonstrate that this notion is equivalent to conditional independence in all probability distributions on a finite factored set.
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Cited by 2 Pith papers
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A Theory of Structural Independence
A measure-theoretic characterization: X and Y are independent of each other given Z in all product distributions exactly when their histories are almost surely disjoint.
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Factored space models: Towards causality between levels of abstraction
Structural independence in a factored space is equivalent to conditional independence in all product distributions, generalizing d-separation to deterministic functions.
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