Temporal Inference with Finite Factored Sets

TL;DR

This paper introduces a novel method for temporal inference using finite factored sets, providing a new framework that parallels causal inference concepts without relying on directed acyclic graphs.

Contribution

It develops the concept of finite factored sets and an analog of d-separation, establishing their equivalence to conditional independence in probabilistic models.

Findings

Finite factored sets effectively infer temporal relations.

Conditional orthogonality is equivalent to conditional independence.

The approach offers a new perspective distinct from Pearl's causal graphs.

Abstract

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.