# Temporal Inference with Finite Factored Sets

arXiv: https://arxiv.org/abs/2109.11513 · HTML: https://mlsanity.com/paper/2109.11513/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 12 references that are in the map.
- First posted on arXiv 23 Sep 2021.

## Builds on (most cited first, 2 of 2)

- [Embedded Agency](https://mlsanity.com/paper/1902.09469/) (2019)
- [Logical Induction](https://mlsanity.com/paper/1609.03543/) (2016)

## Built on by (most cited first, 2 of 2)

- [A Theory of Bounded Inductive Rationality](https://mlsanity.com/paper/2307.05068/) (2023)
- [Factored space models: Towards causality between levels of abstraction](https://mlsanity.com/paper/2412.02579/) (2024)

## Abstract (arXiv)

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.