Representing Independence Models with Elementary Triplets

TL;DR

This paper introduces a method for representing independence models using elementary triplets, enabling efficient operations like union, intersection, and causal reasoning in probabilistic models.

Contribution

It demonstrates how elementary triplets can unambiguously represent independence models and facilitate various operations, including causal inference and minimal map computation.

Findings

Elementary triplets effectively represent independence models.

Operations like union, intersection, and finding minimal maps are feasible with this representation.

Rephrasing Pearl's causal effect computations in terms of conditional independences.

Abstract

In an independence model, the triplets that represent conditional independences between singletons are called elementary. It is known that the elementary triplets represent the independence model unambiguously under some conditions. In this paper, we show how this representation helps performing some operations with independence models, such as finding the dominant triplets or a minimal independence map of an independence model, or computing the union or intersection of a pair of independence models, or performing causal reasoning. For the latter, we rephrase in terms of conditional independences some of Pearl's results for computing causal effects.