Patterns of conjunctive forks

TL;DR

This paper characterizes patterns of conjunctive forks among events using linear equations, enabling their recognition in polynomial time and connecting to causal and independence structures.

Contribution

It introduces a polynomial-time method to identify conjunctive fork patterns via linear systems, linking them to causal betweenness and independence.

Findings

Conjunctive fork patterns are characterized by systems of linear equations.

Recognition of these patterns can be performed in polynomial time.

Connections to causal betweenness and conditional independence are established.

Abstract

Three events in a probability space form a conjunctive fork if they satisfy specific constraints on conditional independence and covariances. Patterns of conjunctive forks within collections of events are characterized by means of systems of linear equations that have positive solutions. This characterization allows patterns of conjunctive forks to be recognized in polynomial time. Relations to previous work on causal betweenness and on patterns of conditional independence among random variables are discussed.