On the Semi-Markov Equivalence of Causal Models

TL;DR

This paper explores the structure variability within semi-Markov equivalence classes of causal models and introduces a systematic method to construct models with specific marginal dependencies.

Contribution

It extends the characterization of causal model equivalence to semi-Markov cases and provides a systematic approach for model construction based on desired dependencies.

Findings

Characterized the structure variability in semi-Markov equivalence classes.

Proposed a systematic method for constructing models with specific marginal dependencies.

Extended the understanding of causal model equivalence beyond causal sufficiency.

Abstract

The variability of structure in a finite Markov equivalence class of causally sufficient models represented by directed acyclic graphs has been fully characterized. Without causal sufficiency, an infinite semi-Markov equivalence class of models has only been characterized by the fact that each model in the equivalence class entails the same marginal statistical dependencies. In this paper, we study the variability of structure of causal models within a semi-Markov equivalence class and propose a systematic approach to construct models entailing any specific marginal statistical dependencies.