Identifying Causal Effects with Computer Algebra

TL;DR

This paper introduces a computer algebra approach to systematically determine the identifiability of causal effects in graphical models, providing precise results for small linear models.

Contribution

It presents a novel application of computer algebra to analyze causal effect identifiability, covering all small linear models with three and four vertices.

Findings

Identifies which causal effects are generically identifiable in small linear models.

Provides a systematic algebraic method for causal effect identification.

Results are specific to models with three and four vertices.

Abstract

The long-standing identification problem for causal effects in graphical models has many partial results but lacks a systematic study. We show how computer algebra can be used to either prove that a causal effect can be identified, generically identified, or show that the effect is not generically identifiable. We report on the results of our computations for linear structural equation models, where we determine precisely which causal effects are generically identifiable for all graphs on three and four vertices.