Causal Razors

TL;DR

This paper reviews various causal razors used in causal discovery, compares their assumptions logically, and highlights the implications of choosing different razors, especially focusing on the less popular parameter minimality.

Contribution

It provides a comprehensive logical comparison of causal razors and analyzes the role of parameter minimality in multinomial causal models.

Findings

Parameter minimality has a unique logical relation with other causal razors.

The choice of causal razor affects scoring criteria in causal discovery algorithms.

The paper clarifies the assumptions underlying different causal razors.

Abstract

When performing causal discovery, assumptions have to be made on how the true causal mechanism corresponds to the underlying joint probability distribution. These assumptions are labeled as causal razors in this work. We review numerous causal razors that appeared in the literature, and offer a comprehensive logical comparison of them. In particular, we scrutinize an unpopular causal razor, namely parameter minimality, in multinomial causal models and its logical relations with other well-studied causal razors. Our logical result poses a dilemma in selecting a reasonable scoring criterion for score-based casual search algorithms.