@inproceedings{
richardson2024qualitative,
title={Qualitative Mechanism Independence},
author={Oliver Ethan Richardson and Spencer J Peters and Joseph Halpern},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=RE5LSV8QYH}
}
We define what it means for a joint probability distribution to be compatible with aset of independent causal mechanisms, at a qualitative level—or, more precisely with a directed hypergraph $\mathcal A$, which is the qualitative structure of a probabilistic dependency graph (PDG). When A represents a qualitative Bayesian network, QIM-compatibility with $\mathcal A$ reduces to satisfying the appropriate conditional independencies. But giving semantics to hypergraphs using QIM-compatibility lets us do much more. For one thing, we can capture functional dependencies. For another, we can capture important aspects of causality using compatibility: we can use compatibility to understand cyclic causal graphs, and to demonstrate structural compatibility, we must essentially produce a causal model. Finally, compatibility has deep connections to information theory. Applying compatibility to cyclic structures helps to clarify a longstanding conceptual issue in information theory.
Qualitative Mechanism Independence
Oliver Ethan Richardson Spencer J Peters Joseph Halpern