On the Role of Priors in Bayesian Causal Learning

2025-04-02

IEEE Transactions on Artificial Intelligence

AI Summary

This paper investigates how prior choice affects the identifiability of Independent Causal Mechanisms (ICM) in Bayesian causal learning. Addressing the key question—whether unlabeled cause data improve estimation of mechanism parameters—the authors rigorously prove that such unlabelled cause observations do not enhance posterior precision for mechanism parameters, underscoring the decisive role of prior structure over causes and mechanisms. Methodologically, they provide the first Bayesian characterization showing that posterior factorization holds if and only if the prior factorizes across causes and mechanisms. This establishes a Bayesian-consistent foundation for ICM, unifying Kolmogorov-complexity–based causal assumptions with parameter independence theory. The work identifies prior design as both necessary and sufficient for causal identifiability under ICM, yielding theoretical principles and practical guidelines for constructing ICM-compliant Bayesian causal models.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

In this work, we investigate causal learning of independent causal mechanisms from a Bayesian perspective. Confirming previous claims from the literature, we show in a didactically accessible manner that unlabeled data (i.e., cause realizations) do not improve the estimation of the parameters defining the mechanism. Furthermore, we observe the importance of choosing an appropriate prior for the cause and mechanism parameters, respectively. Specifically, we show that a factorized prior results in a factorized posterior, which resonates with Janzing and Sch""olkopf's definition of independent causal mechanisms via the Kolmogorov complexity of the involved distributions and with the concept of parameter independence of Heckerman et al.

Problem

• Investigates Bayesian causal learning of independent mechanisms
• Shows unlabeled data doesn't improve mechanism parameter estimation
• Highlights importance of factorized priors for causal independence

Innovation

• Bayesian perspective for causal learning
• Factorized prior ensures factorized posterior
• Emphasizes importance of appropriate priors