Compositional Abstraction Error and a Category of Causal Models

2021/03/29 by Eigil Fjeldgren Rischel, Rischel, Eigil F., Sebastian Weichwald +1 · 4 citations
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Scientific Computing and Data Management #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.2103.15758

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and make predictions about the variables upon intervening on the system. Yet, it is difficult to formalise how we may change the underlying variables used to describe the system, say moving from fine-grained to coarse-grained variables. Here, we argue that compositionality is a desideratum for such model transformations and the associated errors: When abstracting a reference model M iteratively, first obtaining M' and then further simplifying that to obtain M'', we expect the composite transformation from M to M'' to exist and its error to be bounded by the errors incurred by each individual transformation step. Category theory, the study of mathematical objects via compositional transformations between them, offers a natural language to develop our framework for model transformations and abstractions. We introduce a category of finite interventional causal models and, leveraging theory of enriched categories, prove the desired compositionality properties for our framework.

Citations

• Causal Feature Learning for Utility-Maximizing Agents

Cited by

• Distributionally Robust Causal Abstractions
• Learning Nonlinear Causal Reductions to Explain Reinforcement Learning Policies
• Identifiability in Causal Abstractions: A Hierarchy of Criteria
• Causal discovery on vector-valued variables and consistency-guided aggregation

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