
TL;DR
This paper introduces topos causal models (TCMs), a new categorical framework for causal inference that leverages topos properties like limits, subobject classifiers, and exponentials to enhance causal reasoning and approximation.
Contribution
The paper develops the theory of TCMs, proving their (co)completeness, and demonstrates how to model interventions, approximations, and equivalences within a topos-based causal framework.
Findings
TCMs are (co)complete, allowing solutions for complex causal diagrams.
Subobject classifiers enable categorical modeling of causal interventions.
Exponential objects facilitate reasoning about causal equivalences and homotopies.
Abstract
We propose topos causal models (TCMs), a novel class of causal models that exploit the key properties of a topos category: they are (co)complete, meaning all (co)limits exist, they admit a subobject classifier, and allow exponential objects. The main goal of this paper is to show that these properties are central to many applications in causal inference. For example, subobject classifiers allow a categorical formulation of causal intervention, which creates sub-models. Limits and colimits allow causal diagrams of arbitrary complexity to be ``solved", using a novel interpretation of causal approximation. Exponential objects enable reasoning about equivalence classes of operations on causal models, such as covered edge reversal and causal homotopy. Analogous to structural causal models (SCMs), TCMs are defined by a collection of functions, each defining a ``local autonomous" causal…
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Taxonomy
TopicsBayesian Modeling and Causal Inference · Logic, Reasoning, and Knowledge · Cognitive Science and Mapping
