Topos Causal Models

• URL: http://arxiv.org/abs/2508.08295v1
• Date: Tue, 05 Aug 2025 21:50:57 GMT
• Title: Topos Causal Models
• Authors: Sridhar Mahadevan,
• Abstract summary: We propose topos causal models (TCMs), a class of causal models that exploit the key properties of a topos category.<n>The main goal of this paper is to show that these properties are central to many applications in causal inference.
• Score: 3.0316063849624477
• License: http://creativecommons.org/licenses/by/4.0/
• 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 mechanism that assemble to induce a unique global function from exogenous to endogenous variables. Since the category of TCMs is (co)complete, which we prove in this paper, every causal diagram has a ``solution" in the form of a (co)limit: this implies that any arbitrary causal model can be ``approximated" by some global function with respect to the morphisms going into or out of the diagram. Natural transformations are crucial in measuring the quality of approximation. In addition, we show that causal interventions are modeled by subobject classifiers: any sub-model is defined by a monic arrow into its parent model. Exponential objects permit reasoning about entire classes of causal equivalences and interventions. Finally, as TCMs form a topos, they admit an internal logic defined as a Mitchell-Benabou language with an associated Kripke-Joyal semantics. We show how to reason about causal models in TCMs using this internal logic.

Related papers

• Canonical Representations of Markovian Structural Causal Models: A Framework for Counterfactual Reasoning [0.7106986689736826]
  Counterfactual reasoning aims at answering contrary-to-fact questions like Would have Alice recovered had she taken aspirin?''<n>We propose an alternative approach to structural causal models to represent counterfactuals compatible with a given causal graphical model.<n>We present a normalization procedure to disentangle the (arbitrary and unfalsifiable) counterfactual choice from the (typically testable) interventional constraints.
  arXiv  Detail & Related papers  (2025-07-22T09:13:02Z)
• Towards Characterizing Domain Counterfactuals For Invertible Latent Causal Models [15.817239008727789]
  In this work, we analyze a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain. We show that recovering the latent Structural Causal Model (SCM) is unnecessary for estimating domain counterfactuals. We also develop a theoretically grounded practical algorithm that simplifies the modeling process to generative model estimation.
  arXiv  Detail & Related papers  (2023-06-20T04:19:06Z)
• Causal models in string diagrams [0.0]
  The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. We present this framework in the language of string diagrams, interpreted formally using category theory. We argue and demonstrate that causal reasoning according to the causal model framework is most naturally and intuitively done as diagrammatic reasoning.
  arXiv  Detail & Related papers  (2023-04-15T21:54:48Z)
• Unifying Causal Inference and Reinforcement Learning using Higher-Order Category Theory [4.119151469153588]
  We present a unified formalism for structure discovery of causal models and predictive state representation models in reinforcement learning. Specifically, we model structure discovery in both settings using simplicial objects.
  arXiv  Detail & Related papers  (2022-09-13T19:04:18Z)
• On The Universality of Diagrams for Causal Inference and The Causal Reproducing Property [4.119151469153588]
  We propose a framework based on category theory that defines the universal property that underlies causal inference. We present two foundational results in universal causal inference.
  arXiv  Detail & Related papers  (2022-07-06T18:54:15Z)
• Markov categories, causal theories, and the do-calculus [7.061298918159947]
  We give a category-theoretic treatment of causal models that formalizes the syntax for causal reasoning over a directed acyclic graph (DAG) This framework enables us to define and study important concepts in causal reasoning from an abstract and "purely causal" point of view.
  arXiv  Detail & Related papers  (2022-04-11T01:27:41Z)
• Causality Inspired Representation Learning for Domain Generalization [47.574964496891404]
  We introduce a general structural causal model to formalize the Domain generalization problem. Our goal is to extract the causal factors from inputs and then reconstruct the invariant causal mechanisms. We highlight that ideal causal factors should meet three basic properties: separated from the non-causal ones, jointly independent, and causally sufficient for the classification.
  arXiv  Detail & Related papers  (2022-03-27T08:08:33Z)
• Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learning [76.00395335702572]
  A central goal for AI and causality is the joint discovery of abstract representations and causal structure. Existing environments for studying causal induction are poorly suited for this objective because they have complicated task-specific causal graphs. In this work, our goal is to facilitate research in learning representations of high-level variables as well as causal structures among them.
  arXiv  Detail & Related papers  (2021-07-02T05:44:56Z)
• The Causal Neural Connection: Expressiveness, Learnability, and Inference [125.57815987218756]
  An object called structural causal model (SCM) represents a collection of mechanisms and sources of random variation of the system under investigation. In this paper, we show that the causal hierarchy theorem (Thm. 1, Bareinboim et al., 2020) still holds for neural models. We introduce a special type of SCM called a neural causal model (NCM), and formalize a new type of inductive bias to encode structural constraints necessary for performing causal inferences.
  arXiv  Detail & Related papers  (2021-07-02T01:55:18Z)
• Causal Expectation-Maximisation [70.45873402967297]
  We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs. We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
  arXiv  Detail & Related papers  (2020-11-04T10:25:13Z)
• Structural Causal Models Are (Solvable by) Credal Networks [70.45873402967297]
  Causal inferences can be obtained by standard algorithms for the updating of credal nets. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks. Experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.
  arXiv  Detail & Related papers  (2020-08-02T11:19:36Z)
• A Critical View of the Structural Causal Model [89.43277111586258]
  We show that one can identify the cause and the effect without considering their interaction at all. We propose a new adversarial training method that mimics the disentangled structure of the causal model. Our multidimensional method outperforms the literature methods on both synthetic and real world datasets.
  arXiv  Detail & Related papers  (2020-02-23T22:52:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.