Causal models in string diagrams

• URL: http://arxiv.org/abs/2304.07638v1
• Date: Sat, 15 Apr 2023 21:54:48 GMT
• Title: Causal models in string diagrams
• Authors: Robin Lorenz and Sean Tull
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory. A class of string diagrams, called network diagrams, are in 1-to-1 correspondence with directed acyclic graphs. A causal model is given by such a diagram with its components interpreted as stochastic maps, functions, or general channels in a symmetric monoidal category with a 'copy-discard' structure (cd-category), turning a model into a single mathematical object that can be reasoned with intuitively and yet rigorously. Building on prior works by Fong and Jacobs, Kissinger and Zanasi, as well as Fritz and Klingler, we present diagrammatic definitions of causal models and functional causal models in a cd-category, generalising causal Bayesian networks and structural causal models, respectively. We formalise general interventions on a model, including but beyond do-interventions, and present the natural notion of an open causal model with inputs. We also give an approach to conditioning based on a normalisation box, allowing for causal inference calculations to be done fully diagrammatically. We define counterfactuals in this setup, and treat the problems of the identifiability of causal effects and counterfactuals fully diagrammatically. The benefits of such a presentation of causal models lie in foundational questions in causal reasoning and in their clarificatory role and pedagogical value. This work aims to be accessible to different communities, from causal model practitioners to researchers in applied category theory, and discusses many examples from the literature for illustration. Overall, we argue and demonstrate that causal reasoning according to the causal model framework is most naturally and intuitively done as diagrammatic reasoning.

Related papers

• Counterfactual Generation from Language Models [64.55296662926919]
  We show that counterfactual reasoning is conceptually distinct from interventions. We propose a framework for generating true string counterfactuals. Our experiments demonstrate that the approach produces meaningful counterfactuals.
  arXiv  Detail & Related papers  (2024-11-11T17:57:30Z)
• Towards Compositional Interpretability for XAI [3.3768167170511587]
  We present an approach to defining AI models and their interpretability based on category theory. We compare a wide range of AI models as compositional models. We find that what makes the standard 'intrinsically interpretable' models so transparent is brought out most clearly diagrammatically.
  arXiv  Detail & Related papers  (2024-06-25T14:27:03Z)
• Learning Discrete Concepts in Latent Hierarchical Models [73.01229236386148]
  Learning concepts from natural high-dimensional data holds potential in building human-aligned and interpretable machine learning models. We formalize concepts as discrete latent causal variables that are related via a hierarchical causal model. We substantiate our theoretical claims with synthetic data experiments.
  arXiv  Detail & Related papers  (2024-06-01T18:01:03Z)
• What makes Models Compositional? A Theoretical View: With Supplement [60.284698521569936]
  We propose a general neuro-symbolic definition of compositional functions and their compositional complexity. We show how various existing general and special purpose sequence processing models fit this definition and use it to analyze their compositional complexity.
  arXiv  Detail & Related papers  (2024-05-02T20:10:27Z)
• Diagrammatic Modelling of Causality and Causal Relations [0.0]
  This paper concerns diagrammatical (graphic) models of causal relationships. We experiment with using the conceptual language of thinging machines (TMs) as a tool in this context. The results show that the TM depiction of causality is more complete and therefore can provide a foundation for causal graphs.
  arXiv  Detail & Related papers  (2023-10-17T07:17:51Z)
• The Generative Programs Framework [0.0]
  We argue that any quantitative physical theory can be represented in the form of a generative program. We suggest that these graphs can be interpreted as encoding relations of ontological priority,' and that ontological priority is a suitable generalisation of causation.
  arXiv  Detail & Related papers  (2023-07-21T00:57:05Z)
• 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)
• 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)
• 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)

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.