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Causal inference via string diagram surgery

A diagrammatic approach to interventions and counterfactuals

Published online by Cambridge University Press:  16 November 2021

Bart Jacobs Open the ORCID record for Bart Jacobs [Opens in a new window] ,
Aleks Kissinger  and
Fabio Zanasi
Bart Jacobs*
Affiliation:
Department of Computing and Information Science, Radboud Universiteit Faculteit der Natuurwetenschappen Wiskunde en Informatica, Nijmegen, The Netherlands
Aleks Kissinger
Affiliation:
Department of Computer Science, Oxford University, Oxford, UK
Fabio Zanasi
Affiliation:
Department of Computer Science, University College London, London, UK
*
*Corresponding author. Email: [email protected]
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Abstract

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endo-functor which performs ‘string diagram surgery’ within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on two well-known toy examples: one where we predict the causal effect of smoking on cancer in the presence of a confounding common cause and where we show that this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature; the other one is an illustration of counterfactual reasoning where the same interventional techniques are used, but now in a ‘twinned’ set-up, with two version of the world – one factual and one counterfactual – joined together via exogenous variables that capture the uncertainties at hand.

Keywords

Probabilistic reasoningcausalitycounterfactualsstring diagrams
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 31 , Issue 5 , May 2021 , pp. 553 - 574
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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