eprintid: 10140097
rev_number: 15
eprint_status: archive
userid: 608
dir: disk0/10/14/00/97
datestamp: 2021-12-10 13:46:20
lastmod: 2022-07-06 10:48:39
status_changed: 2021-12-10 13:46:20
type: article
metadata_visibility: show
creators_name: Jacobs, B
creators_name: Kissinger, A
creators_name: Zanasi, F
title: Causal inference via string diagram surgery
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
divisions: F48
keywords: Probabilistic reasoning, causality, counterfactuals, string diagrams
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
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.
date: 2021-05
date_type: published
official_url: https://doi.org/10.1017/S096012952100027X
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1907025
doi: 10.1017/S096012952100027X
lyricists_name: Zanasi, Fabio
lyricists_id: FZANA74
actors_name: Zanasi, Fabio
actors_id: FZANA74
actors_role: owner
full_text_status: public
publication: Mathematical Structures in Computer Science
volume: 31
number: 5
pagerange: 553-574
citation:        Jacobs, B;    Kissinger, A;    Zanasi, F;      (2021)    Causal inference via string diagram surgery.                   Mathematical Structures in Computer Science , 31  (5)   pp. 553-574.    10.1017/S096012952100027X <https://doi.org/10.1017/S096012952100027X>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10140097/1/causal-strings-mscs.pdf