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Causal deconvolution by algorithmic generative models

A preprint version of the article is available at arXiv.


Complex behaviour emerges from interactions between objects produced by different generating mechanisms. Yet to decode their causal origin(s) from observations remains one of the most fundamental challenges in science. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based on the seminal concept and the first principles of algorithmic probability, to decompose an observation into its most likely algorithmic generative models. Our approach uses a perturbation-based causal calculus to infer model representations. We demonstrate its ability to deconvolve interacting mechanisms regardless of whether the resultant objects are bit strings, space–time evolution diagrams, images or networks. Although this is mostly a conceptual contribution and an algorithmic framework, we also provide numerical evidence evaluating the ability of our methods to extract models from data produced by discrete dynamical systems such as cellular automata and complex networks. We think that these separating techniques can contribute to tackling the challenge of causation, thus complementing statistically oriented approaches.

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Fig. 1: Proof of concept applied to a binary string composed of two segments with different underlying generating mechanisms (computer programs).
Fig. 2: Training-free separation of intertwined programs despite their statistical similarity from an observer’s perspective.
Fig. 3: Algorithmic similarity and graph hierarchical decomposition leading to causal clustering.
Fig. 4: Unsupervised graph deconvolution identifies each different topological generating mechanism.

Data availability

The data that support the plots within this paper are available from the corresponding author upon request.


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H.Z. was supported by Swedish Research Council (Vetenskapsrådet) grant number 2015-05299. J.T. was supported by the King Abdullah University of Science and Technology.

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Authors and Affiliations



H.Z., N.A.K. and J.T. conceived and designed the algorithms. H.Z. designed the experiments and carried out the calculations and numerical experiments. A.A.Z. and H.Z. conceived the online tool to illustrate the method applied to simple examples based on this paper. All authors contributed to the writing of the paper.

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Correspondence to Hector Zenil, Narsis A. Kiani or Jesper Tegnér.

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The authors declare no competing interests.

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Zenil, H., Kiani, N.A., Zea, A.A. et al. Causal deconvolution by algorithmic generative models. Nat Mach Intell 1, 58–66 (2019).

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