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  Causal Inference Using the Algorithmic Markov Condition

Janzing, D., & Schölkopf, B. (2010). Causal Inference Using the Algorithmic Markov Condition. IEEE Transactions on Information Theory, 56(10), 5168-5194. doi:10.1109/TIT.2010.2060095.

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Janzing, D1, 2, Author              
Schölkopf, B1, 2, Author              
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1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: Inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure Markovian. Here we argue why causal inference is also possible when the sample size is one. We develop a theory how to generate causal graphs explaining similarities between single objects. To this end, we replace the notion of conditional stochastic independence in the causal Markov condition with the vanishing of conditional algorithmic mutual information and describe the corresponding causal inference rules. We explain why a consistent reformulation of causal inference in terms of algorithmic complexity implies a new inference principle that takes into account also the complexity of conditional probability densities, making it possible to select among Markov equivalent causal graphs. This insight provides a theoretical foundation of a heuristic principle proposed in earlier work. We also sketch some ideas on how to replace Kolmogorov complexity with decidable complexity criteria. This can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions on the underlying distribution.

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 Dates: 2010-10
 Publication Status: Published in print
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 Identifiers: DOI: 10.1109/TIT.2010.2060095
BibTex Citekey: 6526
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Title: IEEE Transactions on Information Theory
Source Genre: Journal
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Pages: - Volume / Issue: 56 (10) Sequence Number: - Start / End Page: 5168 - 5194 Identifier: -