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          Institute: MPI für biologische Kybernetik     Collection: Biologische Kybernetik     Display Documents

ID: 548380.0, MPI für biologische Kybernetik / Biologische Kybernetik
Causal Inference Using the Algorithmic Markov Condition
Authors:Janzing, D.; Schölkopf, B.
Date of Publication (YYYY-MM-DD):2010-10
Title of Journal:IEEE Transactions on Information Theory
Issue / Number:10
Start Page:5168
End Page:5194
Audience:Not Specified
Intended Educational Use:No
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Holger Fischer
Affiliations:MPI für biologische Kybernetik/Empirical Inference (Dept. Schölkopf)
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