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=== Causal Emergence Theory Based on Information Decomposition ===

=== Causal Emergence Theory Based on Information Decomposition ===

In addition, in 2020, Rosas et al. <ref name=":5" /> proposed a method based on information decomposition to define causal emergence in systems from an information theory perspective and quantitatively characterize emergence based on synergistic information or redundant information. The so-called information decomposition is a new method to analyze the complex interrelationships of various variables in complex systems. By decomposing information, each partial information is represented by an information atom. At the same time, each partial information is projected into the information atom with the help of an information lattice diagram. Both synergistic information and redundant information can be represented by corresponding information atoms. This method is based on the non-negative decomposition theory of multivariate information proposed by Williams and Beer <ref name=":16">Williams P L, Beer R D. Nonnegative decomposition of multivariate information[J]. arXiv preprint arXiv:10042515, 2010.</ref>. In the paper, partial information decomposition (PID) is used to decompose the mutual information between microstates and macrostates. However, the PID framework can only decompose the mutual information between multiple source variables and one target variable. Rosas extended this framework and proposed the integrated information decomposition method <math>\Phi ID</math> <ref name=":18">P. A. Mediano, F. Rosas, R. L. Carhart-Harris, A. K. Seth, A. B. Barrett, Beyond integrated information: A taxonomy of information dynamics phenomena, arXiv preprint arXiv:1909.02297 (2019).</ref>.

In addition, in 2020, Rosas et al. <ref name=":5" /> proposed a method based on [[information decomposition]] to define causal emergence in systems from an [[information theory|information theory]] perspective and quantitatively characterize emergence based on [[synergistic information]] or [[redundant information]]. The so-called [[information decomposition]] is a new method to analyze the complex interrelationships of various variables in [[complex systems]]. By decomposing information, each partial information is represented by an information atom. At the same time, each partial information is projected into the [[information atom]] with the help of an [[information lattice diagram]]. Both synergistic information and redundant information can be represented by corresponding information atoms. This method is based on the [[non-negative decomposition theory of multivariate information]] proposed by Williams and Beer <ref name=":16">Williams P L, Beer R D. Nonnegative decomposition of multivariate information[J]. arXiv preprint arXiv:10042515, 2010.</ref>. In the paper, [[partial information decomposition]] (PID) is used to decompose the mutual information between microstates and macrostates. However, the PID framework can only decompose the mutual information between multiple source variables and one target variable. Rosas extended this framework and proposed the integrated information decomposition method <math>\Phi ID</math> <ref name=":18">P. A. Mediano, F. Rosas, R. L. Carhart-Harris, A. K. Seth, A. B. Barrett, Beyond integrated information: A taxonomy of information dynamics phenomena, arXiv preprint arXiv:1909.02297 (2019).</ref>.

 

=== Recent Work ===

=== Recent Work ===