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====Approximate method based on Rosas's causal emergence theory====

====Approximate method based on Rosas's causal emergence theory====

[[Rosas's causal emergence theory]] employs quantification method based on both [[synergistic information]] and [[unique information]]. The second method can bypass the combinatorial explosion problem of multivariate variables, but it depends on the coarse-graining method and the selection of macroscopic variable <math>V</math>. To solve this problem, the author gives two solutions. One is to specify a macroscopic state <math>V</math> by the researcher, and the other is a machine learning-based method that allows the system to automatically learn the macroscopic state variable <math>V</math> by maximizing <math>\mathrm{\Psi}</math>.  The following sections introduce these two methods in detail:

[[Rosas's causal emergence theory]] employs quantification method based on both [[synergistic information]] and [[unique information]]. The second method can bypass the combinatorial explosion problem of multivariate variables, but it depends on the coarse-graining method and the selection of macroscopic variable <math>V</math>. To solve this problem, the author gives two solutions. One is to specify a macroscopic state <math>V</math> by the researcher, and the other is a machine learning-based method that allows the system to automatically learn the macroscopic variable <math>V</math> by maximizing <math>\mathrm{\Psi}</math>.  The following sections introduce these two methods in detail:

=====Method based on mutual information approximation=====

=====Method based on mutual information approximation=====