  The classic studies of causal emergence have revealed that in some Markovian
dynamical systems, far stronger causal connections can be found on the
higher-level descriptions than the lower-level of the same systems if we
coarse-grain the system states in an appropriate way. However, identifying this
emergent causality from the data is still a hard problem that has not been
solved because the correct coarse-graining strategy can not be found easily.
This paper proposes a general machine learning framework called Neural
Information Squeezer to automatically extract the effective coarse-graining
strategy and the macro-state dynamics, as well as identify causal emergence
directly from the time series data. By decomposing a coarse-graining operation
into two processes: information conversion and information dropping out, we can
not only exactly control the width of the information channel, but also can
derive some important properties analytically including the exact expression of
the effective information of a macro-dynamics. We also show how our framework
can extract the dynamics on different levels and identify causal emergence from
the data on several exampled systems.
