  Most existing causal structure learning methods assume data collected from
one environment and independent and identically distributed (i.i.d.). In some
cases, data are collected from different subjects from multiple environments,
which provides more information but might make the data non-identical or
non-independent distribution. Some previous efforts try to learn causal
structure from this type of data in two independent stages, i.e., first
discovering i.i.d. groups from non-i.i.d. samples, then learning the causal
structures from different groups. This straightforward solution ignores the
intrinsic connections between the two stages, that is both the clustering stage
and the learning stage should be guided by the same causal mechanism. Towards
this end, we propose a unified Causal Cluster Structures Learning (named CCSL)
method for causal discovery from non-i.i.d. data. This method simultaneously
integrates the following two tasks: 1) clustering samples of the subjects with
the same causal mechanism into different groups; 2) learning causal structures
from the samples within the group. Specifically, for the former, we provide a
Causality-related Chinese Restaurant Process to cluster samples based on the
similarity of the causal structure; for the latter, we introduce a
variational-inference-based approach to learn the causal structures.
Theoretical results provide identification of the causal model and the
clustering model under the linear non-Gaussian assumption. Experimental results
on both simulated and real-world data further validate the correctness and
effectiveness of the proposed method.
