  The inference of the causal relationship between a pair of observed variables
is a fundamental problem in science, and most existing approaches are based on
one single causal model. In practice, however, observations are often collected
from multiple sources with heterogeneous causal models due to certain
uncontrollable factors, which renders causal analysis results obtained by a
single model skeptical. In this paper, we generalize the Additive Noise Model
(ANM) to a mixture model, which consists of a finite number of ANMs, and
provide the condition of its causal identifiability. To conduct model
estimation, we propose Gaussian Process Partially Observable Model (GPPOM), and
incorporate independence enforcement into it to learn latent parameter
associated with each observation. Causal inference and clustering according to
the underlying generating mechanisms of the mixture model are addressed in this
work. Experiments on synthetic and real data demonstrate the effectiveness of
our proposed approach.
