  Although nonstationary data are more common in the real world, most existing
causal discovery methods do not take nonstationarity into consideration. In
this letter, we propose a kernel embedding-based approach, ENCI, for
nonstationary causal model inference where data are collected from multiple
domains with varying distributions. In ENCI, we transform the complicated
relation of a cause-effect pair into a linear model of variables of which
observations correspond to the kernel embeddings of the cause-and-effect
distributions in different domains. In this way, we are able to estimate the
causal direction by exploiting the causal asymmetry of the transformed linear
model. Furthermore, we extend ENCI to causal graph discovery for multiple
variables by transforming the relations among them into a linear nongaussian
acyclic model. We show that by exploiting the nonstationarity of distributions,
both cause-effect pairs and two kinds of causal graphs are identifiable under
mild conditions. Experiments on synthetic and real-world data are conducted to
justify the efficacy of ENCI over major existing methods.
