  In this paper, we focus on the problem of stable prediction across unknown
test data, where the test distribution is agnostic and might be totally
different from the training one. In such a case, previous machine learning
methods might exploit subtly spurious correlations in training data induced by
non-causal variables for prediction. Those spurious correlations are changeable
across data, leading to instability of prediction across data. By assuming the
relationships between causal variables and response variable are invariant
across data, to address this problem, we propose a conditional independence
test based algorithm to separate those causal variables with a seed variable as
priori, and adopt them for stable prediction. By assuming the independence
between causal and non-causal variables, we show, both theoretically and with
empirical experiments, that our algorithm can precisely separate causal and
non-causal variables for stable prediction across test data. Extensive
experiments on both synthetic and real-world datasets demonstrate that our
algorithm outperforms state-of-the-art methods for stable prediction.
