  Most of previous machine learning algorithms are proposed based on the i.i.d.
hypothesis. However, this ideal assumption is often violated in real
applications, where selection bias may arise between training and testing
process. Moreover, in many scenarios, the testing data is not even available
during the training process, which makes the traditional methods like transfer
learning infeasible due to their need on prior of test distribution. Therefore,
how to address the agnostic selection bias for robust model learning is of
paramount importance for both academic research and real applications. In this
paper, under the assumption that causal relationships among variables are
robust across domains, we incorporate causal technique into predictive modeling
and propose a novel Causally Regularized Logistic Regression (CRLR) algorithm
by jointly optimize global confounder balancing and weighted logistic
regression. Global confounder balancing helps to identify causal features,
whose causal effect on outcome are stable across domains, then performing
logistic regression on those causal features constructs a robust predictive
model against the agnostic bias. To validate the effectiveness of our CRLR
algorithm, we conduct comprehensive experiments on both synthetic and real
world datasets. Experimental results clearly demonstrate that our CRLR
algorithm outperforms the state-of-the-art methods, and the interpretability of
our method can be fully depicted by the feature visualization.
