  The foremost challenge to causal inference with real-world data is to handle
the imbalance in the covariates with respect to different treatment options,
caused by treatment selection bias. To address this issue, recent literature
has explored domain-invariant representation learning based on different domain
divergence metrics (e.g., Wasserstein distance, maximum mean discrepancy,
position-dependent metric, and domain overlap). In this paper, we reveal the
weaknesses of these strategies, i.e., they lead to the loss of predictive
information when enforcing the domain invariance; and the treatment effect
estimation performance is unstable, which heavily relies on the characteristics
of the domain distributions and the choice of domain divergence metrics.
Motivated by information theory, we propose to learn the Infomax and
Domain-Independent Representations to solve the above puzzles. Our method
utilizes the mutual information between the global feature representations and
individual feature representations, and the mutual information between feature
representations and treatment assignment predictions, in order to maximally
capture the common predictive information for both treatment and control
groups. Moreover, our method filters out the influence of instrumental and
irrelevant variables, and thus it effectively increases the predictive ability
of potential outcomes. Experimental results on both the synthetic and
real-world datasets show that our method achieves state-of-the-art performance
on causal effect inference. Moreover, our method exhibits reliable prediction
performances when facing data with different characteristics of data
distributions, complicated variable types, and severe covariate imbalance.
