  Estimating conditional average treatment effect from observational data is
highly challenging due to the existence of treatment selection bias. Prevalent
methods mitigate this issue by aligning distributions of different treatment
groups in the latent space. However, there are two critical problems that these
methods fail to address: (1) mini-batch sampling effects (MSE), which causes
misalignment in non-ideal mini-batches with outcome imbalance and outliers; (2)
unobserved confounder effects (UCE), which results in inaccurate discrepancy
calculation due to the neglect of unobserved confounders. To tackle these
problems, we propose a principled approach named Entire Space CounterFactual
Regression (ESCFR), which is a new take on optimal transport in the context of
causality. Specifically, based on the framework of stochastic optimal
transport, we propose a relaxed mass-preserving regularizer to address the MSE
issue and design a proximal factual outcome regularizer to handle the UCE
issue. Extensive experiments demonstrate that our proposed ESCFR can
successfully tackle the treatment selection bias and achieve significantly
better performance than state-of-the-art methods.
