  Although deep learning models have driven state-of-the-art performance on a
wide array of tasks, they are prone to spurious correlations that should not be
learned as predictive clues. To mitigate this problem, we propose a
causality-based training framework to reduce the spurious correlations caused
by observed confounders. We give theoretical analysis on the underlying general
Structural Causal Model (SCM) and propose to perform Maximum Likelihood
Estimation (MLE) on the interventional distribution instead of the
observational distribution, namely Counterfactual Maximum Likelihood Estimation
(CMLE). As the interventional distribution, in general, is hidden from the
observational data, we then derive two different upper bounds of the expected
negative log-likelihood and propose two general algorithms, Implicit CMLE and
Explicit CMLE, for causal predictions of deep learning models using
observational data. We conduct experiments on both simulated data and two
real-world tasks: Natural Language Inference (NLI) and Image Captioning. The
results show that CMLE methods outperform the regular MLE method in terms of
out-of-domain generalization performance and reducing spurious correlations,
while maintaining comparable performance on the regular evaluations.
