  This paper presents a new optimization approach to causal estimation. Given
data that contains covariates and an outcome, which covariates are causes of
the outcome, and what is the strength of the causality? In classical machine
learning (ML), the goal of optimization is to maximize predictive accuracy.
However, some covariates might exhibit a non-causal association with the
outcome. Such spurious associations provide predictive power for classical ML,
but they prevent us from causally interpreting the result. This paper proposes
CoCo, an optimization algorithm that bridges the gap between pure prediction
and causal inference. CoCo leverages the recently-proposed idea of
environments, datasets of covariates/response where the causal relationships
remain invariant but where the distribution of the covariates changes from
environment to environment. Given datasets from multiple environments-and ones
that exhibit sufficient heterogeneity-CoCo maximizes an objective for which the
only solution is the causal solution. We describe the theoretical foundations
of this approach and demonstrate its effectiveness on simulated and real
datasets. Compared to classical ML and existing methods, CoCo provides more
accurate estimates of the causal model and more accurate predictions under
interventions.
