  In the era of big data, the explosive growth of multi-source heterogeneous
data offers many exciting challenges and opportunities for improving the
inference of conditional average treatment effects. In this paper, we
investigate homogeneous and heterogeneous causal data fusion problems under a
general setting that allows for the presence of source-specific covariates. We
provide a direct learning framework for integrating multi-source data that
separates the treatment effect from other nuisance functions, and achieves
double robustness against certain misspecification. To improve estimation
precision and stability, we propose a causal information-aware weighting
function motivated by theoretical insights from the semiparametric efficiency
theory; it assigns larger weights to samples containing more causal information
with high interpretability. We introduce a two-step algorithm, the weighted
multi-source direct learner, based on constructing a pseudo-outcome and
regressing it on covariates under a weighted least square criterion; it offers
us a powerful tool for causal data fusion, enjoying the advantages of easy
implementation, double robustness and model flexibility. In simulation studies,
we demonstrate the effectiveness of our proposed methods in both homogeneous
and heterogeneous causal data fusion scenarios.
