  The advent of the big data era brought new opportunities and challenges to
draw treatment effect in data fusion, that is, a mixed dataset collected from
multiple sources (each source with an independent treatment assignment
mechanism). Due to possibly omitted source labels and unmeasured confounders,
traditional methods cannot estimate individual treatment assignment probability
and infer treatment effect effectively. Therefore, we propose to reconstruct
the source label and model it as a Group Instrumental Variable (GIV) to
implement IV-based Regression for treatment effect estimation. In this paper,
we conceptualize this line of thought and develop a unified framework (Meta-EM)
to (1) map the raw data into a representation space to construct Linear Mixed
Models for the assigned treatment variable; (2) estimate the distribution
differences and model the GIV for the different treatment assignment
mechanisms; and (3) adopt an alternating training strategy to iteratively
optimize the representations and the joint distribution to model GIV for IV
regression. Empirical results demonstrate the advantages of our Meta-EM
compared with state-of-the-art methods.
