  Decentralized data sources are prevalent in real-world applications, posing a
formidable challenge for causal inference. These sources cannot be consolidated
into a single entity owing to privacy constraints. The presence of dissimilar
data distributions and missing values within them can potentially introduce
bias to the causal estimands. In this article, we propose a framework to
estimate causal effects from decentralized data sources. The proposed framework
avoid exchanging raw data among the sources, thus contributing towards
privacy-preserving causal learning. Three instances of the proposed framework
are introduced to estimate causal effects across a wide range of diverse
scenarios within a federated setting. (1) FedCI: a Bayesian framework based on
Gaussian processes for estimating causal effects from federated observational
data sources. It estimates the posterior distributions of the causal effects to
compute the higher-order statistics that capture the uncertainty. (2)
CausalRFF: an adaptive transfer algorithm that learns the similarities among
the data sources by utilizing Random Fourier Features to disentangle the loss
function into multiple components, each of which is associated with a data
source. It estimates the similarities among the sources through transfer
coefficients, and hence requiring no prior information about the similarity
measures. (3) CausalFI: a new approach for federated causal inference from
incomplete data, enabling the estimation of causal effects from multiple
decentralized and incomplete data sources. It accounts for the missing data
under the missing at random assumption, while also estimating higher-order
statistics of the causal estimands. The proposed federated framework and its
instances are an important step towards a privacy-preserving causal learning
model.
