This paper studies the problem of learning the correlation structure of a set
of intervention functions defined on the directed acyclic graph (DAG) of a
causal model. This is useful when we are interested in jointly learning the
causal effects of interventions on different subsets of variables in a DAG,
which is common in field such as healthcare or operations research. We propose
the first multi-task causal Gaussian process (GP) model, which we call DAG-GP,
that allows for information sharing across continuous interventions and across
experiments on different variables. DAG-GP accommodates different assumptions
in terms of data availability and captures the correlation between functions
lying in input spaces of different dimensionality via a well-defined integral
operator. We give theoretical results detailing when and how the DAG-GP model
can be formulated depending on the DAG. We test both the quality of its
predictions and its calibrated uncertainties. Compared to single-task models,
DAG-GP achieves the best fitting performance in a variety of real and synthetic
settings. In addition, it helps to select optimal interventions faster than
competing approaches when used within sequential decision making frameworks,
like active learning or Bayesian optimization.

该论文研究了在有向无环图（DAG）上定义的一组干预函数的相关结构的学习问题，提出了一种多任务因果高斯过程（GP）模型，称为 DAG-GP，该模型捕捉了不同维度输入空间中的函数之间的相关性，并在实验中测试了其预测质量和校准不确定性。