Multi-task Causal Learning with Gaussian Processes
Multi-task Causal Learning with Gaussian Processes
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发表时间：
2020-09
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通讯作者：
Virginia Aglietti;T. Damoulas;Mauricio A Álvarez;Javier Gonz'alez
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作者：
Virginia Aglietti;T. Damoulas;Mauricio A Álvarez;Javier Gonz'alez
研究了因果模型中定义在有向无环图（DAG）上的一组干预函数的相关结构的学习问题。当我们有兴趣共同学习干预措施对DAG中不同变量子集的因果影响时，这很有用，这在医疗保健或运筹学等领域很常见。我们提出了第一个多任务因果高斯过程（GP）模型，我们称之为DAG-GP，它允许在连续干预和不同变量的实验之间共享信息。DAG-GP在数据可用性方面适应不同的假设，并通过定义良好的积分算子捕获不同维度输入空间中函数之间的相关性。我们给出了理论结果，详细说明何时以及如何DAG-GP模型可以制定取决于DAG。我们测试其预测的质量和校准的不确定性。与单任务模型相比，DAG-GP在各种真实的和合成设置中实现了最佳拟合性能。此外，当在顺序决策框架（例如主动学习或贝叶斯优化）中使用时，它有助于比竞争方法更快地选择最佳干预措施。
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.