利用干预数据推断变量联合分布，提升因果特征选择与分布推断精度。
Estimating Joint Interventional Distributions from Marginal Interventional Data
- 基于最大熵原理融合观测与单变量干预数据，构建联合分布模型。
- 在合成数据上优于现有数据融合方法，接近需全变量观测的KCI检验性能。
- 适用于仅有部分变量干预数据的场景，适合因果推断与数据受限研究者。
本文提出一种基于最大熵原理的方法，利用观测数据和单变量干预数据联合推断所有变量的联合条件分布。通过引入拉格朗日对偶性，证明在干预约束下的因果最大熵问题解仍属于指数族分布。该方法可完成两项任务：一是从混合观测与单变量干预数据中进行因果特征选择；二是推断联合干预分布。在合成数据上的实验表明，所提方法在数据融合任务中表现优于现有方法，且性能接近需全变量联合观测的KCI检验，仅需部分变量的干预数据即可实现高精度推断。
原文摘要 · Abstract (English)
In this paper we show how to exploit interventional data to acquire the joint conditional distribution of all the variables using the Maximum Entropy principle. To this end, we extend the Causal Maximum Entropy method to make use of interventional data in addition to observational data. Using Lagrange duality, we prove that the solution to the Causal Maximum Entropy problem with interventional constraints lies in the exponential family, as in the Maximum Entropy solution. Our method allows us to perform two tasks of interest when marginal interventional distributions are provided for any subset of the variables. First, we show how to perform causal feature selection from a mixture of observational and single-variable interventional data, and, second, how to infer joint interventional distributions. For the former task, we show on synthetically generated data, that our proposed method outperforms the state-of-the-art method on merging datasets, and yields comparable results to the KCI-test which requires access to joint observations of all variables.
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