基于加性噪声模型的缺失数据因果推断 *

推断数据间存在的因果关系是很多科学领域中的一个基础问题.然而现在暂时还没有快速有效的方法对缺失数据进行因果推断。为此，文中提出一种基于加性噪声模型下适应缺失数据的因果推断算法.该算法是基于加性噪声模型下利用最大似然估计法结合加权样本修复数据的思想构造以似然函数形式的模型评分函数，并以此度量模型相对于缺失数据集的优劣程度，通过迭代学习确定因果方向.每次迭代学习包括使用参数修复数据和在修复后的完整数据集下估计参数.该方法既解决了加性噪声模型中映射函数的参数学习困难性问题，又避免了现有学习方法所存在的主要问题。实验表明，在数据缺失比例扩大的情况下该算法仍具有较高识别能力.

Causal inference with missing data based on additive noise models

Discovering causality from data set is one of the basic problems in many scientific fields. However, there is still no fast and effective method to discover causality with missing data. For this reason, this article developed an approach based on additive noise model for inferring causality with missing data. The algorithm used maximum likelihood estimation and the thought of filling data with fractional samples based on additive noise model to construct a model score function of the likelihood function,for measuring the quality which the model relative to the missing data set. At last it can infer the causal direction from the results.Each iterative learning included that using parameters to repair the data and estimating parameters with the new complete data. This method can resolve the difficulty estimation of the functions in additive noise model and the main problems in the existing algorithms. Simulation experiments show that the algorithm still has a high ability to identify causal direction in the case of large proportion of data loss.