一种基于最大最小独立性的因果发现算法

A causal discovery algorithm based on maximum and minimum independence

线性非高斯无环模型(LiNGAM)具有在没有任何先验知识的情况下能够仅仅从观察数据中完整地识别因果网络的优势,这使得它得到了越来越多研究者的关注.然而,现有求解LiNGAM模型的算法中一部分存在对初始值敏感,容易陷入局部最优解的问题,一部分存在对于外生变量识别率低的缺陷.为此,提出了一种基于最大最小独立性的因果发现算法.通过引入自适应的独立性判定参数,根据此参数来找出与其余所有变量回归得到的残差都独立的变量,即为外生变量.该算法不仅避免了传统算法对独立性值差异敏感而导致识别率低的问题,而且也避免了不同数据集对固定独立性参数敏感而导致无法识别的缺陷.将该算法应用于虚拟网络和真实网络中,实验结果都表明,各种维度下该算法都优于现有的其他算法.

The linear non-Gaussian acyclic model（LiNGAM）has the advantage of being able to completely identify the causal network only from the observational data without any prior knowledge,which has been attracting more and more researchers＇ attention.However,in the present solution,some of the algorithms are sensitive to the initial values and would easily fall into the local optimal solution.And others have the disadvantage of low recognition rate of the exogenous variable.We propose an effective casual discovery algorithm based on the maximum and minimum independence.In contrast to the previous methods,our algorithm＇s parameters are obtained through adaptive learning.The details are as follows.Firstly,we formalize the maximum and minimum independence criteria,which is applied to find the minimum values that makes each variable and the relative residuals independent.Secondly,we find one maximum value that makes only one variable and its residuals independent from the corresponding minimum values found at the former step.The value we chose finally is regarded as an independence judgment parameter.In a word,we obtain the appropriate parameter values according to the maximum and minimum independence criteria.In the end,we use this parameter to find those variables that are independent of the residuals returned by all the other variables.Such variable is the exogenous variable.Based on this,we can achieve the goal of selecting greater parameters with different data sets through adaptive learning,rather than giving them a fixed initial value.That is to say,we could getexogenous variables which are more precise with our method.Once the exogenous variables are obtained,all we only need to do is to iteratively find a complete causal order.To be concluded,the algorithm could not only avoids the problem that the traditional algorithm is sensitive to the difference of independence value,but also avoids the defect that different data sets are sensitive to fixed independent parameters.To illustrate the effectiveness of our algorithm,we evaluate our method on virtual networks and real networks.The experimental results show that it outperforms previous approaches consistently under different dimensions.