Proposition And Test Of Causal Neural Network Model Based On Unknown Intervention

In recent years,a large number of bayesian causal network learning methods have been used to learn bayesian causal network structures.The commonly used methods include fraction-based method^[42,50],constron-based method^{[22,32,38,48]},asymmetric method^[34,39,46]and continuous optimization method^[52,54],etc.These methods usually learn the structure of bayesian network from observation data.However,there are theoretical limitations to being able to identify causal graphs well from observational data alone,and few have applied these methods to intervention data,whereas intervention data provide more information about the underlying causal structure and are more consistent with real-world conditions.In this paper,based on the principle of neural network and causal inference theory,the causal neural network model is used,and the SDI method（a fractional,iterative and continuous comprehensive optimization method）is adopted for optimization iteration.The proposed model approach（M=5,5,8,and 11）was tested on representative synthetic data sets（Chain M,Collider M,Jungel M,Full M）and real data sets（Bnlearn）（Earthquake M,Cancer M,Asia M,and Sach M）,Where,M represents the number of variables,and partial graph recovery is carried out in real data sets of Barley（M=48）and Alarm（M=37）.For the synthetic dataset Chain N,Collider M,Jungle M,and Full M（M=3...13）,all the neural networks are two-layer feed-forward neural networks（MLPs）with Leaky Re LU activation between layers,neural network parameters are orthogonal initialized in the range of（-2.5,2.5）,and all the experiments with composited diagrams of size 3-8 use the same hyperparameter,Both function and structural parameters are optimized by Adam.The learning rate of function parameters is 0.9,and that of structural parameters is 0.1.Ground＿truth MLP model is adopted for modeling of Bnlearn,a real Bayesian network data set.Parameter Settings of ground＿TRUTH MLP model are similar to those of synthetic data set.However,in order to get closer to the causal structure diagram of real data and speed up optimization,The temp parameter needs to be added,that is,the logarithmic output of ground＿truth MLP needs to be divided by the temp parameter before being used for sampling.Experimental results show that Chain M,Collider M,Jungle M,and Full M（M=3...13）,the model can correctly recover all the composite graphs below 10 variables.However,for graphs with more than 10 variables,the model finds that it is more challenging to recover graphs with higher density（such as full M）,and small graphs（M<10）are less sensitive to hyperparameters than large graphs,especially sparsity and acyclic regularization terms.By comparison,the proposed method,SDI,outperforms all other baseline methods and perfectly learns all graphs of 3 to 13 variables（except full）;Through partial graph restoration of Barley（M=48）and Alarm（M=37）in Bn Learn real database,it is found that the accuracy of SDI method on both graphs is over 90%.Figure for all three variables（chain3 fork3,collider3,confounder3）to evaluate the result of the intervention,unknown results show that the causal model than the causal model has better intervention in the distribution of sample logarithm likelihood attributes,and causal model has better generalization ability in the migration task.