Research Of Causal Reasoning Based On Bayesian Network

Discovering,modeling and understanding causal mechanisms behind natural phenomena are fundamental tasks in numerous scientific disciplines.Causal knowledge can facilitate various machine learning tasks,including semi-supervised learning and domain adaptation.Bayesian network(BN)is an effective tool for knowledge representation and reasoning under uncertainty,it encodes a joint probability distribution over a set of random variables in the form of directed acyclic graph(DAG).BN is also called causal network,which uses a graphical model to represent the dependency relationships between random variables and provides a framework to represent causal information.Bayesian network classifier(BNC)is a special BN,which is specially used to solve classification problems.Naive Bayes(NB)is the simplest BNC,which assumes that all attributes are independent of each other given class variable.However,the independence assumption of NB rarely holds in practice,and may affect its classification performance.To alleviate the assumption of NB,researchers propose to use information-theoretic metrics,such as conditional mutual information to learn dependency relationships between attributes.However,due to the symmetry of conditional mutual information,it cannot be used to identify directed causal relationships.Furthermore,since conditional mutual information can only be used to learn the dependencies between pairs of attributes,thus the resulting network topology is necessarily locally optimal rather than globally optimal solution.The relationship between statistical dependency and causality is at the heart of all statistical approaches to causal inference.To bridge the gap between Bayesian inference and causal reasoning when learning BNC,this paper assumes that strong dependence is an essential prerequisite for significant causality.Log likelihood function can evaluate the extents to which the learned model topologies fit data,based on the log likelihood function,this paper proposes to use the significance of point-wise log-likelihood function to learn the causality implicated in testing instance,and for a given testing instance,different causal relationships can be learned by assigning different class labels.In addition,conditional entropy function can measure the uncertainty of variables under given condition,this paper proposes the point-wise conditional entropy function by extending the conditional entropy function to measure the uncertainty of variable values under given condition.And this paper introduces the point-wise conditional causality function to verify the rationality of the learned causality.The resulting instantiated causal network(ICN)can represent causalities in terms of causal science,and corresponding joint probability can fit training data in terms of data science.To evaluate the effectiveness of our proposed ICN,this paper compares the performance of ICN and other algorithms in terms of zero-one loss,root mean square error(RMSE),bias and variance.Furthermore,this paper uses the Friedman test to analyze the differences between all compared algorithms,and uses the significance test of causality to analyze the ability of the model to express causality.The experimental results on 35 datasets show that ICN achieves competitive classification performance and excellent causal interpretation compared to single-model BNC(e.g.,TAN and SKDB)and ensemble BNCs(e.g.,WATAN,SLB and TAODE).