Research On Multi-objective Bayesian Network Structure Learning And Application

Bayesian network is a probabilistic graph model,which can be used to express the relationship between variables.Structure learning is the key step of Bayesian network modeling,and it is also the basis of network parameter learning and probabilistic reasoning.The existing score-based structure learning algorithms are mostly based on singleobjective optimization,but in essence,the scores are weighted by adding the complexity score and log-likelihood score of the structure.The information provided by the two scores is not fully used to guide the search.In this paper,the multi-objective Bayesian network structure learning algorithm and its application are researched.The main research work is as follows:(1)Aiming at the problem that the the information provided by model complexity and log-likelihood score can not be fully used to guide the search in the structure learning methods based on single-objective optimization,a bi-objective Bayesian network structure learning algorithm(BOS)is proposed.First of all,inspired by the structure learning algorithm in ordering space,BOS designs an initialization strategy based on the node order.Then BOS designed genetic operators based on the exchange and mutation of edges in the structure to avoid the invalid search.After the algorithm stops,BOS can output a set of Pareto optimal solutions.To verify the effectiveness of BOS,the experiments are conducted on eight data sets.Experiments show that the Pareto optimal solution sets searched by BOS on four Bayesian network data sets always contain the ground truth,and BOS’s performance on six Bayesian network data sets is better than that of classical single-objective structure learning algorithms.(2)Aiming at the problem that BOS performs well in small data sets,but due to the lack of space constraint,it can not be extended to large data sets,a bi-objective Bayesian network structure learning algorithm via skeleton(BBS)is proposed.First,BBS designs an random ordering prior initialization operator,which generates a skeleton by conditional independence test.Then,the operator generates individuals by random node orders,thus ensuring that there are no illegal individuals in the initial population.After that,BBS proposes a crossover operator based on Pareto rank to explore the diversity of solutions and uses a skeleton-guided mutation operator to jump out of local optimization.Finally,BBS defines the edge weight function for the final solution selection in Pareto optimal set.Compared with the single-objective structure learning algorithm,BBS can always find a set of solutions closer to the ground truth.Compared with the bi-objective structure learning algorithm,BBS can be applied to larger data sets.To the educational problem of discovering the influencing factors of students’ academic performance,BBS provides higher quality solutions and is featured with the flexibility of solution selection.(3)Aiming at the problem that the existing knowledge tracing algorithms can’t consider both explanatory ability and accuracy,a Bayesian network assisted knowledge tracing model(BAKT)is proposed,which uses the Bayesian network to express and reason the explanatory feature relations in educational problems.First of all,BAKT extracts the information of learners and exercises through the information of learners’ learning records: the mastery of knowledge concepts,the difficulty of exercises,and the ability level of learners.Then BAKT uses the bi-objective structure learning method to construct the Bayesian network structure with these features.Finally,according to the existing data,the inference of the Bayesian network is used to predict whether learners can answer the exercise questions correctly.Experimental results on three classical educational data sets show that BAKT has better prediction performance than common knowledge tracking.Besides,BAKT provides interpretability without a large number of parameters.