Research On Learning Algorithm For Complex Monotonicity Classification Tasks

In the study of learning algorithms for the complex monotonicity classification tasks,it is important to clarify the monotonicity constraints that exist in the data,and effective u-tilization of these constraints helps us gain more potential value from the data.At present,most work is based on the monotonicity constraints between all features and decisions to solve the monotone classification problem,and they also assume that all sample pairs are comparable.However,many tasks in practice cannot meet these requirements at the same time.Therefore,this thesis focuses on several key points of the monotonicity classifica-tion.First,the multivariate decision trees with monotonicity constraints are proposed for the incomparable sample pairs in monotonicity classification tasks.The algorithms ex-press the relationship between the attributes of incomparable sample through a set of non-negative weighted linear combinations,and use these linear functions to transform incomparable sample pairs into comparable sample pairs,thus ensuring the monotonici-ty of the data division.Then,the multivariate decision tree with monotonicity constraints?MMT?is constructed.In order to find the optimal feature subsets,a more compact mono-tonic multivariate decision tree?MMT-L₁?based on L₁-regularization is proposed.These algorithms not only can handle incomparable sample pairs,but also generate non-negative weights to enhance monotonicity.They effectively improve the performance of monotone classifiers.Second,the partially monotonic decision tree is proposed to solve the problem of coexisting criteria and regular attributes in the complex monotonicity classification tasks.Although the proposed monotonic multivariate decision trees can solve the problem of incomparable sample pairs well,the algorithms are based on the monotonicity constraint relationship between all features and decisions,and are the strict monotone classifica-tion algorithms.However,many monotonicity classification tasks do not satisfy the strict monotonicity constraints.Therefore,the ranking inconsistency rate is proposed to dis-criminate if there is a monotonicity constraint between the features and decisions,and use the ranking inconsistency rate to handle the monotone direction of a single feature and decision,and deal with criteria and regular attributes on the complex monotonic classifi-cation tasks separately.The algorithm can not only handle the monotonic relationship be-tween features and decisions,but also deal with the non-monotonic relationship between features and decisions,thus further improving the performance of monotone classifiers.Finally,based on the limitations of the dominance criteria and the dependence on experts,the monotone bayesian network parameter learning algorithm based on the s-tochastic dominance criteria is proposed.The monotonicity constraints are learned from the data,that ensures the stochastic monotone consistency and reduces the workload of experts defining monotonicity constraints.To analyze the classification tasks in practice from the perspective of dominant criteria,sometimes it is not possible to get a satisfactory solution to the actual problem.The dominance criteria in the strict sense mainly indi-cate that object A is not worse than object B in all features or partial features.However,the actual situation is that the probability that object A is better than object B is greater than or at least equal to the probability that object B is better than object A,it is more consistent with the first-order stochastic dominance criteria.The proposed algorithm can not only learn monotonicity constraints directly from the data,but also apply the cumu-lative distribution interval between parameters to learn more accurate bayesian network parameters.In summary,this thesis solves the problem of incomparable sample pairs and par-tially monotonic classification from the perspective of the dominant criterion.Also,the problem of learning monotonicity constraints based on parameters cumulative distribution interval from the data is solved from the perspective of stochastic dominance criterion.It provides an important algorithm basis for adapting to the complex monotonicity classifi-cation tasks.