【作者】 王东明；

【导师】 虞文武； 陈都鑫；

【作者基本信息】 东南大学 ， 数学与应用数学， 2022， 硕士

【摘要】 近年来,随着数据科学的不断发展,在不同的学科背景下产生了大量的时序数据,时序数据的分析和信息挖掘已经成为一个重要的课题。因果推断方法由于可以去除数据中的混杂因素而越来越受到关注。本文主要研究因果熵最优因果理论模型下的因果推断算法以及最优因果推断在时序数据中的应用,具体研究内容有如下两部分。首先,本文在最优因果熵理论和最优因果熵算法的基础上提出了基于邻近度指标的最优因果熵算法,把目标节点的因果父节点搜寻范围控制在邻近度指标要求的范围之内,在保证节点局部因果性被充分挖掘的前提下,大大降低了最优因果熵算法的时间复杂度,使之可以应用到大规模时序网络的因果推断问题中。在推断得到的大规模时序因果网络的基础上,给出了基于社区中心距合并的Louvain社区检测算法,该算法实现了把大规模时序网络划分成为期望个数或期望规模子社区的功能,为交通路网分区控制提供了参考依据。基于KSG因果熵估计方法,本文在Pe Ms交通数据集上应用并验证了算法的有效性,通过研究不同参数的时序因果网络推断结果论证了本算法对邻近度指标参数的选取不敏感,具有一定鲁棒性。考虑到KSG因果熵估计算法需要人为设置超参数,近邻参数k的设置对推断结果的影响很难衡量,因此本文提出了一种基于核密度估计的因果熵估计方法,并基于平均平方积分误差最小给出了最优带宽选取方案,并论证了这是一种非参无偏的因果熵估计方法。此外,为了验证算法的有效性,本文利用结构化因果模型生成序列数据,然后分别采用基于KSG的因果网络推断方法和基于核密度估计的因果网络推断方法对结构化因果模型的图结构进行还原,最终得到结论:基于核密度估计的方法在推断准确度上优于基于KSG估计的方法。最后,本文利用基于核密度估计的方法对鸽群时序数据进行了时序因果网络推断,通过分析时序因果网络结构得到了鸽群在结群飞行时,因果结构切换频繁的结论。本文关于基于熵的因果推断方法的研究扩展了因果理论的应用场景和应用范围,丰富了因果熵估计理论,给出了从样本无偏估计因果熵的方法,对因果理论的发展和应用有一定价值。更多还原

【Abstract】 With the advancement of data science in recent years,a considerable amount of time-series data from many disciplines has been gathered,and the analysis and information mining of time-series data has become a hot issue.And,because of their capacity to eliminate confounding elements from data,causal inference approaches are gaining popularity.The following two parts of this study focus on the causal inference algorithm under the causal entropy optimum causal theory model,as well as the application of optimal causal inference to time-series data.Firstly,an optimal control result algorithm based on the proximity index is implemented in this thesis,based on the theory of target results and the optimal result range algorithm,to ensure that the object’s celestial events are within the proximity target range,ensuring that the equipment is fully utilized.The cause of the accident may be decreased during this period,which can be applied to the problem of network vulnerability exploitation.A community-based prediction model is provided by the network’s fundamental network community,which includes a basic model for computing models,a computing model for predicting network segments,a computing model for predicting network models,and a sub-model for network prediction.One or more sub-community prediction models are provided by a community.The traffic algorithm is calculated using KSG results,and the calculation results of the algorithm’s neighboring degree index are utilized in the calculation results of the probabilistic network parameters applied to the data set,resulting in a high level of accuracy and resilience.The impact of the setting of the neighbor parameter k on the inference outcomes is difficult to assess since the KSG causal entropy estimation technique requires a human hyperparame-ter setup.As a result,using kernel density estimation,this research provides a causal entropy estimate approach that minimizes the mean square integral error.It is proved that the opti-mal bandwidth selection scheme is a nonparametric and unbiased causal entropy estimation approach.To test the algorithm’s effectiveness,this paper generates sequence data using the structured causal model,then restores the graph structure of the structured causal model us-ing the KSG-based causal network inference method and the kernel density estimation-based causal network inference method,and finally obtains Conclusion.In terms of inference accu-racy,the kernel density estimation approach outperforms the KSG estimation method.Finally,we inferred the temporal causal network on the pigeon flock temporal data by using the method based on kernel density estimation,and obtained the conclusion that the causal structure of the pigeon flock switched frequently when the flock flew in a group by analyzing the temporal causal network structure.The research presented in this paper on entropy-based causal inference methods broadens the application scenario and scope of causal theory,enriches the theory of causal entropy es-timation,and provides a method for estimating causal entropy from unbiased samples,all of which are useful for the development and application of causal theory.更多还原