基于Factored Frontier算法的动态贝叶斯网络灵敏性分析方法  

A sensitivity analysis method of dynamic Bayesian networks based on factored frontier algorithm

作　　者：姚宏亮[1] 袁正[1] 王浩[1] 

机构地区：[1]合肥工业大学计算机与信息学院,合肥230009

出　　处：《南京大学学报（自然科学版）》2012年第4期412-420,共9页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(61175051;61070131);国家重点基础研究发展计划(2009CB326203)

摘　　要：贝叶斯网络的灵敏性分析是研究模型局部参数或证据微小变化对于目标结点所产生的影响,以发现复杂系统的重要参数和结构.然而对于动态贝叶斯网络,当前还没有一种有效的灵敏性分析算法.针对隐马尔科夫模型(HMM)灵敏性分方法不能用于分析动态贝叶斯网络灵敏性和灵敏性分析计算复杂性高的问题,提出一种可有效处理动态贝叶斯网络灵敏性分析算法(SA_FF).SA_FF算法利用FF近似推理算法(Factored Frontier)思想求解动态贝叶斯网络的灵敏性函数,通过对马尔可夫毯所构成边界(Frontier)的动态推理建立参数与目标结点条件概率分布之间的函数关系;SA_FF算法在灵敏性函数推理计算过程中,通过对局部性边界的边缘化进行信息传播,不需要对模型的联合概率分布进行更新,显著提高了计算的效率,且可用于多参数灵敏性分析,但会引入一定的误差;进而,通过误差分析证明所引入的误差是有界的.最后,通过实例计算的比较和分析显示SA_FF算法的有效性.The sensitivity analysis of Bayesian networks is to research on the influence for object node when the little change of local parameters or evidence, so the sensitivity analysis is used to discovery important parameters and structure of complex system. H^wever, there is no an effective sensitivity algorithm for Dynamic Bayesian Networks （DBNs）. The sensitivity analysis methods of HMM model can not be used to deal with general DBNs, and the computation complexity is very high. Thus, based on Factored Frontier algorithm, a new sensitivity analysis algorithm（SA_FF） is presented, which can effectively deal with sensitivity analysis problems of DBNs. Based on FF algorithm, SA_FF algorithm can calculate the sensitivity function of regular DBNs. The relation between given parameters and object node distribution is established by dynamic reason for frontier nodes （the nodes in Markov Blanket）. The SA_FF algorithm significantly improves computational efficiency by marginalizating of local frontierrather than updating the joint probability distribution of model. On the other hand, the SA_FF algorithm can be used for multiple parameters sensitivity analysis of DBNs. Although some error is induced, the error is bounded by demonstration. Finally, the effectiveness of SA_FF algorithm is illustrated by some examples.

关 键 词：动态贝叶斯网络 因式边界算法 灵敏性分析 SA_FF算法 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]