概率图模型作为一类有力的工具,能够简洁地表示复杂的概率分布,有效地(近似)计算边缘分布和条件分布,方便地学习概率模型中的参数和超参数.因此,它作为一种处理不确定性的形式化方法,被广泛应用于需要进行自动的概率推理的场合,例如计算机视觉、自然语言处理.回顾了有关概率图模型的表示、推理和学习的基本概念和主要结果,并详细介绍了这些方法在两种重要的概率模型中的应用.还回顾了在加速经典近似推理算法方面的新进展.最后讨论了相关方向的研究前景.

Probabilistic graphical models are powerful tools for compactly representing complex probability distributions, efficiently computing (approximate) marginal and conditional distributions, and conveniently learning parameters and hyperparameters in probabilistic models. As a result, they have been widely used in applications that require some sort of automated probabilistic reasoning, such as computer vision and natural language processing, as a formal approach to deal with uncertainty. This paper surveys the basic concepts and key results of representation, inference and learning in probabilistic graphical models, and demonstrates their uses in two important probabilistic models. It also reviews some recent advances in speeding up classic approximate inference algorithms, followed by a discussion of promising research directions.

从信息效应的视野审视数学推理模式。数学推理并非完全按照演绎方式进行，而是一种由“上位信息”得出“下位信息”的过程，这个过程的产生往往是由“上位信息”中的某个“信息碎片”激活了认知结构中的某个信息加工模块而得出“下位信息”的。若把传统的数学演绎推理视作“依概率为1”的信息加工模式，在日常数学教学活动中则需要更多关注“依概率不为1或不确定概率”的信息加工方式。信息效应观将有助于拓广数学推理教学研究的视野。

As we examine the Mathematical reasoning mode from the perspective of information effect, we will find that Mathematical reasoning doesn’t proceed completely according to the deductive method; it’s a process of obtaining “latter information” from “former information” and this process usually come about by obtaining “latter information” from a certain information processing module in the cognitive structure which is activated by some “information fragment” in the “former information”. If we regard the traditionally consistently used Mathematical deductive reasoning as the information processing models of“the probability of one”, we should pay more attention to the information processing models of“the probability is not one or it’s undetermined”in daily Mathematical education activities. The information effect view will contribute to broaden the horizons of researches of Mathematical reasoning education.

基于MV代数(Many-Valued algebra)语义,通过在MV代数赋值格和全体命题集上分别建立概率测度,利用积分方法提出了一种格值逻辑上命题的概率真度.由此可诱导出命题集上的伪距离,进而在格值逻辑上建立了概率逻辑度量空间并展开程度化推理.本文将计量逻辑学中近似推理方法推广到格值逻辑上,为格值逻辑的程度化提供了一种可行的方法.

Based on the notion of MV-algebra semantics ,probability measure is set up in MV-algebra evaluation lattice and set of all propositions ,and a probability truth degree of propositions in lattice-valued logic is proposed with integral .Thus pseudo-metric in set of all propositions is induced ,probability logic metric space is established in lattice-valued logic ,and graded reasoning is developed .In summary ,approximate reasoning method in quantitative logic is expanded to lattice-valued logic ,and it is feasible in graded in lattice-valued logic .

针对地区电网继电保护装置的动作行为分析问题，建立了继电保护装置运行原因分析和责任部门评价两大规则体系。采用权值法形成的可信度赋予规则体系的概率模型，结合双层推理方式，形成双层不确定推理的过程，有效地反映了系统运行方式与保护逻辑动态过程的结合；采用基于概率模型的不确定推理方式实现责任部门评价过程，以提高评价过程的可靠性。现场试用过程表明：采用该方法评价继电保护装置的实际运行情况的结果正确，具有很好的实用价值。

For the problem of the relay protection device behavior analysis in the regional power grid, two rules of operation reason analysis of relay protection device and the responsibility department evalua-tion were built.Probability model of credibility given rules by weighting method was used to form a double uncertain reasoning process,which combined with double-layer reasoning.The combination of the system operation mode and the protection logic and dynamic process was effectively reflected.Uncer-tainty reasoning based on the probability model was used to evaluate the responsibility department,to improve the reliability of the evaluation process.The trial process shows that it is correct to evaluate the practical operation of relay protection device,and it has highly practicability.

针对一类非线性多模态的化工过程,提出一种基于概率核主元的混合模型（PKPCAM）,并利用贝叶斯推理策略进行过程监控与故障诊断。在提出的模型中,每个操作模态由一个局部化的概率核主元分量描述,从而构建的一系列分量对应了不同的操作模态。首先,将过程数据从原始的度量空间投影到高维特征空间;其次,在该特征空间建立概率主元混合模型,从概率角度刻画数据集的多个局部分量特征;最后,在提取的核主元分量内获得测试样本的后验概率,结合模态内的马氏距离贡献度,提出基于贝叶斯推理的全局概率指标进行故障检测,同时利用模态内变量的相对贡献度,基于全局贡献度指标进行故障诊断。利用TEP仿真平台,与基于k均值聚类的次级主元分析和核主元分析的方法进行了对比分析,验证了提出的贝叶斯推理的PKPCAM方法对非线性多模态过程进行故障检测与诊断的可行性和有效性。

the sub-principal component analysis usingk-means clustering and the kernel principal component analysis, the feasibility and effectiveness by the proposed Bayesian inference based PKPCAM method for fault detection and diagnosis in nonlinear and multimode process was validated on Tennessee Eastman process.