基于定性互信息的定性概率网歧义性约简

针对符号传播算法在符号相反的两条平行路径上进行推理时常常产生歧义性,提出一种基于定性互信息的歧义性约简方法。首先,给出定性互信息的严格定义。然后,提出基于定性互信息影响强度的定性概率网,进一步区分影响强度,并证明具有强度的定性影响的对称性、传递性和复合性。最后在Antibiotics数据集上,通过与已有方法推理结果的对比实验,验证该歧义性约简方法的正确性和高效性。理论分析和实验结果表明,基于定性互信息的定性概率网既保留定性推理的简明性,又能够有效约简定性推理的歧义性。     

基于粗糙集的定性概率网推理冲突解决方法

定性概率是贝叶斯网的定性抽象,它以有向边上的定性影响代替贝叶斯网中的条件概率参数,描述了变量间增减的趋势,具有高效的推理机制。但定性概率网中信息丢失导致推理的过程中往往产生不确定信息,即推理结果产生冲突。以尽可能消除定性推理中的冲突为出发点,在构建定性概率网时,基于粗糙集属性依赖度理论求解出网中节点间的依赖度,以依赖度作为变量间定性影响的权重,并根据依赖度改进已有的定性概率网推理算法,从而解决定性概率网推理冲突。实例验证表明,该方法既保持了定性概率网高效推理的特性,又能有效解决冲突。     

Bayesian network modelling through qualitative patterns

In designing a Bayesian network for an actual problem, developers need to bridge the gap between the mathematical abstractions offered by the Bayesian-network formalism and the features of the problem to be modelled. Qualitative probabilistic networks (QPNs) have been put forward as qualitative analogues to Bayesian networks, and allow modelling interactions in terms of qualitative signs. They thus have the advantage that developers can abstract from the numerical detail, and therefore the gap may not be as wide as for their quantitative counterparts. A notion that has been suggested in the literature to facilitate Bayesian-network development is causal independence. It allows exploiting compact representations of probabilistic interactions among variables in a network. In the paper, we deploy both causal independence and QPNs in developing and analysing a collection of qualitative, causal interaction patterns, called QC patterns. These are endowed with a fixed qualitative semantics, and are intended to offer developers a high-level starting point when developing Bayesian networks.     

Enhanced qualitative probabilistic networks for resolving trade-offs

Qualitative probabilistic networks were designed to overcome, to at least some extent, the quantification problem known to probabilistic networks. Qualitative networks abstract from the numerical probabilities of their quantitative counterparts by using signs to summarise the probabilistic influences between their variables. One of the major drawbacks of these qualitative abstractions, however, is the coarse level of representation detail that does not provide for indicating strengths of influences. As a result, the trade-offs modelled in a network remain unresolved upon inference. We present an enhanced formalism of qualitative probabilistic networks to provide for a finer level of representation detail. An enhanced qualitative probabilistic network differs from a basic qualitative network in that it distinguishes between strong and weak influences. Now, if a strong influence is combined, upon inference, with a conflicting weak influence, the sign of the net influence may be readily determined. Enhanced qualitative networks are purely qualitative in nature, as basic qualitative networks are, yet allow for resolving some trade-offs upon inference.     

基于论据系统的带权定性概率推理机

定性概率推理是不确定性推理领域的一种重要方法。将定性概率推理的论据系统方法和抽象系统方法二者合而为一,在定性概率推理机(QPR)的基础上提出基于论据系统的带权定性概率推理机(WQPR)。首先扩展了带权定性概率网的定义,讨论了带权定性影响的对称性;其次将带权定性概率推理融入到论据系统中,提出WQPR推理系统,相比QPR能够在更精确的尺度进行不确定性推理,并证明了系统的正确性与完备性。     

Context-specific sign-propagation in qualitative probabilistic networks

Qualitative probabilistic networks are qualitative abstractions of probabilistic networks, summarising probabilistic influences by qualitative signs. As qualitative networks model influences at the level of variables, knowledge about probabilistic influences that hold only for specific values cannot be expressed. The results computed from a qualitative network, as a consequence, can be weaker than strictly necessary and may in fact be rather uninformative. We extend the basic formalism of qualitative probabilistic networks by providing for the inclusion of context-specific information about influences and show that exploiting this information upon reasoning has the ability to forestall unnecessarily weak results.     

An adaptive reasoning approach towards efficient ordering of composite hypotheses

A Bayesian network is a knowledge representation framework for encoding both qualitative and quantitative probabilistic dependencies among a set of propositional (or random) variables. An important type of probabilistic inference in a Bayesian network is the derivation of the most probable composite hypotheses — a set of hypotheses composed of multiple variables in a network. Such a type of probabilistic inference, however, is computationally intractable. In this paper an adaptive reasoning approach based on qualitative interval arithmetic is proposed as a method of dealing with the computational problem. Using this approach, a qualitative boundary, which reflects the upper and lower limits of a posterior likelihood, can be derived for each composite hypothesis. The advantage ofbounding each composite hypothesis qualitatively is that the quantitative values of the posterior likelihoods are not all necessary in the course of an inference. Consequently, an exhaustive evaluation can be avoided. The complexity of the proposed approach can be demonstrated to be no worse than that of a direct computation and in some cases, the computation is only a small fraction of that required in a straightforward direct computation.This work was supported in part by a grant to Queens College from the General Research Branch, National Institute of Health under grant No. RR-07064, and in part by a grant from the City University of New York PSC-CUNY Research Award Program.     

Quantitative Inference by Qualitative Semantic Knowledge Mining with Bayesian Model Averaging

In this paper, we consider the problem of performing quantitative Bayesian inference and model averaging based on a set of qualitative statements about relationships. Statements are transformed into parameter constraints which are imposed onto a set of Bayesian networks. Recurrent relationship structures are resolved by unfolding in time to Dynamic Bayesian networks. The approach enables probabilistic inference by model averaging, i.e. it allows to predict probabilistic quantities from a set of qualitative constraints without probability assignment on the model parameters. Model averaging is performed by Monte Carlo integration techniques. The method is applied to a problem in a molecular medical context: We show how the rate of breast cancer metastasis formation can be predicted based solely on a set of qualitative biological statements about the involvement of proteins in metastatic processes.     

Explaining `explaining away'

`Explaining away' is a common pattern of reasoning in which the confirmation of one cause of an observed or believed event reduces the need to invoke alternative causes. The opposite of explaining away also an occur, where the confirmation of one cause increases belief in another. A general qualitative probabilistic analysis of intercausal reasoning is provided and the property of the interaction among the causes (product synergy) that determines which form of reasoning is appropriate is identified. Product synergy extends the qualitative probabilistic network (QPN) formalism to support qualitative intercausal inference about the directions of change in probabilistic belief. The intercausal relation also justifies Occam's razor, facilitating pruning in the search for likely diagnoses     

Qualitative-probabilistic-network-based modeling of temporal causalities and its application to feedback loop identification

Modeling and analysis of time-series data attract much attention in data mining and knowledge discovery community due to their many applications in financial analysis, automation control, etc. In such applications, time-series data usually contain several attributes that may be causally dependent in historical time slices. Dangerous feedback loops of attributes’ dependent relationships can make the system collapse due to amplification or oscillation of attribute values. Motivated by efficient analysis of causalities in time-series data, we propose a temporal qualitative probabilistic graphical model in this paper. From given time-series sample data, we construct the structure of the temporal qualitative probabilistic network (TQPN) and derive the corresponding qualitative influences on directed edges. We then present the approach for TQPN reasoning with time-series features. Consequently, positive time-series feedback loops are defined, and the approach to identify them is proposed. Preliminary experiments show that our proposed method is not only feasible but also efficient.     

Causal independence for probability assessment and inference usingBayesian networks

A Bayesian network is a probabilistic representation for uncertain relationships, which has proven to be useful for modeling real-world problems. When there are many potential causes of a given effect, however, both probability assessment and inference using a Bayesian network can be difficult. In this paper, we describe causal independence, a collection of conditional independence assertions and functional relationships that are often appropriate to apply to the representation of the uncertain interactions between causes and effect. We show how the use of causal independence in a Bayesian network can greatly simplify probability assessment as well as probabilistic inference     

A probabilistic inference model for recommender systems

Recommendation is an important application that is employed on the Web. In this paper, we propose a method for recommending items to a user by extending a probabilistic inference model in information retrieval. We regard the user’s preference as the query, an item as a document, and explicit and implicit factors as index terms. Additional information sources can be added to the probabilistic inference model, particularly belief networks. The proposed method also uses the belief network model to recommend items by combining expert information. Experimental results on real-world data sets show that the proposed method can improve recommendation effectiveness.     

On probabilistic inference by weighted model counting

A recent and effective approach to probabilistic inference calls for reducing the problem to one of weighted model counting (WMC) on a propositional knowledge base. Specifically, the approach calls for encoding the probabilistic model, typically a Bayesian network, as a propositional knowledge base in conjunctive normal form (CNF) with weights associated to each model according to the network parameters. Given this CNF, computing the probability of some evidence becomes a matter of summing the weights of all CNF models consistent with the evidence. A number of variations on this approach have appeared in the literature recently, that vary across three orthogonal dimensions. The first dimension concerns the specific encoding used to convert a Bayesian network into a CNF. The second dimensions relates to whether weighted model counting is performed using a search algorithm on the CNF, or by compiling the CNF into a structure that renders WMC a polytime operation in the size of the compiled structure. The third dimension deals with the specific properties of network parameters (local structure) which are captured in the CNF encoding. In this paper, we discuss recent work in this area across the above three dimensions, and demonstrate empirically its practical importance in significantly expanding the reach of exact probabilistic inference. We restrict our discussion to exact inference and model counting, even though other proposals have been extended for approximate inference and approximate model counting.     

概率图模型推理方法的研究进展

近年来概率图模型已成为不确定性推理的研究热点,在人工智能、机器学习与计算机视觉等领域有广阔的应用前景.根据网络结构与查询问题类型的不同,系统地综述了概率图模型的推理算法.首先讨论了贝叶斯网络与马尔可夫网络中解决概率查询问题的精确推理算法与近似推理算法,其中主要介绍精确推理中的VE算法、递归约束算法和团树算法,以及近似推理中的变分近似推理和抽样近似推理算法,并给出了解决MAP查询问题的常用推理算法;然后分别针对混合网络的连续与混合情况阐述其推理算法,并分析了暂态网络的精确推理、近似推理以及混合情况下的推理;最后指出了概率图模型推理方法未来的研究方向.     

Ising图模型概率推理的计算复杂性

图模型概率推理的主要任务是通过对联合概率分布进行变量求和来计算配分函数、变量边缘概率分布、条件 概率分布等。图模型概率推理计算复杂性及近似概率推理的计算复杂性是一重要的理论问题,也是设计概率推理算 法和近似概率推理算法的理论基础。研究了Ising图模型概率推理的计算复杂性,包括概率推理的难解性及不可近似 性。具体地,通过构建#2 SA"I'问题到Icing图模型概率推理问题的多项式时间计数归约,证明在一般 Ising图模型上 计算配分函数、变量边缘概率分布、条件概率分布的概率推理问题是#P难的,同时证明Icing图模型近似概率推理问 题是NP难的,即一般Icing图模型上的概率推理问题是难解且不可近似的。     

A Bayesian Method for the Induction of Probabilistic Networks from Data

This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.     

Mobile context inference using two-layered Bayesian networks for smartphones

Recently, mobile context inference becomes an important issue. Bayesian probabilistic model is one of the most popular probabilistic approaches for context inference. It efficiently represents and exploits the conditional independence of propositions. However, there are some limitations for probabilistic context inference in mobile devices. Mobile devices relatively lacks of sufficient memory. In this paper, we present a novel method for efficient Bayesian inference on a mobile phone. In order to overcome the constraints of the mobile environment, the method uses two-layered Bayesian networks with tree structure. In contrast to the conventional techniques, this method attempts to use probabilistic models with fixed tree structures and intermediate nodes. It can reduce the inference time by eliminating junction tree creation. To evaluate the performance of this method, an experiment is conducted with data collected over a month. The result shows the efficiency and effectiveness of the proposed method.     

概率生成模型变分推理方法综述

概率生成模型是知识表示的重要方法,在该模型上计算似然函数的概率推理问题一般是难解的.变分推理是重要的确定性近似推理方法,具有较快的收敛速度、坚实的理论基础.尤其随着大数据时代的到来,概率生成模型变分推理方法受到工业界和学术界的极大关注.综述了多种概率生成模型变分推理框架及最新进展,具体包括:首先综述了概率生成模型变分推理一般框架及基于变分推理的生成模型参数学习过程;然后对于条件共轭指数族分布,给出了具有解析优化式的变分推理框架及该框架下可扩展的随机化变分推理;进一步,对于一般概率分布,给出了基于随机梯度的黑盒变分推理框架,并简述了该框架下多种变分推理算法的具体实现;最后分析了结构化变分推理,通过不同方式丰富变分分布提高推理精度并改善近似推理一致性.此外,展望了概率生成模型变分推理的发展趋势.     

对弧进行删除的Bayes网络近似方法

弧的删除是一种对Bayes网络模型进行近似的方法。文中以Kullback-Leibler偏差作为近似网络和原网络概率分布误差的测度,给出了近似网络在此测度意义下的最优参数。同时,也给出了通过对原网络删除多条弧进行近似的启发式算法,当给定一个误差上界时,可以使用此算法寻找满足误差要求的近似网络。     

Probabilistic Reasoning Under Coherence in System P

In this paper we apply a probabilistic reasoning under coherence to System P. We consider a notion of strict probabilistic consistency, we show its equivalence to Adams' probabilistic consistency, and we give a necessary and sufficient condition for probabilistic entailment. We consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our coherence-based approach, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of the degradation of the inference rules when interpreted in probabilistic terms. We also examine the disjunctive Weak Rational Monotony rule of System P⁺ proposed by Adams in his extended probabilistic logic. Finally, we examine the propagation of lower bounds with real -values and, to illustrate our probabilistic reasoning, we consider an example.