Integration, inference, and management of spatial information usingBayesian networks: perceptual organization

The formalism of Bayesian networks provides a very elegant solution, in a probabilistic framework, to the problem of integrating top-down and bottom-up visual processes, as well serving as a knowledge base. The formalism is modified to handle spatial data, and thus the application of Bayesian networks is extended to visual processing. The modified form is called the perceptual inference network (PIN). The theoretical background of a PIN is presented, and its viability is demonstrated in the context of perceptual organization. Perceptual organization imparts robustness, efficiency, and a qualitative and holistic nature to vision. Thus far, the approaches to the problem of perceptual organization have been purely bottom up, without much top-down knowledge-base influence, and are therefore entirely dependent on the inputs, which are obviously imperfect. The knowledge base, besides coping with such input imperfection, also makes it possible to integrate multiple organizations and form a composite organization hypothesis. The PIN imparts an active inferential and integrating nature to perceptual organization in an elegant probabilistic framework     

Causal dynamic inference

We suggest a general logical framework for causal dynamic reasoning. As a first step, we introduce a uniform structural formalism and assign it two kinds of semantics, abstract dynamic models and relational models. The corresponding completeness results are proved. As a second step, we extend the structural formalism to a two-sorted state-transition calculus, and prove its completeness with respect to the associated relational semantics.     

Fuzzy independence and extended conditional probability

In many applications, the use of Bayesian probability theory is problematical. Information needed to feasibility calculate is unavailable. There are different methodologies for dealing with this problem, e.g., maximal entropy and Dempster-Shafer Theory. If one can make independence assumptions, many of the problems disappear, and in fact, this is often the method of choice even when it is obviously incorrect. The notion of independence is a 0–1 concept, which implies that human guesses about its validity will not lead to robust systems. In this paper, we propose a fuzzy formulation of this concept. It should lend itself to probabilistic updating formulas by allowing heuristic estimation of the “degree of independence.” We show how this can be applied to compute a new notion of conditional probability (we call this “extended conditional probability”). Given information, one typically has the choice of full conditioning (standard dependence) or ignoring the information (standard independence). We list some desiderata for the extension of this to allowing degree of conditioning. We then show how our formulation of degree of independence leads to a formula fulfilling these desiderata. After describing this formula, we show how this compares with other possible formulations of parameterized independence. In particular, we compare it to a linear interpolant, a higher power of a linear interpolant, and to a notion originally presented by Hummel and Manevitz [Tenth Int. Joint Conf. on Artificial Intelligence, 1987]. Interestingly, it turns out that a transformation of the Hummel-Manevitz method and our “fuzzy” method are close approximations of each other. Two examples illustrate how fuzzy independence and extended conditional probability might be applied. The first shows how linguistic probabilities result from treating fuzzy independence as a linguistic variable. The second is an industrial example of troubleshooting on the shop floor.     

Least-squares independence regression for non-linear causal inference under non-Gaussian noise

The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model through the minimization of an estimator of the squared-loss mutual information between inputs and residuals. A notable advantage of LSIR is that tuning parameters such as the kernel width and the regularization parameter can be naturally optimized by cross-validation, allowing us to avoid overfitting in a data-dependent fashion. Through experiments with real-world datasets, we show that LSIR compares favorably with a state-of-the-art causal inference method.     

Causal inference for time series analysis: problems,methods and evaluation

Knowledge and Information Systems - Time series data are a collection of chronological observations which are generated by several domains such as medical and financial fields. Over the years,...     

Conditional independence in probability theory on MV-algebras

Conditional independence relation of observables on an MV-algebra with product is formulated and basic properties are proven. An analogy with a classical definition of conditional independence of random variables is discussed and the MV-algebraic concept of conditioning is further explored.     

Evidence aggregation networks for fuzzy logic inference

Fuzzy logic has been applied in many engineering disciplines. The problem of fuzzy logic inference is investigated as a question of aggregation of evidence. A fixed network architecture employing general fuzzy unions and intersections is proposed as a mechanism to implement fuzzy logic inference. It is shown that these networks possess desirable theoretical properties. Networks based on parameterized families of operators (such as Yager's union and intersection) have extra predictable properties and admit a training algorithm which produces sharper inference results than were earlier obtained. Simulation studies corroborate the theoretical properties.     

Discrete recurrent neural networks for grammatical inference

Describes a novel neural architecture for learning deterministic context-free grammars, or equivalently, deterministic pushdown automata. The unique feature of the proposed network is that it forms stable state representations during learning-previous work has shown that conventional analog recurrent networks can be inherently unstable in that they cannot retain their state memory for long input strings. The authors have previously introduced the discrete recurrent network architecture for learning finite-state automata. Here they extend this model to include a discrete external stack with discrete symbols. A composite error function is described to handle the different situations encountered in learning. The pseudo-gradient learning method (introduced in previous work) is in turn extended for the minimization of these error functions. Empirical trials validating the effectiveness of the pseudo-gradient learning method are presented, for networks both with and without an external stack. Experimental results show that the new networks are successful in learning some simple pushdown automata, though overfitting and non-convergent learning can also occur. Once learned, the internal representation of the network is provably stable; i.e., it classifies unseen strings of arbitrary length with 100% accuracy.     

Causal temporal constraint networks for representing temporal knowledge

In this work we describe causal temporal constraint networks (CTCN) as a new computable model for representing temporal information and efficiently handling causality. The proposed model enables qualitative and quantitative temporal constraints to be established, introduces the representation of causal constraints, and suggests mechanisms for representing inexact temporal knowledge. The temporal handling of information is achieved by structuring the information in different interpretation contexts, linked to each other through an inference mechanism which obtains interpretations that are consistent with the original temporal information. In carrying out inferences, we take into account the temporal relationships between events, the possible inexactitude associated with the events, and the atemporal or static information which affects the interpretation pattern being considered. The proposed schema is illustrated with an application developed using the CommonKADS methodology.     

Self-organizing mixture networks for probability density estimation

A self-organizing mixture network (SOMN) is derived for learning arbitrary density functions. The network minimizes the Kullback-Leibler information metric by means of stochastic approximation methods. The density functions are modeled as mixtures of parametric distributions. A mixture needs not to be homogenous, i.e., it can have different density profiles. The first layer of the network is similar to Kohonen's self-organizing map (SOM), but with the parameters of the component densities as the learning weights. The winning mechanism is based on maximum posterior probability, and updating of the weights is limited to a small neighborhood around the winner. The second layer accumulates the responses of these local nodes, weighted by the learned mixing parameters. The network possesses a simple structure and computational form, yet yields fast and robust convergence. The network has a generalization ability due to the relative entropy criterion used. Applications to density profile estimation and pattern classification are presented. The SOMN can also provide an insight to the role of neighborhood function used in the SOM.     

混合加噪声模型与条件独立性检测的因果方向推断算法

从可观测的变量中推导出潜在的因果关系是人工智能领域的热点研究之一。传统的基于独立性检测的方法是通过检测V结构来确定一组马尔科夫等价类而非最终的因果关系;而加噪声模型算法却只能适应于低维度的因果网络结构。为此,提出一种采取分治策略的混合加噪声模型与条件独立性检测的因果方向推断方法。首先是将一个n维因果网络分解成n个诱导子网络,分别归入三种基本结构（单度结构、非三角结构和存在三角的结构）中的一种,从理论上分别证明其有效性;其次对每个诱导子网络进行基于加噪声模型算法与条件独立性检测相结合的方向推断;最后把所有子网络合并起来构建成完整的因果关系网络。实验表明,该方法比传统的因果关系推断方法更加有效。     

基于加性噪声模型的缺失数据因果推断 *

推断数据间存在的因果关系是很多科学领域中的一个基础问题.然而现在暂时还没有快速有效的方法对缺失数据进行因果推断。为此,文中提出一种基于加性噪声模型下适应缺失数据的因果推断算法.该算法是基于加性噪声模型下利用最大似然估计法结合加权样本修复数据的思想构造以似然函数形式的模型评分函数,并以此度量模型相对于缺失数据集的优劣程度,通过迭代学习确定因果方向.每次迭代学习包括使用参数修复数据和在修复后的完整数据集下估计参数.该方法既解决了加性噪声模型中映射函数的参数学习困难性问题,又避免了现有学习方法所存在的主要问题。实验表明,在数据缺失比例扩大的情况下该算法仍具有较高识别能力.     

Causal probabilistic networks with both discrete and continuousvariables

An extension of the expert system shell known as handling uncertainty by general influence networks (HUGIN) to include continuous variables, in the form of linear additive normally distributed variables, is presented. The theoretical foundation of the method was developed by S.L. Lauritzen, whereas this report primarily focus on implementation aspects. The approach has several advantages over purely discrete systems. It enables a more natural model of of the domain in question, knowledge acquisition is eased, and the complexity of belief revision is most often reduced considerably     

基于混淆因子隐压缩表示模型的因果推断方法

因果推断方法可以用于在观察数据上发现因果关系。在因果结构含混淆因子的数据上进行因果推断时,可能会受混淆因子的影响而得到错误的因果关系。针对上述问题,提出了一种基于混淆因子隐压缩表示（CHCR）模型的因果推断方法。首先,根据CHCR模型,构造含有对原因变量进行压缩表示的中间隐变量的备选模型;其次,利用贝叶斯信息准则（BIC）计算备选模型评分并选出得分最高的最佳模型;最后,根据最佳模型中的压缩情况判断变量间真正的因果关系。理论分析表明,所提出的方法能够识别经典的基于约束的方法所无法正确分辨的、带有混淆因子的因果结构,且在样本量较小等情况下,BIC评分也可以提高所提方法的表现。实验结果表明,在样本数变化时,所提出的方法在准确率指标上相较于极快因果推断算法（RFCI）等经典方法有显著提升,并适用于各种变量可能取值数不同的情况;在混合不同类型的因果结构时,该方法在准确率指标上高于最大最小爬山算法（MMHC）等经典方法;且该方法能够在Abalone数据集上得到正确的因果关系。     

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.     

Use of conditional probability networks for environmental monitoring

Causal or conditional probability networks (CPNs) are shown to provide a natural framework for combining a time sequence of classified satellite images with other maps for environmental monitoring. The key features of CPNs are described by way of application to an example involving the monitoring of salinization of farmland over time using satellite images and an ancillary dataset derived from a digital terrain model. It is shown that CPNs can be used to improve mapping accuracies by incorporating knowledge about the spatial and temporal variation of the map classes of interest. The methods provide a practical solution to the challenging problem of mapping and monitoring salt in farmland. The representation and propagation of uncertainty within this framework is discussed, as well as the spatial and temporal prediction of images and maps.     

网络内部链路报文丢失率的推测

提出了一种网络内部链路报文丢失率的推测方法。利用端到端测量得到的路径累积生成函数,可以推测链路的累积生成函数,从而得到链路的报文丢失率。基于链路累积生成函数保留的统计信息,运用切尔洛夫界限定理,可以判断报文丢失严重的链路,从而判断链路瓶颈。仿真实验结果验证了方法的有效性。