Learning directed probabilistic logical models: ordering-search versus structure-search

We discuss how to learn non-recursive directed probabilistic logical models from relational data. This problem has been tackled before by upgrading the structure-search algorithm initially proposed for Bayesian networks. In this paper we show how to upgrade another algorithm for learning Bayesian networks, namely ordering-search. For Bayesian networks, ordering-search was found to work better than structure-search. It is non-obvious that these results carry over to the relational case, however, since there ordering-search needs to be implemented quite differently. Hence, we perform an experimental comparison of these upgraded algorithms on four relational domains. We conclude that also in the relational case ordering-search is competitive with structure-search in terms of quality of the learned models, while ordering-search is significantly faster.     

Two kinds of optimal controls for probabilistic mix-valued logical dynamic networks

This paper addresses two kinds of optimal control problems of probabilistic mix-valued logical control networks by using the semi-tensor product of matrices, and presents a number of new results on the optimal finite-horizon control and the first-passage model based control problems, respectively. Firstly, the probabilistic mix-valued logical control network is expressed in an algebraic form by the semi-tensor product method, based on which the optimal finite-horizon control problem is studied and a new algorithm for choosing a sequence of control actions is established to minimize a given cost functional over finite steps. Secondly, the first-passage model of probabilistic mix-valued logical networks is given and a new algorithm for designing the optimal control scheme is proposed to maximize the corresponding probability criterion. FinMly, an illustrative example is studied to support our new results/algorithms.     

Full-parameter vision navigation based on scene matching for aircrafts

Vision navigation based on scene matching between real-time images and a reference image has many advantages over the commonly used inertial navigation system （INS）, such as no cumulative measurement errors for long-endurance flight. Recent developments in vision navigation are mainly used for partial navigation parameters measurements, such as the position and the relative velocity, which cannot meet the requirements of completely autonomous navigation. We present the concept, principle and method of full-parameter vision navigation （FPVN） based on scene matching. The proposed method can obtain the three-dimensional （3D） position and attitude angles of an aircraft by the scene matching for multiple feature points instead of a single point in existing vision navigations. Thus, FPVN can achieve the geodetic position coordinates and attitude angles of the aircraft and then the velocity vector, attitude angular velocity and acceleration can be derived by the time differentials, which provide a full set of navigation parameters for aircrafts and unmanned aerial vehicles （UAVs）. The method can be combined with the INS and the cumulative errors of the INS can be corrected using the measurements of FPVN rather than satellite navigation systems. The approach provides a completely autonomous and accurate navigation method for long-endurance flight without the help of satellites.     

Constraint-based probabilistic modeling for statistical abduction

We introduce a new framework for logic-based probabilistic modeling called constraint-based probabilistic modeling which defines CBPMs (constraint-based probabilistic models) , i.e. conditional joint distributions P(⋅∣KB) over independent propositional variables constrained by a knowledge base KB consisting of clauses. We first prove that generative models such as PCFGs and discriminative models such as CRFs have equivalent CBPMs as long as they are discrete. We then prove that CBPMs in infinite domains exist which give existentially closed logical consequences of KB probability one. Finally we derive an EM algorithm for the parameter learning of CBPMs and apply it to statistical abduction.     

EXPLOITING SYNTACTIC,SEMANTIC, AND LEXICAL REGULARITIES IN LANGUAGE MODELING VIA DIRECTED MARKOV RANDOM FIELDS

We present a directed Markov random field (MRF) model that combines n‐gram models, probabilistic context‐free grammars (PCFGs), and probabilistic latent semantic analysis (PLSA) for the purpose of statistical language modeling. Even though the composite directed MRF model potentially has an exponential number of loops and becomes a context‐sensitive grammar, we are nevertheless able to estimate its parameters in cubic time using an efficient modified Expectation‐Maximization (EM) method, the generalized inside–outside algorithm, which extends the inside–outside algorithm to incorporate the effects of the n‐gram and PLSA language models. We generalize various smoothing techniques to alleviate the sparseness of n‐gram counts in cases where there are hidden variables. We also derive an analogous algorithm to find the most likely parse of a sentence and to calculate the probability of initial subsequence of a sentence, all generated by the composite language model. Our experimental results on the Wall Street Journal corpus show that we obtain significant reductions in perplexity compared to the state‐of‐the‐art baseline trigram model with Good–Turing and Kneser–Ney smoothing techniques.     

Constructing probabilistic graphical model from predicate formulas for fusing logical and probabilistic knowledge

Expressing knowledge as expert experience and discovering knowledge implied in data are two important ways for knowledge acquisition. Consistent combination of these two kinds of knowledge has attracted much attention due to the potential applications to knowledge fusion and wide requirements of decision support. In this paper, we focus on the probabilistic modeling of expert experience represented as logical predicate formulas, aiming at the effective fusion of logical and probabilistic knowledge. Taking qualitative probabilistic network (QPN) as the underlying framework of probabilistic knowledge implied in data as well as the abstraction of general Bayesian networks (BNs), we are to construct the probabilistic graphical model for both the given predicate formulas and the ultimate result of knowledge fusion. We first propose the concept and the construction algorithm of predicate graph (PG) to describe the dependence relations among predicate formulas, and discuss PG’s probabilistic semantics correspondingly. We then prove that PG is a probability dependency model and has the same semantics with a general probabilistic graphical model. Consequently, we give the method for fusing PG and QPN. Experimental results show the effectiveness of our methods.     

概率SDG 模型及故障分析推理方法

符号有向图（SDG）是用来表示大规模复杂系统中变量之间因果影响关系的一种重要工具,但其存在一些不易克服的缺点.为此,首先提出一种新的模型--概率SDG模型,用条件概率描述故障之间的传递关系;然后在概率SDG模型的框架下,提出一种故障分析诊断的推理方法,即利用图消去算法和连接树算法进行贝叶斯推理,并计算出故障概率.最后以65 t/h锅炉系统为例,研究建立其概率SDG模型,并在此基础上验证了上述模型和推理方法的有效性.     

Regional category parsing in undirected graphical models

This article presents an approach for regional categorization in complex natural scenes with undirected graphs. A novel MRF-like model is proposed with spatial constraints in the feature space based on existing directed graphs, and an approximation of pseudo-likelihood is introduced for probability inference and parameter estimation. With this approximation, we can deal with the intractability of potential functions and get spatial relations between patches of different classes for more information in their co-occurrence matrix. The Receiver-Operating-Characteristic curves in our experiments demonstrate a better performance from our proposed method in comparison with directed probabilistic models such as LDA and constellation.     

Interval-valued probabilistic hesitant fuzzy set and its application in the Arctic geopolitical risk evaluation

The probabilistic hesitant fuzzy set (PHFS) associates the probability with the hesitant fuzzy set (HFS), which has been proposed to improve the granularity of the HFS and can remain more information, is significant to solve the multicriteria group decision-making (MCGDM) problems when the decision makers fail to provide their preferences completely. To express the probability information existing in the hesitancy more conveniently, we propose a generalized form of P-HFS named interval-valued probabilistic hesitant fuzzy set (IVPHFS). In addition, we define some basic operation laws and aggregation operators of IVPHFSs. Based on which, we provide an efficient approach to deal with the practical MCGDM problems by IVPHFSs aggregation operators under the interval-valued probabilistic hesitant fuzzy environment. Last but not least, we apply the proposed approach to the research of the Arctic geopolitical risk evaluation. The method based on the score function of the probabilistic dual hesitant fuzzy set is also introduced for comparison. The comparing results demonstrate that our approach is more reasonable and logical.     

Variational Bayes via propositionalized probability computation in PRISM

We propose a logic-based approach to variational Bayes (VB) via propositionalized probability computation in a symbolic-statistical modeling language PRISM. PRISM computes probabilities of logical formulas by reducing them to AND/OR boolean formulas called explanation graphs containing probabilistic ${\tt msw/2}$ atoms. We put Dirichlet priors on parameters of ${\tt msw/2}$ atoms and derive a variational Bayes EM algorithm that learns their hyper parameters from data. It runs on explanation graphs deduced from a program and a goal and computes probabilities in a dynamic programming manner in time linear in the size of the graphs. To show the genericity and effectiveness of Bayesian modeling by the proposed approach, we conducted two learning experiments, one with a probabilistic right-corner grammar and the other with a profile-HMM. To our knowledge, no previous report has been made of VB applied to these models.     

Using PRISM model checker as a validation tool for an analytical model of IEEE 802.15.4 networks

Commonly, simulation by using an existing network simulation tool or a simulator developed from scratch is employed for validation of analytical network performance models. An analytical model of star-shaped wireless sensor networks has been proposed in the literature in which, upon receiving a query from the coordinator, each sensor node sends one data frame to it by executing the IEEE 802.15.4 unslotted carrier-sense multiple access with collision avoidance algorithm. The model consists of expressions for calculation of the probability of successful receipt of the data at a certain time and the like. The authors of the model have written a special simulation program in order to validate the expressions. Our aim was to employ probabilistic model checker PRISM instead. PRISM only requires the user to formally specify the network as a kind of state machine and the queries about the probabilities sought in the form of logical formulas. It finds the probabilities automatically and can present them on graphs. We show how to specify the networks formally in such a way that all the expressions from the analytical model can be validated with PRISM. For those networks containing a few nodes, the validation can be carried out by normal model checking, which, in contrast to the simulation, always checks all the possible network behaviors, whereas statistical model checking can be used for the larger networks.     

Unfalsified probability estimation for a model set based on frequency domain data

This paper deals with the problem of estimating the probability under which a model set is not falsified by a set of measured plant frequency response samples. A definition of sample unfalsified probability has been proposed, and an explicit formula has been derived. Computation issues are also discussed. Moreover, an efficient algorithm has been developed for sample unfalsified probability calculation. Monte Carlo simulations show that the defined sample unfalsified probability is appropriate in the evaluation of the quality of a model set. Compared with the deterministic approach, simulation results suggest that the probabilistic approach is more suitable in model set validation.     

基于最小最大概率分割准则的图像阈值分割方法

最小最大概率机是基于错分概率最小化的新型分类器。文中讨论一维空间两类别最小最大概率问题的求解。以此为基础,给出图像阈值分割最小最大概率分割点的定义,提出设计阈值分割准则函数的方法,同时提出基于最小最大概率准则的阈值分割算法,此算法保证图像阈值分割正确率的下界。实验表明,文中方法是有效的。     

A language for construction of belief networks

A method for incrementally constructing belief networks, which are directed acyclic graph representations for probability distributions, is described. A network-construction language, FRAIL3, which is similar to a forward-chaining language using data dependencies but has additional features for specifying distributions, was developed. A particularly important feature of this language is that is allows the user to conveniently specify conditional probability matrices using stereotyped models of intercausal interaction. Using FRAIL3, one can define parmeterized classes of probabilistic models. These parameterized models make it possible to apply probabilistic reasoning to problems for which it is impractical to have a single large, static model     

Learning symmetric causal independence models

Causal independence modelling is a well-known method for reducing the size of probability tables, simplifying the probabilistic inference and explaining the underlying mechanisms in Bayesian networks. Recently, a generalization of the widely-used noisy OR and noisy AND models, causal independence models based on symmetric Boolean functions, was proposed. In this paper, we study the problem of learning the parameters in these models, further referred to as symmetric causal independence models. We present a computationally efficient EM algorithm to learn parameters in symmetric causal independence models, where the computational scheme of the Poisson binomial distribution is used to compute the conditional probabilities in the E-step. We study computational complexity and convergence of the developed algorithm. The presented EM algorithm allows us to assess the practical usefulness of symmetric causal independence models. In the assessment, the models are applied to a classification task; they perform competitively with state-of-the-art classifiers.     

Dynamic Uncertain Causality Graph for Knowledge Representation and Reasoning: Discrete DAG Cases

Developed from the dynamic causality diagram (DCD) model,a new approach for knowledge representation and reasoning named as dynamic uncertain causality graph (DUCG) is presented,which focuses on the co...     

基于有向哈希树的认证跳表算法

作为一种重要的认证数据结构,认证跳表在数据认证机制中有着广泛的应用。由于哈希模式对认证跳表的代价有显著的影响,因此提出哈希模式和数据存储模式分离的思想,设计了一种新的认证哈希模式—有向哈希树,并在其基础上设计了新的认证跳表算法。应用分层数据处理、概率分析等数学方法对所提出算法的代价进行了理论分析,并与已有的认证跳表算法做了性能比较。结果表明,本算法在时间、通信和存储代价方面有了较大的改进。     

Probabilistic voxel mapping using an adaptive confidence measure of stereo matching

In this paper, we describe a probabilistic voxel mapping algorithm using an adaptive confidence measure of stereo matching. Most of the 3D mapping algorithms based on stereo matching usually generate a map formed by point cloud. There are many reconstruction errors. The reconstruction errors are due to stereo reconstruction error factors such as calibration errors, stereo matching errors, and triangulation errors. A point cloud map with reconstruction errors cannot accurately represent structures of environments and needs large memory capacity. To solve these problems, we focused on the confidence of stereo matching and probabilistic representation. For evaluation of stereo matching, we propose an adaptive confidence measure that is suitable for outdoor environments. The confidence of stereo matching can be reflected in the probability of restoring structures. For probabilistic representation, we propose a probabilistic voxel mapping algorithm. The proposed probabilistic voxel map is a more reliable representation of environments than the commonly used voxel map that just contains the occupancy information. We test the proposed confidence measure and probabilistic voxel mapping algorithm in outdoor environments.     

A unified model for abduction-based reasoning

In the last decade, abduction has been a very active research area. This has resulted in a variety of models mechanizing abduction, namely within a probabilistic or logical framework. Recently, a few abductive models have been proposed within a neural framework. Unfortunately, these neural/probablistic/logical-based models cannot address complex abduction problems. In this paper, we propose a new extended neural-based model to deal with abduction problems which could be monotonic, open, and incompatible