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Clustering analysis is a fundamental technique in machine learning, which is also widely used in information granulation. Multiple clustering systems granulate a data set into multiple granular structures. Therefore, clustering ensemble can serve as an important branch of multigranulation information fusion. Many approaches have been proposed to solve the clustering ensemble problem. This paper focuses on the direct approaches which involve two steps: finding cluster correspondence and utilizing a fusion strategy to produce a final result. The existing direct approaches mainly discuss the process of finding cluster correspondence, while the fusing process is simply done by voting. In this paper, we mainly focus on the fusing process and propose a Dempster-Shafer evidence theory-based clustering ensemble algorithm. The advantage of the algorithm is that the information of an object’s surrounding cluster structure is taken into consideration by using its neighbors to describe it. First, we find neighbors of each object and generate its label probability outputs in every base partition. Second, these label probability outputs are integrated based on DS theory. Theoretically, our method is superior to other voting methods. Besides, several experiments show that the proposed algorithm is statistically better than seven other clustering ensemble methods. [ABSTRACT FROM AUTHOR]

Highlights • We prove some properties of the Pari Mutuel Model as a coherent lower (and upper) probability. • We show that a Pari Mutuel Model is a particular case of a probability interval. • We give the maximal number of extreme points of the credal set associated with a Pari Mutuel Model and we give the form of those extreme points. • We give sufficient and necessary conditions for the Pari Mutuel Model to induce a belief function. • We show how to merge information given in terms of Pari Mutuel Models. Abstract The pari-mutuel model is a betting scheme that has its origins in horse racing, and that has been applied in a number of contexts, mostly economics. In this paper, we consider the set of probability measures compatible with a pari-mutuel model, characterize its extreme points, and investigate the properties of the associated lower and upper probabilities. We show that the pari-mutuel model can be embedded within the theory of probability intervals, and prove necessary and sufficient conditions for it to be a belief function or a minitive measure. In addition, we also investigate the combination of different pari-mutuel models and their definition on product spaces. [ABSTRACT FROM AUTHOR]

Recently, Yang and Li (2014) studied a bidimensional renewal risk model with constant force of interest and dependent subexponential claims. Under the special Farlie–Gumbel–Morgenstern dependence structure and a technical moment condition on the claim-number process, they derived an asymptotic expansion for the finite-time ruin probability. In this paper, we show that their result can be extended to a much more general dependence structure without any extra condition on the renewal claim-number process. We also give some asymptotic expansions for the corresponding infinite-time ruin probability within the scope of extended regular variation. [ABSTRACT FROM AUTHOR]

Outbreaks of highly pathogenic avian influenza (HPAI) in commercial poultry flocks are rare but highly disruptive to the industry. There is evidence that low pathogenic avian influenza (LPAI) can transfer from wild birds to domestic flocks, where it may mutate to HPAI, and the industry is concerned that an increasing demand for free-range produce may affect the risk of LPAI and HPAI outbreaks. In this paper we focus on LPAI introduction and establishment, and formulate a branching process model to compare risk between sectors and their contribution to overall industry-level risk. Our aim is to determine how heterogeneity in avian influenza viruses and the distinct population structures of each sector – caged, barn and free-range, meat and layer – interact with a continuous risk of virus introduction to affect outbreak probabilities. We show that free-range access is the most influential driver of LPAI outbreaks, with production cycle length having relatively little effect. We demonstrate that variation in virus transmission rates is particularly important when modelling avian influenza introduction to domestic poultry. Virus-free status is of interest for biosecurity and we distinguish how it differs from the usual probability of extinction, and discuss how production cycle length affects this difference. We also use the nonlinear relationship between shed size and risk to identify conditions for which shed size is most influential. [ABSTRACT FROM AUTHOR]

This paper aims at modeling opinion diffusion among agents with a logical approach by assuming that opinions are propositional formulas. In a first part, we present a model in which an agent changes its opinion by merging the opinions of some influential agents, its influencers. More precisely, it merges these opinions, which may be contradictory, by taking into account an order of importance among its influencers. In a second part, we generalize this model so that influencers are ordered according to several orders of influence which depend on the topics of opinions. [ABSTRACT FROM AUTHOR]

Consider the classical insurance surplus model with a parametric family for the claim distribution. Although we can construct an asymptotically normal estimator of the ruin probability from the claim data, the asymptotic variance is not easy to estimate since it includes the derivative of the ruin probability with respect to the parameter. This paper gives an explicit asymptotic formula for the asymptotic variance, which is easy to estimate, and gives an asymptotic confidence interval of ruin probability. [ABSTRACT FROM AUTHOR]

Handling uncertain knowledge is crucial for modeling many real world domains. Ontologies and ontology-based data access (OBDA) have proven to be versatile methods to capture this knowledge. Multiple systems for OBDA have been developed and there is theoretical work towards probabilistic OBDA, namely identifying efficiently processable queries. These queries are called safe queries. However, there is no analysis on the safeness of probabilistic queries in real-world applications, and there exists no tool support for applying the existing formalisms to the standard query language of SPARQL. In this paper we investigate queries collected from several public SPARQL endpoints and determine the distribution of safe and unsafe queries. This analysis shows that many queries in practice are safe, making probabilistic OBDA feasible and practical to fulfill real-world users' information needs. Furthermore, we design and conduct benchmarks on real-world and generated data sets which show that the approach of answering safe queries in the appropriate way is scalable to large amounts of data. [ABSTRACT FROM AUTHOR]

The artificial bee colony (ABC) algorithm is a new branch of evolutionary algorithms (EAs) that is inspired by the collective foraging behavior of real honey bee colonies. Due to its foraging model and its solution search equation, ABC generally performs well in exploration but badly in exploitation. To address this concerning issue and obtain a good balance between exploration and exploitation, in this paper, we mainly introduce into the ABC an adaptive method for the population size (AMPS). AMPS is inspired by the natural principle that the size of a population is affected by the availability of food resources. When food resources are abundant, a population tends to expand; otherwise, a decrease in the availability of food resources leads to a shrinkage in the population size. Specifically, when the algorithm performs well in exploration, AMPS will shrink the population to enhance exploitation by periodically removing some inferior solutions that have low success rates. In contrast, AMPS will enlarge the population to improve exploration by introducing some reserved solutions. Furthermore, to make AMPS perform better, we design a new solution search equation for employed bees and onlooker bees. Moreover, we also improve the probability model of the onlooker bees. By embedding our three proposed algorithmic components into ABC, we propose a novel ABC variant, called APABC. To demonstrate the performance of APABC, we compare APABC with some state-of-the-art ABC variants and some other non-ABC methods on 22 scalable benchmark functions and 30 CEC2014 test functions. The simulation results show that APABC is better than or at least competitive with the competitors in terms of its solution quality, robustness and convergence speed. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the contact process on the hypercube lattice Z d . The contact process intuitively describes the spread of the infectious disease on a graph, where an infectious vertex becomes healthy at a constant rate while a healthy vertex is infected at rate proportional to the number of infectious neighbors. As the dimension of the lattice grows to infinity, we give a mean field limit for the survival probability of the process conditioned on the event that only the origin of the lattice is infected at t = 0 . The binary contact path process is a main auxiliary tool for our proof. [ABSTRACT FROM AUTHOR]

Abstract: In imprecise probability theories, independence modeling and computational tractability are two important issues. The former is essential to work with multiple variables and multivariate spaces, while the latter is essential in practical applications. When using lower probabilities to model uncertainty about the value assumed by a variable, satisfying the property of 2-monotonicity decreases the computational burden of inference, hence answering the latter issue. In a first part, this paper investigates whether the joint uncertainty obtained by main existing notions of independence preserve the 2-monotonicity of marginal models. It is shown that it is usually not the case, except for the formal extension of random set independence to 2-monotone lower probabilities. The second part of the paper explores the properties and interests of this extension within the setting of lower probabilities. [Copyright &y& Elsevier]

Abstract: In this paper, by adopting a coherence-based probabilistic approach to default reasoning, we focus the study on the logical operation of quasi conjunction and the Goodman–Nguyen inclusion relation for conditional events. We recall that quasi conjunction is a basic notion for defining consistency of conditional knowledge bases. By deepening some results given in a previous paper we show that, given any finite family of conditional events and any nonempty subset of , the family p-entails the quasi conjunction ; then, given any conditional event , we analyze the equivalence between p-entailment of from and p-entailment of from , where is some nonempty subset of We also illustrate some alternative theorems related with p-consistency and p-entailment. Finally, we deepen the study of the connections between the notions of p-entailment and inclusion relation by introducing for a pair the (possibly empty) class of the subsets of such that implies . We show that the class satisfies many properties; in particular is additive and has a greatest element which can be determined by applying a suitable algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the stationary distribution of the facultative population model with a degenerate noise. The contributions of this paper lie in: (a) providing sufficient conditions which allow the noise intensity matrix to be degenerate, and, in particular, guarantee the existence and uniqueness of the stationary distribution of our model; (b) discussing the property of positive recurrence of the model and revealing that the associated transition probability function converges exponentially to the unique stationary distribution; (c) showing the integral equation that the Laplace transform of the stationary distribution satisfies. [Copyright &y& Elsevier]

Errors in reasoning about probabilistic evidence can have severe consequences. In the legal domain a number of recent miscarriages of justice emphasises how severe these consequences can be. These cases, in which forensic evidence was misinterpreted, have ignited a scientific debate on how and when probabilistic reasoning can be incorporated in (legal) argumentation. One promising approach is to use Bayesian networks (BNs), which are well-known scientific models for probabilistic reasoning. For non-statistical experts, however, Bayesian networks may be hard to interpret. Especially since the inner workings of Bayesian networks are complicated, they may appear as black box models. Argumentation models, on the contrary, can be used to show how certain results are derived in a way that naturally corresponds to everyday reasoning. In this paper we propose to explain the inner workings of a BN in terms of arguments. We formalise a two-phase method for extracting probabilistically supported arguments from a Bayesian network. First, from a Bayesian network we construct a support graph , and, second, given a set of observations we build arguments from that support graph. Such arguments can facilitate the correct interpretation and explanation of the relation between hypotheses and evidence that is modelled in the Bayesian network. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this letter is to confirm the achievements in and answer all the mentioned comments in . Meanwhile some other drawbacks in the comment paper are also presented in this paper. [Copyright &y& Elsevier]

The paper characterizes the invariant filtering measures resulting from Kalman filtering with intermittent observations in which the observation arrival is modeled as a Bernoulli process with packet arrival probability \overline\gamma. Our prior work showed that, for \overline\gamma>0, the sequence of random conditional error covariance matrices converges weakly to a unique invariant distribution \mu^\overline\gamma. This paper shows that, as \overline\gamma approaches one, the family \\mu^\overline\gamma\_\overline\gamma>0 satisfies a moderate deviations principle with good rate function I(\cdot): 1) as \overline\gamma\uparrow 1, the family \\mu^\overline\gamma\ converges weakly to the Dirac measure \deltaP^{\ast} concentrated on the fixed point of the associated discrete time Riccati operator; 2) the probability of a rare event (an event bounded away from P^\ast) under \mu^\overline\gamma decays to zero as a power law of (1-\overline\gamma) as \overline\gamma\uparrow 1; and, 3) the best power law decay exponent is obtained by solving a deterministic variational problem involving the rate function I(\cdot). For specific scenarios, the paper develops computationally tractable methods that lead to efficient estimates of rare event probabilities under \mu^\overline\gamma. [ABSTRACT FROM AUTHOR]

Pawlak's rough sets model describes an uncertain target set (concept) with two crisp boundary lines (i.e. lower and upper approximation sets) and as an effective tool has successfully been used to deal with uncertain information systems. Based on the rough sets model, a probabilistic rough sets model with a pair of thresholds was proposed to improve the fault-tolerance ability of rough sets. The uncertainty of Pawlak's rough sets model is rooted in the objects contained in the boundary region of the target concept, while the uncertainty of probabilistic rough sets model comes from three regions, because the objects in the positive or negative regions are probably uncertain, and the membership degrees of these objects are not necessary equal to 1 or 0. In this paper, a method for measuring the uncertainty of probabilistic rough sets is proposed, and the change rules of uncertainty with changing knowledge spaces are presented and analyzed. Then, for an uncertain target concept, the uncertainties of the three regions are discussed, and the related change rules of uncertainty with changing knowledge spaces are revealed and successfully proved. Finally, a comparative analysis on the uncertainty of a target concept in rough sets and probabilistic rough sets model is presented. These results are important to further enrich and improve probabilistic rough sets theory, and effectively promote the development of uncertainty artificial intelligence. [ABSTRACT FROM AUTHOR]

There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is Contextuality-by-Default, put forth by Dzhafarov and Kujala. The goal of this paper is to present a tutorial on a different approach: negative probabilities. We do so by presenting the overall theory of negative probabilities in a way that is consistent with Contextuality-by-Default and by examining with this theory some simple examples where contextuality appears, both in physics and psychology. [ABSTRACT FROM AUTHOR]

The paper starts with an introduction to the basic mathematical model of classical probability (CP), i.e. the Kolmogorov (1933) measure-theoretic model. Its two basic interpretations are discussed: statistical and subjective. We then present the probabilistic structure of quantum mechanics (QM) and discuss the problem of interpretation of a quantum state and the corresponding probability given by Born’s rule. Applications of quantum probability (QP) to modeling of cognition and decision making (DM) suffer from the same interpretational problems as QM. Here the situation is even more complicated than in physics. We analyze advantages and disadvantages of the use of subjective and statistical interpretations of QP. The subjective approach to QP was formalized in the framework of Quantum Bayesianism (QBism) as the result of efforts from C. Fuchs and his collaborators. The statistical approach to QP was presented in a variety of interpretations of QM, both in nonrealistic interpretations, e.g., the Copenhagen interpretation (with the latest version due to A. Plotnitsky), and in realistic interpretations (e.g., the recent Växjö interpretation). At present, we cannot make a definite choice in favor of any of the interpretations. Thus, quantum-like DM confronts the same interpretational problem as quantum physics does. [ABSTRACT FROM AUTHOR]

Abstract: This paper distinguishes between objective probability—or chance—and subjective probability. Most statistical methods in machine learning are based on the hypothesis that there is a random experiment from which we get a set of observations. This random experiment could be identified with a chance or objective probability, but these probabilities depend on some unknown parameters. Our knowledge of these parameters is not objective and in order to learn about them, we must assess some epistemic probabilities about their values. In some cases, our objective knowledge about these parameters is vacuous, so the question is: What epistemic probabilities should be assumed? In this paper we argue for the assumption of non-vacuous (a proper subset of [0,1]) interval probabilities. There are several reasons for this; some are based on the betting interpretation of epistemic probabilities while others are based on the learning capabilities under the vacuous representation. The implications of the selection of epistemic probabilities in different concepts as conditioning and learning are studied. It is shown that in order to maintain some reasonable learning capabilities we have to assume more informative prior models than those frequently used in the literature, such as the imprecise Dirichlet model. [Copyright &y& Elsevier]

Abstract: The paper deals with the fuzzy extension of the weighted average operation. First, we study the convenient ways how uncertain weights and weighted values can be modeled by fuzzy vectors. We show that, in comparison to a tuple of fuzzy numbers that have been used for modeling uncertain values of particular weights and weighted values up to now, fuzzy vectors extend the possibilities of utilizing the vague expert information concerning the weights and weighted values. Next, we focus on computation of a fuzzy weighted average of a fuzzy vector of weighted values with a fuzzy vector of weights. We derive a general formula and we study its special forms. The advantage of the approach presented in the paper is that the resulting fuzzy weighted average is not overly imprecise since every available information about its variables is involved in computation. This fact is illustrated by several examples. Finally, we briefly discuss the problem of defuzzification of the resulting fuzzy weighted average. [Copyright &y& Elsevier]

Abstract: Multi-dimensional classification aims at finding a function that assigns a vector of class values to a given vector of features. In this paper, this problem is tackled by a general family of models, called multi-dimensional Bayesian network classifiers (MBCs). This probabilistic graphical model organizes class and feature variables as three different subgraphs: class subgraph, feature subgraph, and bridge (from class to features) subgraph. Under the standard 0–1 loss function, the most probable explanation (MPE) must be computed, for which we provide theoretical results in both general MBCs and in MBCs decomposable into maximal connected components. Moreover, when computing the MPE, the vector of class values is covered by following a special ordering (gray code). Under other loss functions defined in accordance with a decomposable structure, we derive theoretical results on how to minimize the expected loss. Besides these inference issues, the paper presents flexible algorithms for learning MBC structures from data based on filter, wrapper and hybrid approaches. The cardinality of the search space is also given. New performance evaluation metrics adapted from the single-class setting are introduced. Experimental results with three benchmark data sets are encouraging, and they outperform state-of-the-art algorithms for multi-label classification. [Copyright &y& Elsevier]

Abstract: The goal of the paper is twofold. The first is to show that some of the ideas for representation of multidimensional distributions in probability and possibility theories can be transferred into evidence theory. Namely, we show that multidimensional basic assignments can be rather efficiently represented in a form of so-called compositional models. These models are based on the iterative application of the operator of composition, whose definition for basic assignments as well as its properties are presented. We also prove that the operator of composition in evidence theory is in a sense generalization of its probabilistic counterpart. The second goal of the paper is to introduce a new definition of conditional independence in evidence theory and to show in what sense it is superior to that formerly introduced by other authors. [Copyright &y& Elsevier]

Abstract: In a recent series of papers, Fine and colleagues [P.I. Fierens, T.L. Fine, Towards a frequentist interpretation of sets of measures, in: G. de Cooman, T.L. Fine, T. Seidenfeld (Eds.), Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, Shaker Publishing, 2001; P.I. Fierens, T.L. Fine, Towards a chaotic probability model for frequentist probability, in: J. Bernard, T. Seidenfeld, M. Zaffalon (Eds.), Proceedings of the Third International Symposium on Imprecise Probabilities and Their Applications, Carleton Scientific, 2003; L.C. Rêgo, T.L. Fine, Estimation of chaotic probabilities, in: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications, 2005] have presented the first steps towards a frequentist understanding of sets of measures as imprecise probability models which have been called chaotic models. Simulation of the chaotic variables is an integral part of the theory. Previous models, however, dealt only with sets of probability measures on finite algebras, that is, probability measures which can be related to variables with a finite number of possible values. In this paper, an extension of chaotic models is proposed in order to deal with the more general case of real-valued variables. This extension is based on the introduction of real-valued test functions which generalize binary-valued choices in the previous work. [Copyright &y& Elsevier]

This paper investigates the evaluation of infinitesimal perturbation analysis (IPA) estimates that have been derived based on a stochastic fluid model (SFM) using data observed from the sample path of a discrete event system (DES). First, we show that a straightforward implementation of the SFM-based IPA estimates may yield biased estimates when the data are obtained from the actual DES. Then, in order to better approximate the sample path of the DES, we propose a special case of SFM where the arrival and service processes are modeled by piecewise constant ON/OFF sources. The proposed SFM violates some of the assumptions made in [1]-[4], and, as a result, the sample derivatives no longer exist. However, using the proposed SFM, we obtain the left and right sided sample derivative estimates. As shown in this paper, the sided sample derivatives are much better in approximating the required derivatives compared to the straightforward implementation of the SFM-based IPA estimates. [ABSTRACT FROM AUTHOR]

It is a deep-seated tradition in science to view uncertainty as a province of probability theory. The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a much broader perspective. Uncertainty is an attribute of information. A fundamental premise of GTU is that information, whatever its form, may be represented as what is called a generalized constraint. The concept of a generalized constraint is the centerpiece of GTU. In GTU, a probabilistic constraint is viewed as a special—albeit important—instance of a generalized constraint. A generalized constraint is a constraint of the form X isr R, where X is the constrained variable, R is a constraining relation, generally non-bivalent, and r is an indexing variable which identifies the modality of the constraint, that is, its semantics. The principal constraints are: possibilistic (r = blank); probabilistic (r = p); veristic (r = r); usuality (r = u); random set (r = rs); fuzzy graph (r =fg,); bimodal (r = bin); and group (r = g). Generalized constraints may be qualified, combined and propagated. The set of all generalized constraints together with rules governing qualification, combination and propagation constitutes the generalized constraint language (GCL). The generalized constraint language plays a key role in GTU by serving as a precisiation language for propositions, commands and questions expressed in a natural language. Thus, in GTU the meaning of a proposition drawn from a natural language is expressed as a generalized constraint. Furthermore, a proposition plays the role of a carrier of information. This is the basis for equating information to a generalized constraint. In GTU, reasoning under uncertainty is treated as propagation of generalized constraints, in the sense that rules of deduction are equated to rules which govern propagation of generalized constraints. A concept which plays a key role in deduction is that of a protoform (abbreviation of prototypical form). Basically, a protoform is an abstracted summary—a summary which serves to identify the deep semantic structure of the object to which it applies. A deduction rule has two parts: symbolic expressed in terms of protoforms—and computational. GTU represents a significant change both in perspective and direction in dealing with uncertainty and information. The concepts and techniques introduced in this paper are illustrated by a number of examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an overview of graphical models that can handle imprecision in probability values. The paper first reviews basic concepts and presents a brief historical account of the field. The main characteristics of the credal network model are then discussed, as this model has received considerable attention in the literature. [Copyright &y& Elsevier]

Most state-of-the-art visual attention models estimate the probability distribution of fixating the eyes in a location of the image, the so-called saliency maps. Yet, these models do not predict the temporal sequence of eye fixations, which may be valuable for better predicting the human eye fixations, as well as for understanding the role of the different cues during visual exploration. In this paper, we present a method for predicting the sequence of human eye fixations, which is learned from the recorded human eye-tracking data. We use least-squares policy iteration (LSPI) to learn a visual exploration policy that mimics the recorded eye-fixation examples. The model uses a different set of parameters for the different stages of visual exploration that capture the importance of the cues during the scanpath. In a series of experiments, we demonstrate the effectiveness of using LSPI for combining multiple cues at different stages of the scanpath. The learned parameters suggest that the low-level and high-level cues (semantics) are similarly important at the first eye fixation of the scanpath, and the contribution of high-level cues keeps increasing during the visual exploration. Results show that our approach obtains the state-of-the-art performances on two challenging data sets: 1) OSIE data set and 2) MIT data set. [ABSTRACT FROM PUBLISHER]

This work provides a computational framework for meaningful probabilistic evaluation of attack–defense scenarios involving dependent actions. We combine the graphical security modeling technique of attack–defense trees with probabilistic information expressed in terms of Bayesian networks. In order to improve the efficiency of probability computations on attack–defense trees, we make use of inference algorithms and encoding techniques from constraint reasoning. The proposed approach is illustrated on a running example and the computations are automated with the help of suitable software tools. We show that the computational routines developed in this paper form a conservative generalization of the attack–defense tree formalism defined previously. We discuss the algebraic theory underlying our framework and point out several generalizations which are possible thanks to the use of semiring theory. Finally, our results apply directly to the analysis of the industrially recognized model of attack trees. [ABSTRACT FROM AUTHOR]

This paper establishes small ball probabilities for a class of time-changed processes X ∘ E , where X is a self-similar process and E is an independent continuous process, each with a certain small ball probability. In particular, examples of the outer process X and the time change E include an iterated fractional Brownian motion and the inverse of a general subordinator with infinite Lévy measure, respectively. The small ball probabilities of such time-changed processes show power law decay, and the rate of decay does not depend on the small deviation order of the outer process X , but on the self-similarity index of X . [ABSTRACT FROM AUTHOR]

How to automatically mining the spatial association patterns in spatial data is a challenging task in spatial data mining. In this paper, we propose three indices that represent the per-class, inter-class, and overall spatial associations of a nominal variable, which are based on the conditional probabilities of surface object categories. These indices represent relative quantities and are normalized to the region [ − 1 , 1 ] , which more accord with the intuitive cognition of people. We present some algorithms for detecting spatial associations that are based on these indices. The proposed method can be regarded as an extension of join count statistics and Transiogram. Several constructive examples were used to illustrate the advantages of the new method. Using two real data sets, vegetation types in Qingxian, Shanxi, China and neural tube birth defects in Heshun, Shanxi, China, we ran comparative experiments with other commonly used methods, including join count statistics, co-location quotient, and Q ( m ) statistics. The experimental results show that the proposed method can detect more subtle spatial associations, and is not sensitive to the sequence of neighbors. [ABSTRACT FROM AUTHOR]

Probabilistic selling can expand the market and decrease uncertain demand. In this paper, we study a scenario that two manufacturers delegate a retailer to sell two substitute brand-products through traditional selling channel and probabilistic products through probabilistic selling channel; the customer has risk aversion behavior for probabilistic product. A non-cooperative dynamic price Stackelberg game model is developed based on limited rational expectation. The influences of parameters on the system stability are further analyzed; the phenomenon of flip bifurcation, chaos, and other complex phenomena are reported using bifurcation, attractor and power spectrum etc. The results show that the system stability could be robust with increase in customer's risk aversion and the probability of each product becoming to probability product, and frail with increase in price discount. The manufacturer may benefit from a larger proportion of its product becoming to probabilistic product. When the chaos occurs, the market becomes abnormal, irregular and unpredictable; the two manufacturers should determine their price adjustment speed according to the parameters’ values, to ensure the up and downstream enterprises keep stable. The nonlinear feedback control method is used to control the system's chaos. The derived results have very important theoretical and practical values for the two manufacturers and the common retailer. [ABSTRACT FROM AUTHOR]

In this paper, we describe foxPSL , a fast, optimized and extended implementation of Probabilistic Soft Logic (PSL) based on the distributed graph processing framework Signal/Collect . PSL is one of the leading formalisms of statistical relational learning, a recently developed field of machine learning that aims at representing both uncertainty and rich relational structures, usually by combining logical representations with probabilistic graphical models. PSL can be seen as both a probabilistic logic and a template language for hinge-loss Markov Random Fields, a type of continuous Markov Random fields (MRF) in which Maximum a Posteriori inference is very efficient, since it can be formulated as a constrained convex minimization problem, as opposed to a discrete optimization problem for standard MRFs. From the logical perspective, a key feature of PSL is the capability to represent soft truth values, allowing the expression of complex domain knowledge, like degrees of truth, in parallel with uncertainty. foxPSL supports the full PSL pipeline from problem definition to a distributed solver that implements the Alternating Direction Method of Multipliers (ADMM) consensus optimization. It provides a Domain Specific Language that extends standard PSL with a class system and existential quantifiers, allowing for efficient grounding. Moreover, it implements a series of configurable optimizations, like optimized grounding of constraints and lazy inference, that improve grounding and inference time. We perform an extensive evaluation, comparing the performance of foxPSL to a state-of-the-art implementation of ADMM consensus optimization in GraphLab, and show an improvement in both inference time and solution quality. Moreover, we evaluate the impact of the optimizations on the execution time and discuss the trade-offs related to each optimization. [ABSTRACT FROM AUTHOR]

In this paper, generalized versions of two ensemble methods for regression based on variants of the original AdaBoost algorithm are proposed. The generalization of these regression methods consists in restricting the unit simplex for the weights of the instances to a smaller set of weighting probabilities. Various imprecise statistical models can be used to obtain a restricted set of weighting probabilities, whose sizes each depend on a single parameter. For particular choices of this parameter, the proposed algorithms reduce to standard AdaBoost-based regression algorithms or to standard regression. The main advantage of the proposed algorithms compared to the basic AdaBoost-based regression methods is that they have less tendency to over-fitting, because the weights of the hard instances are restricted. Several simulations and applications furthermore indicate a better performance of the proposed regression methods in comparison with the corresponding standard regression methods. [ABSTRACT FROM AUTHOR]

The probabilistic rough set (PRS) and the graded rough set (GRS) are two quantification models that measure relative and absolute quantitative information between the equivalence class and a basic concept, respectively. As a special PRS model, the decision-theoretic rough set (DTRS) mainly utilizes the conditional probability to express relative quantification. However, it ignores absolute quantitative information of the overlap between equivalence class and the basic set, and it cannot reflect the distinctive degrees of information and extremely narrow their applications in real life. In order to overcome these defects, this paper proposes a framework of double-quantitative decision-theoretic rough set (Dq-DTRS) based on Bayesian decision procedure and GRS. Two kinds of Dq-DTRS model are constructed, which essentially indicate the relative and absolute quantification. After further studies to discuss decision rules and the inner relationship between these two models, we introduce an illustrative case study about the medical diagnosis to interpret and express the theories, which is valuable for applying these theories to deal with practical issues. [ABSTRACT FROM AUTHOR]

This paper investigates a model of decision making under uncertainty comprising opposite epistemic states of complete ignorance and probability. In the first part, a new utility theory under complete ignorance is developed that combines Hurwicz–Arrow's theory of decision under ignorance with Anscombe–Aumann's idea of reversibility and monotonicity used to characterize subjective probability. The main result is a representation theorem for preference under ignorance by a particular one-parameter function – the τ -anchor utility function. In the second part, we study decision making under uncertainty comprising an ignorant variable and a probabilistic variable. We show that even if the variables are independent, they are not reversible in Anscombe–Aumann's sense. This insight leads to the development of a new proposal for decision under uncertainty represented by a preference relation that satisfies the weak order and monotonicity assumptions but rejects the reversibility assumption. A distinctive feature of the new proposal is that the certainty equivalent of a mapping from the state space of uncertain variables to the prize space depends on the order in which the variables are revealed. Explicit modeling of the order of variables explains some of the puzzles in multiple-prior model and the models for decision making with Dempster–Shafer belief function. [ABSTRACT FROM AUTHOR]

Keypoint matching is the task of accurately finding the location of a scene point in two images. Many keypoint descriptors have been proposed in the literature aiming at providing robustness against scale, translation and rotation transformations, each having advantages and disadvantages. This paper proposes a novel approach to fuse the information from multiple keypoint descriptors using Dempster–Shafer theory of evidence [1] , which has proven particularly efficient in combining sources of information providing incomplete, imprecise, biased, and conflictive knowledge. The matching results of each descriptor are transformed into an evidence distribution on which a confidence factor is computed making use of its entropy. Then, the evidence distributions are fused using Dempster–Shafer Theory (DST), considering its confidence. As a result of the fusion, a new evidence distribution that improves the result of the best descriptor is obtained. Our method has been tested with SIFT, SURF, ORB, BRISK and FREAK descriptors using all possible their combinations. Results on the Oxford keypoint dataset [2] show that the proposed approach obtains an improvement of up to 10 % compared to the best one (FREAK). [ABSTRACT FROM AUTHOR]

Stochastic Trust-Region Response-Surface method (STRONG) is a new response-surface-based framework for simulation optimization. The appeal of STRONG lies in that it preserves the advantages, yet eliminates the disadvantages, of traditional response surface methodology (RSM) that has been used for more than 50 years. Specifically, STRONG does not require human involvement in the search process and can guarantee to converge to the true optimum with probability one (w.p.1). In this paper, we propose an improved framework, called STRONG-X, that enhances the efficiency and efficacy of STRONG to widen its applicability to more practical problems. For efficiency improvement, STRONG-X includes a newly-developed experimental scheme that consists of construction of optimal simulation designs and an assignment strategy for random number streams to obtain computational gains. For efficacy improvement, a new variant, called STRONG-XG, is developed to achieve convergence under generally-distributed responses, as opposed to STRONG and STRONG-X where convergence is guaranteed only when the response is normal. An extensive numerical study is conducted to evaluate the efficiency and efficacy of STRONG-X and STRONG-XG. Moreover, two illustrative examples are provided to show the viability of STRONG-X and STRONG-XG in practical settings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive new near-ignorance models on the probability simplex, which do not directly involve the Dirichlet distribution and, thus, are alternative to the Imprecise Dirichlet Model (IDM). We focus our investigation on a particular class of distributions on the simplex which is known as the class of Normalized Infinitely Divisible (NID) distributions; it includes the Dirichlet distribution as a particular case. For this class it is possible to derive general formulae for prior and posterior predictive inferences, by exploiting the Lévy–Khintchine representation theorem. This allows us to generally characterize the near-ignorance properties of the NID class. After deriving these general properties, we focus our attention on three members of this class. We will show that one of these near-ignorance models satisfies the representation invariance principle and, for a given value of the prior strength, always provides inferences that encompass those of the IDM. The other two models do not satisfy this principle, but their imprecision depends linearly or almost linearly on the number of observed categories; we argue that this is sometimes a desirable property for a predictive model. [ABSTRACT FROM AUTHOR]

In the paper we investigate the criteria of choosing generalized Dempster–Shafer rules for aggregating sources whose information is represented by belief functions. The approach is based on measuring various types of uncertainty in information and we use for this purpose in particular linear imprecision indices. Some results concerning properties of such rules are also presented. [ABSTRACT FROM AUTHOR]

Embedding conglomerability as a rationality requirement in probability was among the aims of Walley's behavioural theory of coherent lower previsions. However, recent work has shown that this attempt has only been partly successful. If we focus in particular on the extension of given assessments to a rational and conglomerable model (in the least-committal way), we have that the procedure used in Walley's theory, the natural extension , provides only an approximation to the model that is actually sought for: the so-called conglomerable natural extension . In this paper we consider probabilistic assessments in the form of a coherent lower prevision P ̲ , which is another name for a lower expectation functional, and make an in-depth mathematical study of the problem of computing the conglomerable natural extension for this case: that is, where it is defined as the smallest coherent lower prevision F ̲ ≥ P ̲ that is conglomerable, in case it exists. Past work has shown that F ̲ can be approximated by an increasing sequence ( E ̲ n ) n ∈ N of coherent lower previsions. We solve an open problem by showing that this sequence can consist of infinitely many distinct elements. Moreover, we give sufficient conditions, of quite broad applicability, to make sure that the point-wise limit of the sequence is F ̲ in case P ̲ is the lower envelope of finitely many linear previsions. In addition, we study the question of the existence of F ̲ and its relationship with the notion of marginal extension. [ABSTRACT FROM AUTHOR]

Abstract: The specification of conditional probability tables (CPTs) is a difficult task in the construction of probabilistic graphical models. Several types of canonical models have been proposed to ease that difficulty. Noisy-threshold models generalize the two most popular canonical models: the noisy-or and the noisy-and. When using the standard inference techniques the inference complexity is exponential with respect to the number of parents of a variable. More efficient inference techniques can be employed for CPTs that take a special form. CPTs can be viewed as tensors. Tensors can be decomposed into linear combinations of rank-one tensors, where a rank-one tensor is an outer product of vectors. Such decomposition is referred to as Canonical Polyadic (CP) or CANDECOMP-PARAFAC (CP) decomposition. The tensor decomposition offers a compact representation of CPTs which can be efficiently utilized in probabilistic inference. In this paper we propose a CP decomposition of tensors corresponding to CPTs of threshold functions, exactly ℓ-out-of-k functions, and their noisy counterparts. We prove results about the symmetric rank of these tensors in the real and complex domains. The proofs are constructive and provide methods for CP decomposition of these tensors. An analytical and experimental comparison with the parent-divorcing method (which also has a polynomial complexity) shows superiority of the CP decomposition-based method. The experiments were performed on subnetworks of the well-known QMRT-DT network generalized by replacing noisy-or by noisy-threshold models. [Copyright &y& Elsevier]

Highlights: [•] This paper examines the effect of vaccination on the spread of computer virus. [•] A novel computer virus propagation model is proposed. [•] The two equilibria are globally asymptotically stable. [•] Some effective strategies for eradicating viruses are suggested. [ABSTRACT FROM AUTHOR]

Abstract: The classical probabilistic rough set model is established based on a crisp binary relation. As a generalization of crisp binary relation, fuzzy relation makes descriptions of the objective world more realistic, practical, and accurate in some cases. Thus probabilistic rough set model based on a crisp binary relation limits its application domain. In this paper, based on a fuzzy relation, we propose a fuzzy probabilistic rough set model on two universes. Meanwhile, the concepts of the inverse lower and upper approximation operators are presented. We also study some properties of these approximation operators. Finally, a numerical example of the clinical diagnosis systems is applied to illustrate the validity of the proposed model. And we compare the proposed model with other models to show the superiority of the proposed model. [Copyright &y& Elsevier]

In this paper, we propose an environment-assisted error correction scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an /V-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an /V-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum entangled state beyond the standard RU scheme. [ABSTRACT FROM AUTHOR]

Abstract: In 2009, Yu et al. proposed a multimodal probability model (MPM) for clustering. This paper makes advanced clustering constructions on the MPM. We first reconstruct most existing clustering algorithms, such as the k-means, fuzzy c-means, possibilistic c-means, mean shift, classification maximum likelihood, and latent class methods, by establishing the relationships between these clustering algorithms and the MPM. Under our clustering construction, we find that the MPM can be seen as a basic probability model for most existing clustering algorithms. We then construct new clustering frameworks based on the MPM. One of the frameworks develops new penalized-type clustering algorithms. Another one induces entropy-type clustering algorithms, especially with sample-weighted clustering. Several numerical and real data sets are made for comparisons. These experimental results show that our clustering constructions based on the MPM can produce useful and effective clustering algorithms. [Copyright &y& Elsevier]

Abstract: Probabilistic compositional models, similarly to graphical Markov models, are able to represent multidimensional probability distributions using factorization and closely related concept of conditional independence. Compositional models represent an algebraic alternative to the graphical models. The system of related conditional independencies is not encoded explicitly (e.g. using a graph) but it is hidden in a model structure itself. This paper provides answers to the question how to recognize whether two different compositional model structures are equivalent – i.e., whether they induce the same system of conditional independencies. Above that, it provides an easy way to convert one structure into an equivalent one in terms of some elementary operations on structures, closely related ability to generate all structures equivalent with a given one, and a unique representative of a class of equivalent structures. [Copyright &y& Elsevier]

Abstract: Probabilistic models of information retrieval rank objects (e.g. documents) in response to a query according to the probability of some matching criterion (e.g. relevance). These models rarely yield an actual probability and their scoring functions are interpreted to be purely ordinal within a given retrieval task. In this paper we show that some scoring functions possess a likelihood property, which means that the scoring function indicates the likelihood of matching when compared to other retrieval tasks. This is potentially more useful than pure ranking even though it cannot be interpreted as an actual probability. This property can be detected by using two modified effectiveness measures, entire precision and entire recall. Experimental evidence is offered to show the existence of this property both for traditional document retrieval and for the analysis of crime data where suspects of an unsolved crime are ranked according to the probability of culpability. [Copyright &y& Elsevier]

Abstract: This paper investigates the finite-time ruin probability in a risk model with constant force of interest, upper tail asymptotically independent claims, and a general claim arrival process. We obtain a uniformly asymptotic formula for times in a finite interval. In particular, with a certain dependence among the inter-arrival times, the formula holds uniformly for all times. [Copyright &y& Elsevier]

Abstract: Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion. [Copyright &y& Elsevier]