Distributions of multi-estimates for multistage stochastic inclusions

The problems of constructing recursive relations for conditional and unconditional distributions of random informational sets are considered. These sets, which are called multi-estimates in the paper, appear naturally in the problems of estimation of states and parameters of multistage stochastic inclusions.     

Practical representations of incomplete probabilistic knowledge

The compact representation of incomplete probabilistic knowledge which can be encountered in risk evaluation problems, for instance in environmental studies is considered. Various kinds of knowledge are considered such as expert opinions about characteristics of distributions or poor statistical information. The approach is based on probability families encoded by possibility distributions and belief functions. In each case, a technique for representing the available imprecise probabilistic information faithfully is proposed, using different uncertainty frameworks, such as possibility theory, probability theory, and belief functions, etc. Moreover the use of probability-possibility transformations enables confidence intervals to be encompassed by cuts of possibility distributions, thus making the representation stronger. The respective appropriateness of pairs of cumulative distributions, continuous possibility distributions or discrete random sets for representing information about the mean value, the mode, the median and other fractiles of ill-known probability distributions is discussed in detail.     

Probabilistic Type-2 Operators and “Almost”-Classes

We define and examine several probabilistic operators ranging over sets (i.e., operators of type 2), among them the formerly studied ALMOST-operator. We compare their power and prove that they all coincide for a wide variety of classes. As a consequence, we characterize the ALMOST-operator which ranges over infinite objects (sets) by a bounded-error probabilistic operator which ranges over strings, i.e., finite objects. This leads to a number of consequences about complexity classes of current interest. As applications, we obtain (a) a criterion for measure 1 inclusions of complexity classes, (b) a criterion for inclusions of complexity classes relative to a random oracle, (c) a new upper time bound for ALMOST-PSPACE, and (d) a characterization of ALMOST-PSPACE in terms of checking stack automata. Finally, a connection between the power of ALMOST-PSPACE and that of probabilistic circuits is given. Received: 16 April 1996     

基于支持向量机自适应核的改进算法

支持向量机是在一个向量空间中依靠样本集中的训练向量获取两个样本集之间最优边界的方法.针对支持向量机中基于高斯核的动态自适应核进行了分析,并将传统算法进行改进,通过对点到平面的距离z<,1>的调整,对中间变量a<,1>的细致讨论,以及对迭代停止条件的控制,得到了适合手写体汉字识别系统的新的自适应核算法,并通过其在手写体汉字识别中的实验,验证了新的自适应算法在识别率、泛化误差边界最小化和核参数选择方面的有效性.算法使得在大的核参数空间中没有额外代价的探索变的可行.     

Comparison of linear and nonlinear methods of confidence estimation for statistically uncertain systems

In this paper, we consider a problem of confidence sets design for the estimation problem with observations in the system that contains both random perturbations with given distributions and uncertain perturbations with information completely defined by the domain of their possible values. Two approaches are compared: the first is based on application of a posteriori distributions and relations of the Kalman filter for systems with uncertain parameters, the other is connected with design of optimal confidence sets. It was shown that nonlinear estimates are better for the estimation problem under consideration.     

Computationally Efficient Approximation of a Probabilistic Model for Document Representation in the WEBSOM Full-Text Analysis Method

WEBSOM is a recently developed neural method for exploring full-text document collections, for information retrieval, and for information filtering. In WEBSOM the full-text documents are encoded as vectors in a document space somewhat like in earlier information retrieval methods, but in WEBSOM the document space is formed in an unsupervised manner using the Self-Organizing Map algorithm. In this article the document representations the WEBSOM creates are shown to be computationally efficient approximations of the results of a certain probabilistic model. The probabilistic model incorporates information about the similarity of use of different words to take into account their semantic relations.     

多重概率粗糙集模型

基于多重集合,对Z.Pawlak粗集意义下的概率粗糙集模型的论域进行了扩展,提出了基于多重集的概率粗糙集模型,即多重概率粗糙集模型,给出了该模型的完整定义、相关定理和重要性质,其中包括多重论域定义、多重概率粗糙近似集的定义及其各种性质的证明、多重概率粗糙集的近似精度定义、可定义集与属性约简的定义、多重集意义下的粗糙近似算子之间的关系及其与Z.Pawlak意义下的粗糙近似算子之间的关系等。多重概率粗糙集可充分反映知识颗粒间的重叠性,对象的重要度差别及其多态性,这样有利于用粗糙集理论从保存在关系数据库中的具有一对多、多对多依赖性的且具有不完全性或存在统计性的数据中挖掘知识。     

Stochastic dynamics simulation with generalized interval probability

Two types of uncertainties are generally recognized in modelling and simulation, including variability caused by inherent randomness and incertitude due to the lack of perfect knowledge. In this paper, a generalized interval-probability theory is used to model both uncertainty components simultaneously, where epistemic uncertainty is quantified by generalized interval in addition to probability measure. Conditioning, independence, and Markovian probabilities are uniquely defined in generalized interval probability such that its probabilistic calculus resembles that in the classical probability theory. A path-integral approach can be taken to solve the interval Fokker–Planck equation for diffusion processes. A Krylov subspace projection method is proposed to solve the interval master equation for jump processes. Thus, the time evolution of both uncertainty components can be simulated simultaneously, which provides the lower and upper bound information of evolving probability distributions as an alternative to the traditional sensitivity analysis.     

Dynamic Hybrid Random Fields for the Probabilistic Graphical Modeling of Sequential Data: Definitions,Algorithms, and an Application to Bioinformatics

The paper introduces a dynamic extension of the hybrid random field (HRF), called dynamic HRF (D-HRF). The D-HRF is aimed at the probabilistic graphical modeling of arbitrary-length sequences of sets of (time-dependent) discrete random variables under Markov assumptions. Suitable maximum likelihood algorithms for learning the parameters and the structure of the D-HRF are presented. The D-HRF inherits the computational efficiency and the modeling capabilities of HRFs, subsuming both dynamic Bayesian networks and Markov random fields. The behavior of the D-HRF is first evaluated empirically on synthetic data drawn from probabilistic distributions having known form. Then, D-HRFs (combined with a recurrent autoencoder) are successfully applied to the prediction of the disulfide-bonding state of cysteines from the primary structure of proteins in the Protein Data Bank.     

Similarity classifier using similarities based on modified probabilistic equivalence relations

This paper examines a classifier based on similarity measures originating from probabilistic equivalence relations with a generalized mean. Equivalences are weighted and weight optimization is carried out with differential evolution algorithms. In the classifier, a similarity measure based on the ?ukasiewicz structure has previously been used, but this paper concentrates on measures which can be considered to be weighted similarity measures defined in a probabilistic framework, applied variable by variable and aggregated along the features using a generalized mean. The weights for these measures are determined using a differential evolution process. The classification accuracy with these measures are tested on different data sets. Classification results are obtained with medical data sets, and the results are compared to other classifiers, which gives quite good results. The result presented in this paper are promising, and in several cases better results were achieved.     

An efficient indexing method for nearest neighbor searches inhigh-dirnensional image databases

Nearest neighbor (NN) search is emerging as an important search paradigm in a variety of applications in which objects are represented as vectors of d numeric features. However, despite decades of efforts, except for the filtering approach such as the VA-file, the current solutions to find exact kNNs are far from satisfactory for large d. The filtering approach represents vectors as compact approximations and by first scanning these smaller approximations, only a small fraction of the real vectors are visited. In this paper, we introduce the local polar coordinate file (LPC-file) using the filtering approach for nearest-neighbor searches in high-dimensional image databases. The basic idea is to partition the vector space into rectangular cells and then to approximate vectors by polar coordinates on the partitioned local cells. The LPC information significantly enhances the discriminatory power of the approximation. To demonstrate the effectiveness of the LPC-file, we conducted extensive experiments and compared the performance with the VA-file and the sequential scan by using synthetic and real data sets. The experimental results demonstrate that the LPC-file outperforms both of the VA-file and the sequential scan in total elapsed time and in the number of disk accesses and that the LPC-file is robust in both "good" distributions (such as random) and "bad" distributions (such as skewed and clustered)     

Distributions of Euclidean distances between copies of the set of 2D points when one copy is randomly rotated or reflected

Theorems are stated on the form of probabilistic distributions of Euclidean distances between ordered sets of 2D points with random transformations of their subsets. The theorems provide formulas for the probability distribution densities and ordinary moments. First, several variants of transformations are considered, including random rotation as a whole, random reflection as a whole, simultaneous independent random rotations of two ordered nonoverlapping subsets that form the initial ordered set, and simultaneous independent random reflections of two ordered nonoverlapping subsets that form the initial ordered set. Upon completion of the work, two theorems are stated on the form of probability distribution densities of Euclidean distances for the initial set decomposed into any number of nonoverlapping subsets.     

Exogenous Probabilistic Computation Tree Logic

We define a logic EpCTL for reasoning about the evolution of probabilistic systems. System states correspond to probability distributions over classical states and the system evolution is modelled by probabilistic Kripke structures that capture both stochastic and non–deterministic transitions. The proposed logic is a temporal enrichment of Exogenous Probabilistic Propositional Logic (EPPL). The model-checking problem for EpCTL is analysed and the logic is compared with PCTL; the semantics of the former is defined in terms of probability distributions over sets of propositional symbols, whereas the latter is designed for reasoning about distributions over paths of possible behaviour. The intended application of the logic is as a specification formalism for properties of communication protocols, and security protocols in particular; to demonstrate this, we specify relevant security properties for a classical contract signing protocol and for the so–called quantum one–time pad.     

基于概率犹豫信息集成方法的群决策模型*

现有犹豫模糊集在描述决策信息时会导致决策信息大量损失,因此文中基于概率犹豫模糊信息集成算子,构建多属性群决策模型.首先在概率犹豫模糊环境下引入Archimedean范数,定义概率犹豫模糊运算法则.基于该运算法则,提出广义概率犹豫模糊有序加权平均(GPHFOWA)算子和广义概率犹豫模糊有序加权几何(GPHFOWG)算子,并讨论它们的基本性质.然后分析GPHFOWA算子和GPHFOWG算子的常见形式和相互关系.最后运用提出的2类算子构建概率犹豫模糊多属性群决策模型,并且通过供应商的选择实例验证决策模型的可行性和有效性.     

Probabilistic reasoning in an augmented fact-proposition space and its applications

A simple and versatile probabilistic reasoning scheme is presented. Based on an augmentation of a multi-dimensional inference space indexed by a Cartesian product of the fact and proposition sets, the scheme simplifies the processes involved in the representation and computation of a probabilistic reasoning system. In the augmented space, a set of auxiliary fields is utilized in addition to the fact-proposition relations to manipulate the uncertainty and incompleteness of the information presented. The scheme enhances the functionality of a probabilistic reasoning and facilitates the building of practical reasoning systems. The utilization of the augmented space in reasoning is illustrated by two problems in computer-vision applications.     

DESCRIPTION OF PROBABILISTICAL SYSTEMS WITH STRONGLY STATISTICALLY DEPENDENT ELEMENTS

We propose the f-divergences of two probability distributions as the measures of the organization of a probabilistic system with respect to its probabilistic uncertainty. A probabilistic system consist of stochastical objects on which random variables are defined which are statistically dependent. Using Shannon's f-divergence for the organization of a probabilistic system we express it in terms of the probability distributions of the element random variables and their statistical linkages. Then we find the maximum entropy of a probabilistic system if the statistical linkages between its elements are given as input data. We show that an important class of physical statistical systems can be described by the probabilistic systems of Gibbsian type.     

三支决策-基于粗糙集与粒计算研究视角

从三支决策3个历史发展阶段出发,通过粗糙集和粒计算两个研究视角对三支决策的发展踪迹和演化过程进行介绍。分析了三支决策与粗糙集理论的历史脉络、内在联系和相互关系,探讨了决策粗糙集、概率粗糙集、粗糙集和三支决策之间的包含关系;探讨了基于多层次粒计算和多视角粒计算下的三支决策方法;提出了一个基于三支决策的粒计算研究框架模型。最后,给出了三支决策的研究现状和未来发展方向。     

Possibility theory and statistical reasoning

Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished from uncertainty due to incomplete information. This paper proposes an overview of numerical possibility theory. Its aim is to show that some notions in statistics are naturally interpreted in the language of this theory. First, probabilistic inequalites (like Chebychev's) offer a natural setting for devising possibility distributions from poor probabilistic information. Moreover, likelihood functions obey the laws of possibility theory when no prior probability is available. Possibility distributions also generalize the notion of confidence or prediction intervals, shedding some light on the role of the mode of asymmetric probability densities in the derivation of maximally informative interval substitutes of probabilistic information. Finally, the simulation of fuzzy sets comes down to selecting a probabilistic representation of a possibility distribution, which coincides with the Shapley value of the corresponding consonant capacity. This selection process is in agreement with Laplace indifference principle and is closely connected with the mean interval of a fuzzy interval. It sheds light on the “defuzzification” process in fuzzy set theory and provides a natural definition of a subjective possibility distribution that sticks to the Bayesian framework of exchangeable bets. Potential applications to risk assessment are pointed out.