Simulation of lognormal random fields with varying resolution scale and local average for Darcy flow

The paper presents a new method for generating isotropic realizations of a random field with varying resolution scales and local block averages in one, two, or three dimensions. The random field has a lognormal distribution as found for the hydraulic conductivity in Darcy's flow in hydrology. We also present a fast method for generating anisotropic realizations of aGaussian random field using superposition of harmonic modes. Both methods are implemented in a software package which is presented. The realizations of the rescaled random field are made up ofupscaled local averages of the underlying random field which are consistentwith the level of resolution and which can be conditioned. The approach is motivated by the need to represent engineering properties aslocal averages and to be able to easily condition the realizations to incorporate known data or to change the resolution within sub-regions. The numerical results show that the method is very efficient computationally.     

Comorbidity of chronic diseases in the elderly: Patterns identified by a copula design for mixed responses

Joint modeling of multiple health related random variables is essential to develop an understanding for the public health consequences of an aging population. This is particularly true for patients suffering from multiple chronic diseases. The contribution is to introduce a novel model for multivariate data where some response variables are discrete and some are continuous. It is based on pair copula constructions (PCCs) and has two major advantages over existing methodology. First, expressing the joint dependence structure in terms of bivariate copulas leads to a computationally advantageous expression for the likelihood function. This makes maximum likelihood estimation feasible for large multidimensional data sets. Second, different and possibly asymmetric bivariate (conditional) marginal distributions are allowed which is necessary to accurately describe the limiting behavior of conditional distributions for mixed discrete and continuous responses. The advantages and the favorable predictive performance of the model are demonstrated using data from the Second Longitudinal Study of Aging (LSOA II).     

Issues related to the computer realization of a multidisciplinary and multiobjective optimization system

Issues and novel ideas to be considered when developing computer realizations of complex multidisciplinary and multiobjective optimization systems are introduced. The aim is to discuss computer realizations that make possible both computationally efficient multidisciplinary analysis and multiobjective optimization of real world problems. We introduce software tools that make typically very time-consuming simulation processes more effective and, thus, enable even interactive multiobjective optimization with a real decision maker. In this paper, we first define a multidisciplinary and multiobjective optimization system and after that present an implementation overview of such problems including basic components participating in the solution process. Furthermore, interfaces and data flows between the components are described. A couple of important features related to the implementation are discussed in detail, for example, the usage of automatic differentiation. Finally, the ideas presented are illustrated with an industrial multiobjective optimization problem, when we describe numerical experiments related to quality properties in paper making.     

Discovering causality in large databases

A causal rule between two variables, X M Y, captures the relationship that the presence of X causes the appearance of Y. Because of its usefulness (compared to association rules), techniques for mining causal rules are beginning to be developed. However, the effectiveness of existing methods (such as the LCD and CU-path algorithms) are limited to mining causal rules among simple variables, and are inadequate to discover and represent causal rules among multi-value variables. In this paper, we propose that the causality between variables X and Y be represented in the form X M Y with conditional probability matrix M Y|X . We also propose a new approach to discover causality in large databases based on partitioning. The approach partitions the items into item variables by decomposing "bad" item variables and composing "not-good" item variables. In particular, we establish a method to optimize causal rules that merges the "useless" information in conditional probability matrices of extracted causal rules.     

Random field modeling with insufficient field data for probability analysis and design

Often engineered systems entail randomness as a function of spatial (or temporal) variables. The random field can be found in the form of geometry, material property, and/or loading in engineering products and processes. In some applications, consideration of the random field is a key to accurately predict variability in system performances. However, existing methods for random field modeling are limited for practical use because they require sufficient field data. This paper thus proposes a new random field modeling method using a Bayesian Copula that facilitates the random field modeling with insufficient field data and applies this method for engineering probability analysis and robust design optimization. The proposed method is composed of three key ideas: (i) determining the marginal distribution of random field realizations at each measurement location, (ii) determining optimal Copulas to model statistical dependence of the field realizations at different measurement locations, and (iii) modeling a joint probability density function of the random field. A mathematical problem was first employed for the purpose of demonstrating the accuracy of the random field modeling with insufficient field data. The second case study deals with the assembly process of a two-door refrigerator that challenges predicting the door assembly tolerance and minimizing the tolerance by designing the random field and parameter variables in the assembly process with insufficient random field data. It is concluded that the proposed random field modeling can be used to successfully conduct the probability analysis and robust design optimization with insufficient random field data.     

Conditional copulas, association measures and their applications

One way to model a dependence structure is through the copula function which is a mean to capture the dependence structure in the joint distribution of variables. Association measures such as Kendall’s tau or Spearman’s rho can be expressed as functionals of the copula. The dependence structure between two variables can be highly influenced by a covariate, and it is of real interest to know how this dependence structure changes with the value taken by the covariate. This motivates the need for introducing conditional copulas, and the associated conditional Kendall’s tau and Spearman’s rho association measures. After the introduction and motivation of these concepts, two nonparametric estimators for a conditional copula are proposed and discussed. Then nonparametric estimates for the conditional association measures are derived. A key issue is that these measures are now looked at as functions in the covariate. The performances of all estimators are investigated via a simulation study which also includes a data-driven algorithm for choosing the smoothing parameters. The usefulness of the methods is illustrated on two real data examples.     

Likelihood and Pseudo-likelihood Methods for Semiparametric Joint Models for a Primary Endpoint and Longitudinal Data

Inference on the association between a primary endpoint and features of longitudinal profiles of a continuous response is of central interest in medical and public health research. Joint models that represent the association through shared dependence of the primary and longitudinal data on random effects are increasingly popular; however, existing inferential methods may be inefficient or sensitive to assumptions on the random effects distribution. We consider a semiparametric joint model that makes only mild assumptions on this distribution and develop likelihood-based inference on the association and distribution, which offers improved performance relative to existing methods that is insensitive to the true random effects distribution. Moreover, the estimated distribution can reveal interesting population features, as we demonstrate for a study of the association between longitudinal hormone levels and bone status in peri-menopausal women.     

Implementation of conditional simulation by successive residuals

Conditional simulation of ergodic and stationary Gaussian random fields using successive residuals is a new approach used to overcome the size limitations of the LU decomposition algorithm as well as provide fast updating of existing simulated realizations with new data. This paper discusses two different implementations of this approach. The implementations differ in the use of the new information available; in the first implementation new information is partially used to generate updated realizations; however, in the second implementation, the realizations are updated using all the new information available. The implementations are validated using the Walker Lake data set, and compared through a case study at a stockwork gold deposit.     

Whole-sentence exponential language models: a vehicle for linguistic-statistical integration

We introduce an exponential language model which models a whole sentence or utterance as a single unit. By avoiding the chain rule, the model treats each sentence as a “bag of features", where features are arbitrary computable properties of the sentence. The new model is computationally more efficient, and more naturally suited to modeling global sentential phenomena, than the conditional exponential (e.g. maximum entropy) models proposed to date. Using the model is straightforward. Training the model requires sampling from an exponential distribution. We describe the challenge of applying Monte Carlo Markov Chain and other sampling techniques to natural language, and discuss smoothing and step-size selection. We then present a novel procedure for feature selection, which exploits discrepancies between the existing model and the training corpus. We demonstrate our ideas by constructing and analysing competitive models in the Switchboard and Broadcast News domains, incorporating lexical and syntactic information.     

Causality, conditional independence, and graphical separation in settable systems

We study the connections between causal relations and conditional independence within the settable systems extension of the Pearl causal model (PCM). Our analysis clearly distinguishes between causal notions and probabilistic notions, and it does not formally rely on graphical representations. As a foundation, we provide definitions in terms of suitable functional dependence for direct causality and for indirect and total causality via and exclusive of a set of variables. Based on these foundations, we provide causal and stochastic conditions formally characterizing conditional dependence among random vectors of interest in structural systems by stating and proving the conditional Reichenbach principle of common cause, obtaining the classical Reichenbach principle as a corollary. We apply the conditional Reichenbach principle to show that the useful tools of d-separation and D-separation can be employed to establish conditional independence within suitably restricted settable systems analogous to Markovian PCMs.     

Data Uncertainty in Virtual Network Embedding: Robust Optimization and Protection Levels

We address the virtual network embedding problem (VNE) which, given a physical (substrate) network and a collection of virtual networks (VNs), calls for an embedding of the most profitable subset of VNs onto the physical substrate, subject to capacity constraints. In practical applications, node and link demands of the different VNs are, typically, uncertain and difficult to know a priori. To face this issue, we first model VNE as a chance-constrained Mixed-Integer Linear Program (MILP) where the uncertain demands are assumed to be random variables. We then propose a \(\varGamma \)-robust optimization approach to approximate the original chance-constrained formulation, capable of yielding solutions with a large profit that are feasible for almost all the possible realizations of the uncertain demands. To solve larger scale instances, for which the exact approach is computationally too demanding, we propose two MILP-based heuristics: a parametric one, which relies on a parameter setting chosen a priori, and an adaptive one, which does not. We conclude by reporting on extensive computational experiments where the different methods and approaches are compared.     

3D segmentation of abdominal CT imagery with graphical models,conditional random fields and learning

Probabilistic graphical models have had a tremendous impact in machine learning and approaches based on energy function minimization via techniques such as graph cuts are now widely used in image segmentation. However, the free parameters in energy function-based segmentation techniques are often set by hand or using heuristic techniques. In this paper, we explore parameter learning in detail. We show how probabilistic graphical models can be used for segmentation problems to illustrate Markov random fields (MRFs), their discriminative counterparts conditional random fields (CRFs) as well as kernel CRFs. We discuss the relationships between energy function formulations, MRFs, CRFs, hybrids based on graphical models and their relationships to key techniques for inference and learning. We then explore a series of novel 3D graphical models and present a series of detailed experiments comparing and contrasting different approaches for the complete volumetric segmentation of multiple organs within computed tomography imagery of the abdominal region. Further, we show how these modeling techniques can be combined with state of the art image features based on histograms of oriented gradients to increase segmentation performance. We explore a wide variety of modeling choices, discuss the importance and relationships between inference and learning techniques and present experiments using different levels of user interaction. We go on to explore a novel approach to the challenging and important problem of adrenal gland segmentation. We present a 3D CRF formulation and compare with a novel 3D sparse kernel CRF approach we call a relevance vector random field. The method yields state of the art performance and avoids the need to discretize or cluster input features. We believe our work is the first to provide quantitative comparisons between traditional MRFs with edge-modulated interaction potentials and CRFs for multi-organ abdominal segmentation and the first to explore the 3D adrenal gland segmentation problem. Finally, along with this paper we provide the labeled data used for our experiments to the community.     

Mean and variance bounds and propagation for ill-specified random variables

Foundations, models, and algorithms are provided for identifying optimal mean and variance bounds of an ill-specified random variable. A random variable is ill-specified when at least one of its possible realizations and/or its respective probability mass is not restricted to a point but rather belongs to a set or an interval. We show that a nonexhaustive sensitivity-analysis approach does not always identify the optimal bounds. Also, a procedure for determining the mean and variance bounds of an arithmetic function of ill-specified random variables is presented. Estimates of pairwise correlation among the random variables can be incorporated into the function. The procedure is illustrated in the context of a case study in which exposure to contaminants through the inhalation pathway is modeled.     

HOSIM: A high-order stochastic simulation algorithm for generating three-dimensional complex geological patterns

The three-dimensional high-order simulation algorithm HOSIM is developed to simulate complex non-linear and non-Gaussian systems. HOSIM is an alternative to the current MP approaches and it is based upon new high-order spatial connectivity measures, termed high-order spatial cumulants. The HOSIM algorithm implements a sequential simulation process, where local conditional distributions are generated using weighted orthonormal Legendre polynomials, which in turn define the so-called Legendre cumulants. The latter are high-order conditional spatial cumulants inferred from both the available data and training images. This approach is data-driven and reconstructs both high and lower-order spatial complexity in simulated realizations, while it only borrows from training images information that is not available in the data used. However, the three-dimensional implementation of the algorithm is computationally very intensive. To address his topic, the contribution of high-order conditional spatial cumulants is assessed in this paper through the number of Legendre cumulants with respect to the order of approximation used to estimate a conditional distribution and the number of data used within the respective neighbourhood. This leads to discarding the terms of Legendre cumulants with negligible contributions and allows an efficient simulation algorithm to be developed. The current version of the HOSIM algorithm is several orders of magnitude faster than the original version of the algorithm. Application and comparisons in a controlled environment show the excellent performance and efficiency of the HOSIM algorithm.     

基于生成对抗网络的漫画草稿图简化

在漫画绘制的过程中,按草稿绘制出线条干净的线稿是很重要的一环.现有的草图简化方法已经具有一定的线条简化能力,然而由于草图的绘制方式的多样性以及画面复杂程度的不同,这些方法适用范围有限且效果不理想.本文提出了一种新颖的草图简化方法,利用条件随机场（Conditional random field,CRF）和最小二乘生成式对抗网络（Least squares generative adversarial networks,LSGAN）理论搭建了深度卷积神经网络的草图简化模型,通过该网络生成器与判别器之间的零和博弈与条件约束,得到更加接近真实的简化线稿图.同时,为了训练对抗模型的草图简化能力,本文建立了包含更多绘制方式与不同内容的草图与简化线稿图对的训练数据集.实验表明,本文算法对于复杂情况下的草图,相比于目前的方法,具有更好的简化效果.     

Dual Stochastic Dominance and Quantile Risk Measures

Following the seminal work by Markowitz, the portfolio selection problem is usually modeled as a bicriteria optimization problem where a reasonable trade–off between expected rate of return and risk is sought. In the classical Markowitz model, the risk is measured with variance. Several other risk measures have been later considered thus creating the entire family of mean–risk (Markowitz type) models. In this paper, we analyze mean–risk models using quantiles and tail characteristics of the distribution. Value at risk (VAR), defined as the maximum loss at a specified confidence level, is a widely used quantile risk measure. The corresponding second order quantile measure, called the worst conditional expectation or Tail VAR, represents the mean shortfall at a specified confidence level. It has more attractive theoretical properties and it leads to LP solvable portfolio optimization models in the case of discrete random variables, i.e., in the case of returns defined by their realizations under the specified scenarios. We show that the mean–risk models using the worst conditional expectation or some of its extensions are in harmony with the stochastic dominance order. For this purpose, we exploit duality relations of convex analysis to develop the quantile model of stochastic dominance for general distributions.     

Non-redundant data clustering

Data clustering is a popular approach for automatically finding classes, concepts, or groups of patterns. In practice, this discovery process should avoid redundancies with existing knowledge about class structures or groupings, and reveal novel, previously unknown aspects of the data. In order to deal with this problem, we present an extension of the information bottleneck framework, called coordinated conditional information bottleneck, which takes negative relevance information into account by maximizing a conditional mutual information score subject to constraints. Algorithmically, one can apply an alternating optimization scheme that can be used in conjunction with different types of numeric and non-numeric attributes. We discuss extensions of the technique to the tasks of semi-supervised classification and enumeration of successive non-redundant clusterings. We present experimental results for applications in text mining and computer vision.     

Correlation coefficient of linguistic variables and its applications to quantifying relations in imprecise management data

We frequently use the standard correlation coefficient to quantify linear relation between two given variables of interest in crisp industrial data. On the other hand, in many real world applications involving the opinions of experts, the domain of a variable of interest, e.g. the rating of the innovativeness of a new product idea, is oftentimes composed of subjective linguistic concepts such as very poor, poor, average, good and excellent. In this article, we extend the standard correlation coefficient to the subjective, linguistic setting, so as to quantify relations in imprecise industrial and management data. Unlike the correlation measures for fuzzy variables proposed in the literature, the present approach allows one to develop a correlation coefficient for linguistic variables that can account for and reflect the conditional dependence assumptions underlying a given data set. We apply the proposed method to quantify the degree of correlation between technology and management achievements of 15 large-scale machinery firms in Taiwan. It is shown that the flexibility of the present framework in allowing for the incorporation of appropriate conditional dependence assumptions to derive a correlation measure for linguistic variables can be essential in approximate reasoning applications.     

基于约束条件随机场的Web数据语义标注

Web数据语义标注是Web信息抽取中的关键步骤.条件随机场是利用序列特征处理序列标注问题的经典方法.然而现有条件随机场模型无法综合利用已有的Web数据库信息和Web数据元素之间的逻辑关系,导致Web数据语义标注准确率不高.因此,提出一种约束条件随机场模型(CCRF).该模型通过引入可信约束和逻辑约束,有效利用了已有的Web数据库信息和Web数据元素之间的逻辑关系.为了克服现有条件随机场模型Viterbi推理方法无法综合利用这2类约束的不足,该模型采用整数线性规划推理方法,将两类约束同时引入推理过程.通过在多个领域的真实数据集上的实验结果表明,所提出的模型能够显著提高Web数据语义标注的性能,并且为Web信息抽取奠定了良好的基础.