Use of a relevance vector machine for groundwater quality monitoring network design under uncertainty

This paper presents a methodology for groundwater quality monitoring network design. This design takes into account uncertainties in aquifer properties, pollution transport processes, and climate. The methodology utilizes a statistical learning algorithm called relevance vector machines (RVM), which is a sparse Bayesian framework that can be used for obtaining solutions to regression and classification tasks. Application of the methodology is illustrated using the Eocene Aquifer in the northern part of the West Bank, Palestine. The procedure presented in this paper utilizes a Monte Carlo (MC) simulation process to capture the uncertainties in recharge, hydraulic conductivity, and nitrate reaction processes through the application of a groundwater flow model and a nitrate fate and transport model. This MC modeling approach provides several thousand realizations of nitrate distribution in the aquifer. Subsets of these realizations are then used to design the monitoring network. This is done by building a best-fit model of nitrate concentration distribution everywhere in the aquifer for each Monte Carlo subset using RVM. The outputs from the RVM model are the distribution of nitrate concentration everywhere in the aquifer, the uncertainty in the characterization of those concentrations, and the number and locations of “relevance vectors” (RVs). The RVs form the basis of the optimal characterization of nitrate throughout the aquifer and represent the optimal locations of monitoring wells. In this paper, the number of monitoring wells and their locations where chosen based on the performance of the RVM model runs. The results from 100 model runs show the consistency of the model in selecting the number and locations of RV‘s. After implementing the design, the data collected from the monitoring sites can be used to estimate nitrate concentration distribution throughout the entire aquifer and to quantify the uncertainty in those estimates.     

Bayesian optimization for learning gaits under uncertainty

Designing gaits and corresponding control policies is a key challenge in robot locomotion. Even with a viable controller parametrization, finding near-optimal parameters can be daunting. Typically, this kind of parameter optimization requires specific expert knowledge and extensive robot experiments. Automatic black-box gait optimization methods greatly reduce the need for human expertise and time-consuming design processes. Many different approaches for automatic gait optimization have been suggested to date. However, no extensive comparison among them has yet been performed. In this article, we thoroughly discuss multiple automatic optimization methods in the context of gait optimization. We extensively evaluate Bayesian optimization, a model-based approach to black-box optimization under uncertainty, on both simulated problems and real robots. This evaluation demonstrates that Bayesian optimization is particularly suited for robotic applications, where it is crucial to find a good set of gait parameters in a small number of experiments.     

基于贝叶斯网络的本体不确定性推理

运用OWL语言扩展了本体对领域知识的不确定性表示,并基于贝叶斯网络实现了本体领域知识的不确定性推理。实验表明将贝叶斯网络与本体结合起来,能够充分发挥本体在知识描述方面的优势和贝叶斯网络的推理能力,实现依据部分信息的概率描述获取知识,指导实践。     

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.     

Decision making under uncertainty in a decision support system for the Red River

Decision support systems (DSSs) are increasingly being used in water management for the evaluation of impacts of policy measures under different scenarios. The exact impacts generally are unknown and surrounded with considerable uncertainties. It may therefore be difficult to make a selection of measures relevant for a particular water management problem. In order to support policy makers to make a strategic selection between different measures in a DSS while taking uncertainty into account, a methodology for the ranking of measures has been developed. The methodology has been applied to a pilot DSS for flood control in the Red River basin in Vietnam and China. The decision variable is the total flood damage and possible flood reducing measures are dike heightening, reforestation and the construction of a retention basin. The methodology consists of a Monte Carlo uncertainty analysis employing Latin Hypercube Sampling and a ranking procedure based on the significance of the difference between output distributions for different measures. The mean flood damage in the base situation is about 2.2 billion US$ for the year 1996 with a standard deviation due to parameter uncertainty of about 1 billion US$. Selected applications of the measures reforestation, dike heightening and the construction of a retention basin reduce the flood damage by about 5, 55 and 300 million US$, respectively. The construction of a retention basin significantly reduces flood damage in the Red River basin, while dike heightening and reforestation reduce flood damage, but not significantly.     

Multi-objective biogeography-based optimization for supply chain network design under uncertainty

This paper proposes a new two-stage optimization method for multi-objective supply chain network design (MO-SCND) problem with uncertain transportation costs and uncertain customer demands. On the basis of risk-neutral and risk-averse criteria, we develop two objectives for our SCND problem. We introduce two solution concepts for the proposed MO-SCND problem, and use them to define the multi-objective value of fuzzy solution (MOVFS). The value of the MOVFS measures the importance of uncertainties included in the model, and helps us to understand the necessity of solving the two-stage multi-objective optimization model. When the uncertain transportation costs and customer demands have joined continuous possibility distributions, we employ an approximation approach (AA) to compute the values of two objective functions. Using the AA, the original optimization problem becomes an approximating mixed-integer multi-objective programming model. To solve the hard approximating optimization problem, we design an improved multi-objective biogeography-based optimization (MO-BBO) algorithm integrated with LINGO software. We also compare the improved MO-BBO algorithm with the multi-objective genetic algorithm (MO-GA). Finally, a realistic dairy company example is provided to demonstrate that the improved MO-BBO algorithm achieves the better performance than MO-GA in terms of solution quality.     

Design optimization of resource combination for collaborative logistics network under uncertainty

Collaborative logistics networks (CLNs) are considered to be an effective organizational form for business cooperation that provides high stability and low cost. One common key issue regarding CLN resource combination is the network design optimization problem under discrete uncertainty (DU-CLNDOP). Operational environment changes and information uncertainty in network designs, due to partner selection, resource constrains and network robustness, must be effectively controlled from the system perspective. Therefore, a general two-stage quantitative framework that enables decision makers to select the optimal network design scheme for CLNs under uncertainty is proposed in this paper. Phase 1 calculates the simulation result of each hypothetical scenario of CLN resource combination using the expected value model with robust constraints. Phase 2 selects the optimal network design scheme for DU-CLNDOP using the orthogonal experiment design method. The validity of the model and method are verified via an illustrative example.     

An interactive possibilistic programming approach for a multi-objective closed-loop supply chain network under uncertainty

In this article, we first propose a closed-loop supply chain network design that integrates network design decisions in both forward and reverse supply chain networks into a unified structure as well as incorporates the tactical decisions with strategic ones (e.g., facility location and supplier selection) at each period. To do so, various conflicting objectives and constraints are simultaneously taken into account in the presence of some uncertain parameters, such as cost coefficients and customer demands. Then, we propose a novel interactive possibilistic approach based on the well-known STEP method to solve the multi-objective mixed-integer linear programming model. To validate the presented model and solution method, a numerical test is accomplished through the application of the proposed possibilistic-STEM algorithm. The computational results demonstrate suitability of the presented model and solution method.     

Capacitated closed-loop supply chain network design under uncertainty

This study optimizes the design of a closed-loop supply chain network, which contains forward and reverse directions and is subject to uncertainty in demands for new & returned products. To address uncertainty in decision-making, we formulate a two-stage stochastic mixed-integer non-linear programming model to determine the distribution center locations and their corresponding capacity, and new & returned product flows in the supply chain network to minimize total design and expected operating costs. We convert our model to a conic quadratic programming model given the complexity of our problem. Then, the conic model is added with certain valid inequalities, such as polymatroid inequalities, and extended with respect to its cover cuts so as to improve computational efficiency. Furthermore, a tabu search algorithm is developed for large-scale problem instances. We also study the impact of inventory weight, transportation weight, and marginal value of time of returned products by the sensitivity analysis. Several computational experiments are conducted to validate the effectiveness of the proposed model and valid inequalities.     

Competitive closed-loop supply chain network design under uncertainty

This paper studies the competition between two closed-loop supply chains including manufacturers, retailers and recyclers in an uncertain environment. The competition factors are the retail prices of new products and incentives paid to consumers for taking back the used products. Market demands are price sensitive and also the amount of returned products is sensitive to incentives. The primary goal of this paper is to investigate the impact of simultaneous and Stackelberg competitions between two closed-loop supply chains on their profits, demands and returns. A game theoretic approach which is empowered by possibility theory is applied to obtain the optimal solutions under uncertain condition. Finally the theoretical results are analyzed using sample data inspired by a real industrial case.     

Behavior monitoring under uncertainty using Bayesian surprise and optimal action selection

The increasing trend towards delegating tasks to autonomous artificial agents in safety–critical socio-technical systems makes monitoring an action selection policy of paramount importance. Agent behavior monitoring may profit from a stochastic specification of an optimal policy under uncertainty. A probabilistic monitoring approach is proposed to assess if an agent behavior (or policy) respects its specification. The desired policy is modeled by a prior distribution for state transitions in an optimally-controlled stochastic process. Bayesian surprise is defined as the Kullback–Leibler divergence between the state transition distribution for the observed behavior and the distribution for optimal action selection. To provide a sensitive on-line estimation of Bayesian surprise with small samples twin Gaussian processes are used. Timely detection of a deviant behavior or anomaly in an artificial pancreas highlights the sensitivity of Bayesian surprise to a meaningful discrepancy regarding the stochastic optimal policy when there exist excessive glycemic variability, sensor errors, controller ill-tuning and infusion pump malfunctioning. To reject outliers and leave out redundant information, on-line sparsification of data streams is proposed.     

Use of decision models under uncertainty in thermal design

A probabilistic approach is described for analysing the results of computer simulation of the thermal behaviour of buildings. This approach takes into account the uncertainties in predicting the climate. The use of models of decision theory enables the designer to compare several design alternatives of a building and to select the best one in terms of use of energy. The application of decision models under uncertainty in the design process of solarium is presented.     

Minimization of the delay in a data-communication network with centralized control under uncertainty

An adaptive algorithm which minimizes the delay in a data communication network with centralized control under uncertainty is presented. The model considered in Segall [5] is adopted. Additionally it is assumed that each measurement (observation) of the entering traffic to the network, the delays and the gradient of the delays are accompanied with some noise which is a random variable with unknown distribution.     

A novel mechanism in MPLS network under adversarial uncertainty

The advantage of multi-protocol label switching （MPLS） is its capability to route the packets through explicit paths. But the nodes in the paths may be possibly attacked by the adversarial uncertainty. Aiming at this problem in MPLS Network, this paper proposes a novel mechanism in MPLS network under adversarial uncertainty, making use of the theory of artificial intelligence. Firstly, the initialized label switching paths （LSPs） using the A＊ arithmetic is found. Secondly, during the process of data transmission, the transmission path is switched duly by taking advantage of the non-monotone reasoning mechanism. Compared with the traditional route mechanism, the experimental results show that the security can be improved if data transmission remarkably under this novel mechanism in MPLS network.     

回收不确定下WEEE逆向物流网络鲁棒优化设计

电子电器废弃物（WEEE）存在对环境和人体健康的危害,有效对其进行回收能避免此类危害和提高资源的利用率。WEEE逆向物流回收网络的设计为实现这一目标起到了关键的作用。考虑WEEE逆向物流网络运作的不确定性,引入风险偏好系数和约束背离惩罚系数,建立了WEEE逆向物流网络的鲁棒优化模型。该模型能允许决策者对系统运作的鲁棒水平进行调节,同时能允许决策者对风险偏好进行调节。仿真结果表明建立的模型能有效抑制逆向物流系统运作的不确定性,使系统具有更低的风险。     

Full uncertainty analysis for Bayesian nonparametric mixture models

A full posterior analysis for nonparametric mixture models using Gibbs-type prior distributions is presented. This includes the well known Dirichlet process mixture (DPM) model. The random mixing distribution is removed enabling a simple-to-implement Markov chain Monte Carlo (MCMC) algorithm. The removal procedure takes away some of the posterior uncertainty and how it is replaced forms a novel aspect to the work. The removal, MCMC algorithm and replacement of the uncertainty only require the probabilities of a new or an old value associated with the corresponding Gibbs-type exchangeable sequence. Consequently, no explicit representations of the prior or posterior are required and instead only knowledge of the exchangeable sequence is needed. This allows the implementation of mixture models with full posterior uncertainty, not previously possible, including one introduced by Gnedin. Numerous illustrations are presented, as is an R-package called CopRe which implements the methodology, and other supplemental material.     

A comparison of two Bayesian approaches for uncertainty quantification

Statistical calibration of model parameters conditioned on observations is performed in a Bayesian framework by evaluating the joint posterior probability density function (pdf) of the parameters. The posterior pdf is very often inferred by sampling the parameters with Markov Chain Monte Carlo (MCMC) algorithms. Recently, an alternative technique to calculate the so-called Maximal Conditional Posterior Distribution (MCPD) appeared. This technique infers the individual probability distribution of a given parameter under the condition that the other parameters of the model are optimal. Whereas the MCMC approach samples probable draws of the parameters, the MCPD samples the most probable draws when one of the parameters is set at various prescribed values. In this study, the results of a user-friendly MCMC sampler called DREAM_(ZS) and those of the MCPD sampler are compared. The differences between the two approaches are highlighted before running a comparison inferring two analytical distributions with collinearity and multimodality. Then, the performances of both samplers are compared on an artificial multistep outflow experiment from which the soil hydraulic parameters are inferred. The results show that parameter and predictive uncertainties can be accurately assessed with both the MCMC and MCPD approaches.     

Counterfactual explanation of Bayesian model uncertainty

Neural Computing and Applications - Artificial intelligence systems are becoming ubiquitous in everyday life as well as in high-risk environments, such as autonomous driving, medical treatment, and...     

Network effects and embedded options: decision-making under uncertainty for network technology investments

The analysis of network effects in technology-based networks continues to be of significant managerial importance in e-commerce and traditional IS operations. Competitive strategy, economics and IS researchers share this interest, and have been exploring technology adoption, development and product launch contexts where understanding the issues is critical. This article examines settings involving countervailing and complementary network effects, which act as drivers of business value at several levels of analysis: the industry or market level, the firm or process level, the individual or product level, and the technology level. It leverages real options analysis for managerial decision-making under uncertainty across these contexts. We also identify a set of real options—compatibility, sponsorship and ownership option—which are unique to these settings, and which provide a template for managerial thinking and analysis when it is possible to delay an investment decision. We employ a hybrid jump-diffusion process to model countervailing and complementary network effects from the perspective of a user or a firm joining a network. We also do this from the perspective of a network developer. Our analysis shows that when countervailing and complementary network effects occur in the same network technology context, they give rise to real option value effects that may be used to control or modify the valuation trajectory of a network technology. The option value of waiting in these contexts jumps when the related business environment experiences shocks. Further, we find that the functional relationship between network value and the option value is not linear, and that taking into account a risk premium may not always result in a risk-neural investment. We also provide a managerial decision-making template through the different kinds of deferral options that we identify for this IT analysis context.