Статті в журналах: "Stochastic weights"

1

Xiong, Fenfen, Wei Chen, Ying Xiong, and Shuxing Yang. "Weighted stochastic response surface method considering sample weights." Structural and Multidisciplinary Optimization 43, no. 6 (February 3, 2011): 837–49. http://dx.doi.org/10.1007/s00158-011-0621-3.

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2

Li, Yan, and Yi Shen. "Preserving Global Exponential Stability of Hybrid BAM Neural Networks with Reaction Diffusion Terms in the Presence of Stochastic Noise and Connection Weight Matrices Uncertainty." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/486052.

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We study the impact of stochastic noise and connection weight matrices uncertainty on global exponential stability of hybrid BAM neural networks with reaction diffusion terms. Given globally exponentially stable hybrid BAM neural networks with reaction diffusion terms, the question to be addressed here is how much stochastic noise and connection weights matrices uncertainty the neural networks can tolerate while maintaining global exponential stability. The upper threshold of stochastic noise and connection weights matrices uncertainty is defined by using the transcendental equations. We find that the perturbed hybrid BAM neural networks with reaction diffusion terms preserve global exponential stability if the intensity of both stochastic noise and connection weights matrices uncertainty is smaller than the defined upper threshold. A numerical example is also provided to illustrate the theoretical conclusion.

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3

Goldenberg, David H. "Beta Instability and Stochastic Market Weights." Management Science 31, no. 4 (April 1985): 415–21. http://dx.doi.org/10.1287/mnsc.31.4.415.

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4

Caraballo, Luis E., Pablo Pérez-Lantero, Carlos Seara, and Inmaculada Ventura. "Maximum Box Problem on Stochastic Points." Algorithmica 83, no. 12 (October 28, 2021): 3741–65. http://dx.doi.org/10.1007/s00453-021-00882-z.

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AbstractGiven a finite set of weighted points in $${\mathbb {R}}^d$$ R d (where there can be negative weights), the maximum box problem asks for an axis-aligned rectangle (i.e., box) such that the sum of the weights of the points that it contains is maximized. We consider that each point of the input has a probability of being present in the final random point set, and these events are mutually independent; then, the total weight of a maximum box is a random variable. We aim to compute both the probability that this variable is at least a given parameter, and its expectation. We show that even in $$d=1$$ d = 1 these computations are #P-hard, and give pseudo-polynomial time algorithms in the case where the weights are integers in a bounded interval. For $$d=2$$ d = 2 , we consider that each point is colored red or blue, where red points have weight $$+1$$ + 1 and blue points weight $$-\infty $$ - ∞ . The random variable is the maximum number of red points that can be covered with a box not containing any blue point. We prove that the above two computations are also #P-hard, and give a polynomial-time algorithm for computing the probability that there is a box containing exactly two red points, no blue point, and a given point of the plane.

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5

Yang, Zao-li, and Lu-cheng Huang. "Dynamic Stochastic Multiattribute Decision-Making That Considers Stochastic Variable Variance Characteristics under Time-Sequence Contingency Environments." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/7126856.

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This paper presents a dynamic stochastic decision-making method that considers the characteristics of stochastic variable variances under time-sequence contingency environments for solving stochastic decision-making problems with information from different periods and of indeterminate attribute weights. First, time-sequence weights are obtained using the technique for order preference by similarity to ideal solution (TOPSIS), corresponding with the idea of “stressing the present rather than the past.” After determining the time degree and fully considering the characteristics of normally distributed stochastic variable variances, the attribute weight is determined based on vertical projection distance. Decision-making information is then assembled from two dimensions of time-sequence and attributes, based on the two categories of weighted arithmetic averaging operators of normally distributed stochastic variables, resulting in comprehensive dynamic decision-making from single solution dimensions and a priority sequence of solutions per the order relation criteria of normally distributed stochastic variables. Finally, the validity and practicability of the methods proposed in this paper are verified using an example numerical analysis.

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6

Gashi, Bujar. "Optimal stochastic regulators with state-dependent weights." Systems & Control Letters 134 (December 2019): 104522. http://dx.doi.org/10.1016/j.sysconle.2019.104522.

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7

Xu, Liyan, Tony Vladusich, Fabing Duan, Lachlan J. Gunn, Derek Abbott, and Mark D. McDonnell. "Decoding suprathreshold stochastic resonance with optimal weights." Physics Letters A 379, no. 38 (October 2015): 2277–83. http://dx.doi.org/10.1016/j.physleta.2015.05.032.

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8

Brüggemann, Ralf, and Helmut Lütkepohl. "Forecasting contemporaneous aggregates with stochastic aggregation weights." International Journal of Forecasting 29, no. 1 (January 2013): 60–68. http://dx.doi.org/10.1016/j.ijforecast.2012.05.007.

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9

Liu, Qingliang, and Jinmei Lai. "Stochastic Loss Function." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4884–91. http://dx.doi.org/10.1609/aaai.v34i04.5925.

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Training deep neural networks is inherently subject to the predefined and fixed loss functions during optimizing. To improve learning efficiency, we develop Stochastic Loss Function (SLF) to dynamically and automatically generating appropriate gradients to train deep networks in the same round of back-propagation, while maintaining the completeness and differentiability of the training pipeline. In SLF, a generic loss function is formulated as a joint optimization problem of network weights and loss parameters. In order to guarantee the requisite efficiency, gradients with the respect to the generic differentiable loss are leveraged for selecting loss function and optimizing network weights. Extensive experiments on a variety of popular datasets strongly demonstrate that SLF is capable of obtaining appropriate gradients at different stages during training, and can significantly improve the performance of various deep models on real world tasks including classification, clustering, regression, neural machine translation, and objection detection.

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10

Guo, Hao, Jiyong Jin, and Bin Liu. "Stochastic Weight Averaging Revisited." Applied Sciences 13, no. 5 (February 24, 2023): 2935. http://dx.doi.org/10.3390/app13052935.

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Averaging neural network weights sampled by a backbone stochastic gradient descent (SGD) is a simple-yet-effective approach to assist the backbone SGD in finding better optima, in terms of generalization. From a statistical perspective, weight-averaging contributes to variance reduction. Recently, a well-established stochastic weight-averaging (SWA) method was proposed, which featured the application of a cyclical or high-constant (CHC) learning-rate schedule for generating weight samples for weight-averaging. Then, a new insight on weight-averaging was introduced, which stated that weight average assisted in discovering a wider optima and resulted in better generalization. We conducted extensive experimental studies concerning SWA, involving 12 modern deep neural network model architectures and 12 open-source image, graph, and text datasets as benchmarks. We disentangled the contributions of the weight-averaging operation and the CHC learning-rate schedule for SWA, showing that the weight-averaging operation in SWA still contributed to variance reduction, and the CHC learning-rate schedule assisted in exploring the parameter space more widely than the backbone SGD, which could be be under-fitted due to a lack of training budget. We then presented an algorithm termed periodic SWA (PSWA) that comprised a series of weight-averaging operations to exploit such wide parameter space structures as explored by the CHC learning-rate schedule, and we empirically demonstrated that PSWA outperformed its backbone SGD remarkably.

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11

Yamada, Toshihiro. "A weak approximation with Malliavin weights for local stochastic volatility model." International Journal of Financial Engineering 04, no. 01 (March 2017): 1750002. http://dx.doi.org/10.1142/s2424786317500025.

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This paper introduces a new efficient and practical weak approximation for option price under local stochastic volatility model as marginal expectation of stochastic differential equation, using iterative asymptotic expansion with Malliavin weights. The explicit Malliavin weights for SABR model are shown. Numerical experiments confirm the validity of our discretization with a few time steps.

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12

Liu, Xiaoyue, Xiaolu Wang, Li Zhang, and Qinghua Zeng. "A novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance with incomplete weight information." Kybernetes 48, no. 9 (October 7, 2019): 2030–64. http://dx.doi.org/10.1108/k-08-2018-0438.

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PurposeWith respect to multiple attribute group decision-making (MAGDM) in which the assessment values of alternatives are denoted by normal discrete fuzzy variables (NDFVs) and the weight information of attributes is incompletely known, this paper aims to develop a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and then applies the proposed method for selecting the most desirable investment alternative under uncertain environment.Design/methodology/approachFirst, by aggregating the membership degrees of an alternative to a scale provided by all decision-makers into a triangular fuzzy number, the credibility degree and expect the value of a triangular fuzzy number are calculated to construct the group fuzzy stochastic decision matrix. Second, based on determining the credibility distribution functions of NDFVs, the fuzzy stochastic dominance relations between alternatives on each attribute are obtained and the fuzzy stochastic dominance degree matrices are constructed by calculating the dominance degrees that one alternative dominates another on each attribute. Subsequently, calculating the overall fuzzy stochastic dominance degrees of an alternative on each attribute, a single objective non-linear optimization model is established to determine the weights of attributes by maximizing the relative closeness coefficients of all alternatives to positive ideal solution. If the information about attribute weights is completely unknown, the idea of maximizing deviation is used to determine the weights of attributes. Finally, the ranking order of alternatives is determined according to the descending order of corresponding relative closeness coefficients and the best alternative is determined.FindingsThis paper proposes a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and a case study of investment alternative selection problem is provided to illustrate the applicability and sensitivity of the proposed method and its effectiveness is demonstrated by comparison analysis with the proposed method with the existing fuzzy stochastic MAGDM method. The result shows that the proposed method is useful to solve the MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known.Originality/valueThe contributions of this paper are that to describe the dominance relations between fuzzy variables reasonably and quantitatively, the fuzzy stochastic dominance relations between any two fuzzy variables are redefined and the concept of fuzzy stochastic dominance degree is proposed to measure the dominance degree that one fuzzy variable dominate another; Based on credibility theory and fuzzy stochastic dominance, a novel fuzzy stochastic MAGDM method is proposed to solve MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known. The proposed method has a clear logic, which not only can enrich and develop the theories and methods of MAGDM but also provides decision-makers a novel method for solving fuzzy stochastic MAGDM problems.

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13

Alsmeyer, Gerold, and Uwe Rösler. "A Stochastic Fixed Point Equation Related to Weighted Branching with Deterministic Weights." Electronic Journal of Probability 11 (2006): 27–56. http://dx.doi.org/10.1214/ejp.v11-296.

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14

Mayer, Axel, and Felix Thoemmes. "Analysis of Variance Models with Stochastic Group Weights." Multivariate Behavioral Research 54, no. 4 (January 20, 2019): 542–54. http://dx.doi.org/10.1080/00273171.2018.1548960.

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15

Zhou, Bingchang, Xuelin Wang, and Qianqian Qi. "Optimal weights decoding of M-ary suprathreshold stochastic resonance in stochastic pooling network." Chinese Journal of Physics 56, no. 4 (August 2018): 1718–26. http://dx.doi.org/10.1016/j.cjph.2018.06.010.

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16

Sbert, Mateu, Jordi Poch, Shuning Chen, and Víctor Elvira. "Stochastic Order and Generalized Weighted Mean Invariance." Entropy 23, no. 6 (May 25, 2021): 662. http://dx.doi.org/10.3390/e23060662.

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In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

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17

STACEY, ALAN. "Searches on a Binary Tree with Random Edge-Weights." Combinatorics, Probability and Computing 8, no. 6 (November 1999): 555–65. http://dx.doi.org/10.1017/s0963548399004083.

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Each edge of the standard rooted binary tree is equipped with a random weight; weights are independent and identically distibuted. The value of a vertex is the sum of the weights on the path from the root to the vertex. We wish to search the tree to find a vertex of large weight. A very natural conjecture of Aldous states that, in the sense of stochastic domination, an obvious greedy algorithm is best possible. We show that this conjecture is false. We prove, however, that in a weaker sense there is no significantly better algorithm.

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18

Xia, Meimei. "Choquet-Integral-Based Data Envelopment Analysis with Stochastic Multicriteria Acceptability Analysis." Symmetry 14, no. 4 (March 22, 2022): 642. http://dx.doi.org/10.3390/sym14040642.

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Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiencies of decision-making units (DMUs) by using a set of inputs and a set of outputs. However, traditional DEA models always assume that the inputs or outputs are independent of each other, which is unrealistic in practical problems. To reflect the interactions between inputs or outputs, the Choquet integral is employed in DEA models. The traditional DEA models are usually used to find some specific input and output weights of DMUs to optimize the efficiency score of DMUs, but the corresponding input and output weights for the optimal efficiency score of a DMU may not be distributed symmetrically, that is to say, the space of weights may be different for different DMUs. Instead of finding the self-efficiency score and the cross-efficiency score of a DMU in traditional DEA models based on some specific input and output weights, stochastic multicriteria acceptability analysis is used to explore the input or output evaluation space and weight space to calculate the Choquet-integral-based acceptability indices of DMUs. The proposed method considers the interactions between inputs or outputs, which can make more DMUs efficient and can also measure the acceptability of a DMU to become an efficient one by exploring the supporting information space. Examples are given to illustrate the proposed method.

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19

Bernier, O. "Stochastic Analysis of Synchronous Neural Networks with Asymmetric Weights." Europhysics Letters (EPL) 16, no. 6 (October 7, 1991): 531–36. http://dx.doi.org/10.1209/0295-5075/16/6/004.

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20

Robert, Philippe, and Amandine Véber. "A stochastic analysis of resource sharing with logarithmic weights." Annals of Applied Probability 25, no. 5 (October 2015): 2626–70. http://dx.doi.org/10.1214/14-aap1057.

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21

Gupta, Abhimanyu. "ESTIMATION OF SPATIAL AUTOREGRESSIONS WITH STOCHASTIC WEIGHT MATRICES." Econometric Theory 35, no. 2 (May 3, 2018): 417–63. http://dx.doi.org/10.1017/s0266466618000142.

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We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential ‘long memory’, we provide sufficient conditions for consistency and asymptotic normality of instrumental variables, ordinary least squares, and pseudo maximum likelihood estimates. The implications of popular weight matrix normalizations and structures for our theoretical conditions are discussed. A set of Monte Carlo simulations examines the behaviour of the estimates in a variety of situations. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables, and this type of setting is also studied in our simulations.

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22

Chen, Kai, and Sheldon M. Ross. "STATIC STOCHASTIC KNAPSACK PROBLEMS." Probability in the Engineering and Informational Sciences 29, no. 4 (October 2015): 527–46. http://dx.doi.org/10.1017/s0269964815000170.

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Two stochastic knapsack problem (SKP) models are considered: the static broken knapsack problem (BKP) and the SKP with simple recourse and penalty cost problem. For both models, we assume: the knapsack has a constant capacity; there are n types of items and each type has an infinite supply; a type i item has a deterministic reward vi and a random weight with known distribution Fi. Both models have the same objective to maximize expected total return by finding the optimal combination of items, that is, quantities of items of each type to be put in knapsack. The difference between the two models is: if knapsack is broken when total weights of items put in knapsack exceed the knapsack's capacity, for the static BKP model, all existing rewards would be wiped out, while for the latter model, we could still keep the existing rewards in knapsack but have to pay a fixed penalty plus a variant cost proportional to the overcapacity amount. This paper also discusses the special case when knapsack has an exponentially distributed capacity.

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23

Mukherjee, Sayandev, and Terrence L. Fine. "Online Steepest Descent Yields Weights with Nonnormal Limiting Distribution." Neural Computation 8, no. 5 (July 1996): 1075–84. http://dx.doi.org/10.1162/neco.1996.8.5.1075.

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We study the asymptotic properties of the sequence of iterates of weight-vector estimates obtained by training a feedforward neural network with a basic gradient-descent method using a fixed learning rate and no batch-processing. Earlier results based on stochastic approximation techniques (Kuan and Hornik 1991; Finnoff 1993; Bucklew et al. 1993) have established the existence of a gaussian limiting distribution for the weights, but they apply only in the limiting case of a zero learning rate. We here prove, from an exact analysis of the one-dimensional case and constant learning rate, weak convergence to a distribution that is not gaussian in general. We also run simulations to compare and contrast the results of our analysis with those of stochastic approximation.

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24

Elustondo, D., S. Avramidis, and L. Oliveira. "Estimation of green moisture content distribution in hemfir timber by stochastic simulation." Holzforschung 58, no. 4 (July 7, 2004): 413–17. http://dx.doi.org/10.1515/hf.2004.062.

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AbstractThis paper describes an improved stochastic model designed to simulate systems, such as green timbers, that cannot be analyzed as a unit but as a collection of a large number of similar components. The stochastic model provides a piecewise green moisture content frequency distribution curve by using nondestructive measurements such as of timber weight. A new, relatively simple two-parameter function was designed to describe the log-normal moisture concentration distribution above the fiber saturation point, and the parameters of this function were determined by fitting the experimental timber weights with the results of the stochastic model. The simulated green moisture content distributions showed good agreement with the experimental data for Pacific coast hemlock (hemfir) timbers, thus providing a piece of information that is indispensable for applying stochastic simulation to industrial drying of timbers.

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25

Toktaş, Pelin, and Gülin Feryal Can. "Stochastic KEMIRA-M Approach with Consistent Weightings." International Journal of Information Technology & Decision Making 18, no. 03 (May 2019): 793–831. http://dx.doi.org/10.1142/s0219622019500123.

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This study proposes an advanced Modified KEmeny Median Indicator Rank Accordance (KEMIRA-M) approach based on stochastic evaluation process considering consistent weights to improve effective usage of KEMIRA-M. In the proposed approach, tasks related to the decision issue are performed by decision makers to ensure the understanding sufficiency of alternatives in terms of criteria more clearly. The weighting procedure of Analytic Hierarchy Process (AHP) is implemented in a stochastic manner benefited from discrete uniform distribution to provide obtaining consistent criteria weights considering median priority components. Therefore, different trials including different number of replications that shows the number of decision makers are performed and the most consistent weightings are determined for each trial in the stochastic process. In this way, the dependency to the limited numbers of decision makers and to determine criteria weights in a heuristic manner in KEMIRA-M is prevented. Additionally, the effect of the number of decision makers on criteria weightings and alternatives’ ranking process is shown. To obtain the most consistent weighting results, this stochastic process is utilized until acquiring approximate consistency ratios. The proposed stochastic KEMIRA-M approach is utilized to rank nine shopping malls (SMs) in Ankara in terms of technical criteria (TC) and universal design criteria (UDC). It was seen from the ranking results that the first SM (SM1) is the best one.

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26

Shang, Ke, Felix T. S. Chan, Stephen Karungaru, Kenji Terada, Zuren Feng, and Liangjun Ke. "Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights." Complexity 2020 (November 12, 2020): 1–15. http://dx.doi.org/10.1155/2020/5649821.

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In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights.

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Hou, Yuchen, and Lawrence B. Holder. "On Graph Mining With Deep Learning: Introducing Model R for Link Weight Prediction." Journal of Artificial Intelligence and Soft Computing Research 9, no. 1 (January 1, 2019): 21–40. http://dx.doi.org/10.2478/jaiscr-2018-0022.

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Abstract Deep learning has been successful in various domains including image recognition, speech recognition and natural language processing. However, the research on its application in graph mining is still in an early stage. Here we present Model R, a neural network model created to provide a deep learning approach to the link weight prediction problem. This model uses a node embedding technique that extracts node embeddings (knowledge of nodes) from the known links’ weights (relations between nodes) and uses this knowledge to predict the unknown links’ weights. We demonstrate the power of Model R through experiments and compare it with the stochastic block model and its derivatives. Model R shows that deep learning can be successfully applied to link weight prediction and it outperforms stochastic block model and its derivatives by up to 73% in terms of prediction accuracy. We analyze the node embeddings to confirm that closeness in embedding space correlates with stronger relationships as measured by the link weight. We anticipate this new approach will provide effective solutions to more graph mining tasks.

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28

Kalpazidou, S. "Invariant stochastic properties of a class of directed circuits." Journal of Applied Probability 28, no. 4 (December 1991): 727–36. http://dx.doi.org/10.2307/3214676.

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Invariant stochastic properties are studied for circuit processes, i.e. processes whose sample paths can be represented by a denumerable set of overlapping directed circuits c in a denumerable set S and a set of positive weights , when the family of the weights varies.

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Kalpazidou, S. "Invariant stochastic properties of a class of directed circuits." Journal of Applied Probability 28, no. 04 (December 1991): 727–36. http://dx.doi.org/10.1017/s0021900200042649.

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Invariant stochastic properties are studied for circuit processes, i.e. processes whose sample paths can be represented by a denumerable set of overlapping directed circuits c in a denumerable set S and a set of positive weights , when the family of the weights varies.

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30

Arlotto, Alessandro, and Xinchang Xie. "Logarithmic Regret in the Dynamic and Stochastic Knapsack Problem with Equal Rewards." Stochastic Systems 10, no. 2 (June 2020): 170–91. http://dx.doi.org/10.1287/stsy.2019.0055.

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Анотація:

We study a dynamic and stochastic knapsack problem in which a decision maker is sequentially presented with items arriving according to a Bernoulli process over n discrete time periods. Items have equal rewards and independent weights that are drawn from a known nonnegative continuous distribution F. The decision maker seeks to maximize the expected total reward of the items that the decision maker includes in the knapsack while satisfying a capacity constraint and while making terminal decisions as soon as each item weight is revealed. Under mild regularity conditions on the weight distribution F, we prove that the regret—the expected difference between the performance of the best sequential algorithm and that of a prophet who sees all of the weights before making any decision—is, at most, logarithmic in n. Our proof is constructive. We devise a reoptimized heuristic that achieves this regret bound.

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31

Xie, Qian, Changhui Mu, Tong Wang, Gang Wu, and Rong Jia. "Finite-Time Projective Lag Synchronization and Identification between Multiple Weights Markovian Jumping Complex Networks with Stochastic Perturbations." Complexity 2020 (April 8, 2020): 1–25. http://dx.doi.org/10.1155/2020/9713652.

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Two nonidentical dimension Markovian jumping complex networks with stochastic perturbations are taken as objects. The network models under two conditions including single weight and double weights are established, respectively, to study the problem of synchronization and identification. A finite-time projection lag synchronization method is proposed and the unknown parameters of the network are identified. First of all, based on Itô’s formula and the stability theory of finite-time, a credible finite-time adaptive controller is presented to guarantee the synchronization of two nonidentical dimension Markovian jumping complex networks with stochastic perturbations under both conditions. Meanwhile, in order to identify the uncertain parameters of the network with stochastic perturbations accurately, some corresponding sufficient conditions are given. Finally, numerical simulations under two working conditions are given to demonstrate the effectiveness and feasibility of the main theory result.

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32

Jarrahiferiz, Jalil, G. R. Mohtashami Borzadaran, and A. H. Rezaei Roknabadi. "Glaser’s function and stochastic orders for mixture distributions." International Journal of Quality & Reliability Management 33, no. 8 (September 5, 2016): 1230–38. http://dx.doi.org/10.1108/ijqrm-04-2013-0072.

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Purpose The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented. Design/methodology/approach First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components. Findings The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order. Originality/value Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.

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33

Levy, Haim. "First Degree Stochastic Dominance Violations: Decision Weights and Bounded Rationality." Economic Journal 118, no. 528 (March 19, 2008): 759–74. http://dx.doi.org/10.1111/j.1468-0297.2008.02141.x.

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34

Ramponi, Alessandro. "Stochastic adaptive selection of weights in the simulated tempering algorithm." Journal of the Italian Statistical Society 7, no. 1 (April 1998): 27–55. http://dx.doi.org/10.1007/bf03178920.

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35

Rezvanian, Alireza, and Mohammad Reza Meybodi. "Finding Maximum Clique in Stochastic Graphs Using Distributed Learning Automata." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 23, no. 01 (February 2015): 1–31. http://dx.doi.org/10.1142/s0218488515500014.

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Because of unpredictable, uncertain and time-varying nature of real networks it seems that stochastic graphs, in which weights associated to the edges are random variables, may be a better candidate as a graph model for real world networks. Once the graph model is chosen to be a stochastic graph, every feature of the graph such as path, clique, spanning tree and dominating set, to mention a few, should be treated as a stochastic feature. For example, choosing stochastic graph as the graph model of an online social network and defining community structure in terms of clique, and the associations among the individuals within the community as random variables, the concept of stochastic clique may be used to study community structure properties. In this paper maximum clique in stochastic graph is first defined and then several learning automata-based algorithms are proposed for solving maximum clique problem in stochastic graph where the probability distribution functions of the weights associated with the edges of the graph are unknown. It is shown that by a proper choice of the parameters of the proposed algorithms, one can make the probability of finding maximum clique in stochastic graph as close to unity as possible. Experimental results show that the proposed algorithms significantly reduce the number of samples needed to be taken from the edges of the stochastic graph as compared to the number of samples needed by standard sampling method at a given confidence level.

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36

Du, Jiangze. "Modifying Olympics Medal Table via a Stochastic Multicriteria Acceptability Analysis." Mathematical Problems in Engineering 2018 (August 15, 2018): 1–11. http://dx.doi.org/10.1155/2018/8729158.

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This paper addresses the issue of developing a widely accepted Olympics ranking scheme based upon the Olympic Game medal table published by the International Olympic Committee, since the existing lexicographic ranking and sum ranking systems are both criticized as biases. More specifically, the lexicographic ranking system is deemed as overvaluing gold medals, while the sum ranking system fails to reveal the real value of gold medals and fails to discriminate National Olympic Committees that won equal number of medals. To start, we employ a sophisticated mathematical method based upon the incenter of a convex cone to aggregate the lexicographic ranking system. Then, we consider the fact that the preferences between the lexicographic and the sum ranking systems may not be consistent across National Olympic Committees and develop a well-designed mathematical transformation to obtain interval assessment results under typical preference. The formulation of intervals is inspired by the observation that it is extremely difficult to achieve a group consensus on the exact value of weights with respect to each ranking system, since different weight elicitation methods may produce different weight schemes. Finally, regarding the derived decision making problem involving interval-valued data, this paper utilizes the Stochastic Multicriteria Acceptability Analysis to obtain a comprehensive ranking of all National Olympic Committees. Instead of determining precise weights, this work probes the weight space to guarantee each alternative getting the most preferred one. The proposed method is illustrated by presenting a new ranking of 12 National Olympic Committees participating in the London 2012 Summer Olympic Games.

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37

von Hardenberg, J., L. Ferraris, N. Rebora, and A. Provenzale. "Meteorological uncertainty and rainfall downscaling." Nonlinear Processes in Geophysics 14, no. 3 (May 22, 2007): 193–99. http://dx.doi.org/10.5194/npg-14-193-2007.

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Abstract. We explore the sources of forecast uncertainty in a mixed dynamical-stochastic ensemble prediction chain for small-scale precipitation, suitable for hydrological applications. To this end, we apply the stochastic downscaling method RainFARM to each member of ensemble limited-area forecasts provided by the COSMO-LEPS system. Aim of the work is to quantitatively compare the relative weights of the meteorological uncertainty associated with large-scale synoptic conditions (represented by the ensemble of dynamical forecasts) and of the uncertainty due to small-scale processes (represented by the set of fields generated by stochastic downscaling). We show that, in current operational configurations, small- and large-scale uncertainties have roughly the same weight. These results can be used to pinpoint the specific components of the prediction chain where a better estimate of forecast uncertainty is needed.

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38

Dong, Hou, and Gong. "Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory." Symmetry 11, no. 9 (August 29, 2019): 1085. http://dx.doi.org/10.3390/sym11091085.

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To address issues involving inconsistencies, this paper proposes a stochastic multi-criteria group decision making algorithm based on neutrosophic soft sets, which includes a pair of asymmetric functions: Truth-membership and false-membership, and an indeterminacy-membership function. For integrating an inherent stochastic, the algorithm expresses the weights of decision makers and parameter subjective weights by neutrosophic numbers instead of determinate values. Additionally, the algorithm is guided by the prospect theory, which incorporates psychological expectations of decision makers into decision making. To construct the prospect decision matrix, this research establishes a conflict degree measure of neutrosophic numbers and improves it to accommodate the stochastic multi-criteria group decision making. Moreover, we introduce the weighted average aggregation rule and weighted geometric aggregation rule of neutrosophic soft sets. Later, this study presents an algorithm for neutrosophic soft sets in the stochastic multi-criteria group decision making based on the prospect theory. Finally, we perform an illustrative example and a comparative analysis to prove the effectiveness and feasibility of the proposed algorithm.

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39

Liu, Xikui, Guiling Li, and Yan Li. "Stochastic Linear Quadratic Optimal Control with Indefinite Control Weights and Constraint for Discrete-Time Systems." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/476545.

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The Karush-Kuhn-Tucker (KKT) theorem is used to study stochastic linear quadratic optimal control with terminal constraint for discrete-time systems, allowing the control weighting matrices in the cost to be indefinite. A generalized difference Riccati equation is derived, which is different from those without constraint case. It is proved that the well-posedness and the attainability of stochastic linear quadratic optimal control problem are equivalent. Moreover, an optimal control can be denoted by the solution of the generalized difference Riccati equation.

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40

Sun, Gao Rong. "Stochastic Response Surface Method with Enhanced Weighting Strategy." Applied Mechanics and Materials 224 (November 2012): 272–79. http://dx.doi.org/10.4028/www.scientific.net/amm.224.272.

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The weighted stochastic response surface method (WSRSM) has been demonstrated to be effective in improving the accuracy of the estimation of statistical moments and probability of failure (PoF) upon the stochastic response surface method (SRSM). However, it has been noticed that the weighting method in WSRSM may have little and sometimes negative impact on PoF estimation especially in the cases of low PoF. To address this issue, an enhanced weighting strategy is proposed that the weights of sample points are determined based on their importance not only to regression but also to PoF estimation. Specifically, relatively larger weights are assigned to points closer to the failure surface, which significantly accounts for the accuracy of PoF estimation. Comparative studies show that SRSM with the proposed weighting method outperforms WSRSM producing more accurate PoF estimation without incurring additional function evaluations.

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41

Hamm, Lonnie, B. Wade Brorsen, and Martin T. Hagan. "Comparison of Stochastic Global Optimization Methods to Estimate Neural Network Weights." Neural Processing Letters 26, no. 3 (September 1, 2007): 145–58. http://dx.doi.org/10.1007/s11063-007-9048-7.

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42

Evers, Lanah, Kristiaan Glorie, Suzanne van der Ster, Ana Isabel Barros, and Herman Monsuur. "A two-stage approach to the orienteering problem with stochastic weights." Computers & Operations Research 43 (March 2014): 248–60. http://dx.doi.org/10.1016/j.cor.2013.09.011.

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43

Arab, Idir, and Paulo Eduardo Oliveira. "ITERATED FAILURE RATE MONOTONICITY AND ORDERING RELATIONS WITHIN GAMMA AND WEIBULL DISTRIBUTIONS." Probability in the Engineering and Informational Sciences 33, no. 1 (January 24, 2018): 64–80. http://dx.doi.org/10.1017/s0269964817000481.

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Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families.

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44

Wu, Ji, Xian Cheng, and Stephen Shaoyi Liao. "Tourism forecast combination using the stochastic frontier analysis technique." Tourism Economics 26, no. 7 (August 8, 2019): 1086–107. http://dx.doi.org/10.1177/1354816619868089.

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Forecast combination has received a great deal of attention in the tourism domain. In this article, we propose a novel performance-based tourism forecast combination model by applying a multiple-criteria decision-making framework and the stochastic frontier analysis technique to determine combination weights for individual tourism forecast models. Thirteen time-series models are used to generate individual forecast tourism models, and five competing forecast combination models are selected to evaluate the forecast performance. Using the tourism forecast competition data set, we conclude that the proposed combination model significantly and statistically outperforms the five competing combination models in most cases based on multiple performance indicators. Our results show that the proposed model offers a good solution to identify optimal weights for individual tourism forecast models.

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45

DAVIDSON, A., and A. GANESH. "Maximal Steiner Trees in the Stochastic Mean-Field Model of Distance." Combinatorics, Probability and Computing 26, no. 6 (July 27, 2017): 826–38. http://dx.doi.org/10.1017/s0963548317000220.

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Consider the complete graph on n vertices, with edge weights drawn independently from the exponential distribution with unit mean. Janson showed that the typical distance between two vertices scales as log n/n, whereas the diameter (maximum distance between any two vertices) scales as 3 log n/n. Bollobás, Gamarnik, Riordan and Sudakov showed that, for any fixed k, the weight of the Steiner tree connecting k typical vertices scales as (k − 1)log n/n, which recovers Janson's result for k = 2. We extend this to show that the worst case k-Steiner tree, over all choices of k vertices, has weight scaling as (2k − 1)log n/n and finally, we generalize this result to Steiner trees with a mixture of typical and worst case vertices.

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46

Iskander, Maged George. "Using the weighted max–min approach for stochastic fuzzy goal programming: A case of fuzzy weights." Applied Mathematics and Computation 188, no. 1 (May 2007): 456–61. http://dx.doi.org/10.1016/j.amc.2006.09.137.

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47

El-Wahed Khalifa, Hamiden Abd, Pavan Kumar, and Sultan S. Alodhaibi. "Stochastic Multi-Objective Programming Problem: A Two-Phase Weighted Coefficient Approach." Mathematical Modelling of Engineering Problems 8, no. 6 (December 22, 2021): 854–60. http://dx.doi.org/10.18280/mmep.080603.

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This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two- phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology.

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48

Ruß, Matthias, Gunther Gust, and Dirk Neumann. "The Constrained Reliable Shortest Path Problem in Stochastic Time-Dependent Networks." Operations Research 69, no. 3 (May 2021): 709–26. http://dx.doi.org/10.1287/opre.2020.2089.

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49

Krishnan, Ranganath, Mahesh Subedar, and Omesh Tickoo. "Specifying Weight Priors in Bayesian Deep Neural Networks with Empirical Bayes." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4477–84. http://dx.doi.org/10.1609/aaai.v34i04.5875.

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Stochastic variational inference for Bayesian deep neural network (DNN) requires specifying priors and approximate posterior distributions over neural network weights. Specifying meaningful weight priors is a challenging problem, particularly for scaling variational inference to deeper architectures involving high dimensional weight space. We propose MOdel Priors with Empirical Bayes using DNN (MOPED) method to choose informed weight priors in Bayesian neural networks. We formulate a two-stage hierarchical modeling, first find the maximum likelihood estimates of weights with DNN, and then set the weight priors using empirical Bayes approach to infer the posterior with variational inference. We empirically evaluate the proposed approach on real-world tasks including image classification, video activity recognition and audio classification with varying complex neural network architectures. We also evaluate our proposed approach on diabetic retinopathy diagnosis task and benchmark with the state-of-the-art Bayesian deep learning techniques. We demonstrate MOPED method enables scalable variational inference and provides reliable uncertainty quantification.

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50

Moreno Roa, Carmenza, Adolfo Andrés Jaramillo Matta, and Juan David Bastidas Rodríguez. "Stochastic Search Technique with Variable Deterministic Constraints for the Estimation of Induction Motor Parameters." Energies 13, no. 1 (January 6, 2020): 273. http://dx.doi.org/10.3390/en13010273.

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This paper deals with the implementation of a new technique of stochastic search to find the best set of parameters in a mathematical model, applied to the single cage (SC) model of the induction motor (IM). The technique includes a new strategy to generate variable constraints of the domain, seven error functions, weight for the operating zones of the IM, and multi-objective functions. The results are validated with experimental data of the torque and current in an IM, and show better fitting to the experimental curves compared with the results of two different techniques, one deterministic and the other one stochastic. The results obtained allow us to conclude that the best set of parameters for the model depends on the weights assigned to the objective functions and to the operating zones.

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