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Journal articles on the topic 'Quadratic Loss Function'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Shim, Jooyong, Malsuk Kim, and Kyungha Seok. "SVQR with asymmetric quadratic loss function." Journal of the Korean Data and Information Science Society 26, no. 6 (November 30, 2015): 1537–45. http://dx.doi.org/10.7465/jkdi.2015.26.6.1537.

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2

Moskowitz, Herbert, and Kwei Tang. "Bayesian Variables Acceptance-Sampling Plans: Quadratic Loss Function and Step-Loss Function." Technometrics 34, no. 3 (August 1992): 340. http://dx.doi.org/10.2307/1270040.

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3

Jin, Qiu, and Shao Gang Liu. "Research of Asymmetric Quality Loss Function with Triangular Distribution." Advanced Materials Research 655-657 (January 2013): 2331–34. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.2331.

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The asymmetric quality loss functions with the triangular distribution for determining the optimum process mean are studied. The condition of using the linear and quadratic asymmetric quality loss function in the model is considered. The eight mathematical models under an asymmetric quality loss function with the triangular distribution based on the analysis of the linear and quadratic asymmetric quality loss function are presented. Finally, the validity of models is verified by the examples.

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4

KARAL, Omer. "ECG Data Compression Using ε-insensitive Quadratic Loss Function." Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 2 (April 18, 2018): 380. http://dx.doi.org/10.19113/sdufbed.82260.

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5

Shim, Joo-Yong, and Chang-Ha Hwang. "Support Vector Quantile Regression with Weighted Quadratic Loss Function." Communications for Statistical Applications and Methods 17, no. 2 (March 31, 2010): 183–91. http://dx.doi.org/10.5351/ckss.2010.17.2.183.

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6

Lin, Shao-Bo, Jinshan Zeng, and Xiangyu Chang. "Learning Rates for Classification with Gaussian Kernels." Neural Computation 29, no. 12 (December 2017): 3353–80. http://dx.doi.org/10.1162/neco_a_00968.

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This letter aims at refined error analysis for binary classification using support vector machine (SVM) with gaussian kernel and convex loss. Our first result shows that for some loss functions, such as the truncated quadratic loss and quadratic loss, SVM with gaussian kernel can reach the almost optimal learning rate provided the regression function is smooth. Our second result shows that for a large number of loss functions, under some Tsybakov noise assumption, if the regression function is infinitely smooth, then SVM with gaussian kernel can achieve the learning rate of order [Formula: see text], where [Formula: see text] is the number of samples.

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7

Choi, Hoo-Gon R., Man-Hee Park, and Erik Salisbury. "Optimal Tolerance Allocation With Loss Functions." Journal of Manufacturing Science and Engineering 122, no. 3 (September 1, 1999): 529–35. http://dx.doi.org/10.1115/1.1285918.

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The tolerance allocation problem is formulated as a nonlinear integer model under the constraints of process capability. The problem is to minimize the sum of machining cost and quality loss. When the statistical tolerance limits are used and Taguchi’s quadratic loss function is defined, the total cost function becomes a convex function for a given feature and process. A complex search method is used to solve the model and ensure the optimal tolerance allocation. Numerical examples are presented demonstrating successful model implementation for both linear and nonlinear design functions. [S1087-1357(00)02602-2]

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Weinberger, Nir, and Ofer Shayevitz. "On the Optimal Boolean Function for Prediction Under Quadratic Loss." IEEE Transactions on Information Theory 63, no. 7 (July 2017): 4202–17. http://dx.doi.org/10.1109/tit.2017.2686437.

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9

Reyad, Hesham, and Soha Othman Ahmed. "E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme." International Journal of Advanced Mathematical Sciences 3, no. 2 (September 5, 2015): 108. http://dx.doi.org/10.14419/ijams.v3i2.5093.

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<p>This paper seeks to focus on Bayesian and E-Bayesian estimation for the unknown shape parameter of the Gumbel type-II distribution based on type-II censored samples. These estimators are obtained under symmetric loss function [squared error loss (SELF))] and various asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF), Quadratic loss function (QLF) and minimum expected loss function (MELF)]. Comparisons between the E-Bayesian estimators with the associated Bayesian estimators are investigated through a simulation study.</p>

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Reyad, Hesham, and Soha Othman Ahmed. "Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-ii censoring." International Journal of Advanced Mathematical Sciences 4, no. 1 (March 5, 2016): 10. http://dx.doi.org/10.14419/ijams.v4i1.5750.

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<p>This paper introduces the Bayesian and E-Bayesian estimation for the shape parameter of the Kumaraswamy distribution based on type-II censored schemes. These estimators are derived under symmetric loss function [squared error loss (SELF))] and three asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF) and Quadratic loss function (QLF)]. Monte Carlo simulation is performed to compare the E-Bayesian estimators with the associated Bayesian estimators in terms of Mean Square Error (MSE).</p>

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11

Cho, Byung-Rae, and Michael S. Leonard. "Identification and Extensions of Quasiconvex Quality Loss Functions." International Journal of Reliability, Quality and Safety Engineering 04, no. 02 (June 1997): 191–204. http://dx.doi.org/10.1142/s0218539397000138.

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This paper presents a set of related quasiconvex quality loss functions. Characteristics of quasiconvex functions that are desirable for modeling quality loss are noted. Three frequently used univariate quasiconvex quality loss functions are discussed. Bivariate and multivariate quasiconvex quality loss functions are developed. A set of necessary and sufficient conditions is established for the quasiconvexity of multivariate quality loss functions. An industrial product example is used to illustrate the development of a bivariate quadratic quality loss function.

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12

Reyad, Hesham, Adil Mousa Younis, and Amal Alsir Alkhedir. "Comparison of estimates using censored samples from Gompertz model: Bayesian, E-Bayesian, hierarchical Bayesian and empirical Bayesian schemes." International Journal of Advanced Statistics and Probability 4, no. 1 (April 3, 2016): 47. http://dx.doi.org/10.14419/ijasp.v4i1.5914.

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<p>This paper aims to introduce a comparative study for the E-Bayesian criteria with three various Bayesian approaches; Bayesian, hierarchical Bayesian and empirical Bayesian. This study is concerned to estimate the shape parameter and the hazard function of the Gompertz distribution based on type-II censoring. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and three different asymmetric loss functions [quadratic loss function (QLF), entropy loss function (ELF) and LINEX loss function (LLF)]. Comparisons among all estimators are achieved in terms of mean square error (MSE) via Monte Carlo simulation.</p>

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13

Dey, Sanku, and Sudhansu S. Maiti. "Bayesian Inference on the Shape Parameter and Future Observation of Exponentiated Family of Distributions." Journal of Probability and Statistics 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/457472.

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The Bayes estimators of the shape parameter of exponentiated family of distributions have been derived by considering extension of Jeffreys' noninformative as well as conjugate priors under different scale-invariant loss functions, namely, weighted quadratic loss function, squared-log error loss function and general entropy loss function. The risk functions of these estimators have been studied. We have also considered the highest posterior density (HPD) intervals for the parameter and the equal-tail and HPD prediction intervals for future observation. Finally, we analyze one data set for illustration.

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14

ELSAYED, E. A., and A. CHEN. "An economic design of [xbar] control chart using quadratic loss function." International Journal of Production Research 32, no. 4 (April 1994): 873–87. http://dx.doi.org/10.1080/00207549408956976.

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15

Yang, Su‐Fen. "An optimal design of jointX‐ andScontrol charts using quadratic loss function." International Journal of Quality & Reliability Management 14, no. 9 (December 1997): 948–66. http://dx.doi.org/10.1108/02656719710186876.

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16

Al-Fawzan, M. A., and M. A. Rahim. "Optimal control of a deteriorating process with a quadratic loss function." Quality and Reliability Engineering International 17, no. 6 (2001): 459–66. http://dx.doi.org/10.1002/qre.437.

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17

Zhang, Shengguo, Jingtao Huang, and Jingxian Yang. "Raising Power Loss Equalizing Degree of Coil Array by Convex Quadratic Optimization Commutation for Magnetic Levitation Planar Motors." Applied Sciences 9, no. 1 (December 26, 2018): 79. http://dx.doi.org/10.3390/app9010079.

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This paper proposes a convex quadratic optimization commutation method to raise the equalization degree of power loss distribution of coil array for magnetic levitation planar motors. Starting with the modeling of electromagnetic forces/torques and commutation of coil array, the global power loss and the local power losses of coil array are analyzed, and the power loss equalizing degree is defined to evaluate the power loss distribution of coil array being commutated dynamically. Then, in consideration of the fact that the global power loss is the quadratic function of commutated coil currents, the convex quadratic function optimization with equality constraint and boundary constraints is applied to commutate the coil array, and the power loss equalizing degree is raised by decreasing the boundary constraints of optimization. Taking the magnetically levitated planar motor under investigation as examples and using quadprog routine in Matlab Optimization Toolbox, which is a dedicated quadratic optimization routine, it is verified that the power loss equalizing the degree of coil array is raised gradually and the power loss distribution of coil array becomes more uniform along with decrease of the boundary constraints. The convex quadratic optimization commutation is verified experimentally on a constructed multi-dimension force/torque measurement platform. Using the convex quadratic optimization commutation can not only improve the power loss distribution of coil array of magnetically levitated planar motors, but also make it possible to select lower capacity power amplifiers to produce the identical desired electromagnetic forces and torques.

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18

Tsai, Hsien-Tang. "The probabilistic tolerance design for a subsystem using taguchi's quadratic loss function." Communications in Statistics - Theory and Methods 19, no. 9 (January 1990): 3243–58. http://dx.doi.org/10.1080/03610929008830379.

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19

Hasan, M. R., and A. R. Baizid. "Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution." Journal of Scientific Research 9, no. 1 (January 1, 2017): 67–78. http://dx.doi.org/10.3329/jsr.v1i1.29308.

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). Since exponential distribution is the life time distribution, we have studied exponential distribution using gamma prior. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. We have used simulated data using R-coding to find out the mean squared error (MSE) of different loss functions and hence found that non-classical estimator is better than classical estimator. Finally, mean square error (MSE) of the estimators of different loss functions are presented graphically.

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20

Reyad, Hesham, Adil Younis, and Amal Alkhedir. "Quasi-E-Bayesian criteria versus quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian methods for estimating the scale parameter of the Erlang distribution." International Journal of Advanced Statistics and Probability 4, no. 1 (May 10, 2016): 62. http://dx.doi.org/10.14419/ijasp.v4i1.6095.

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This paper proposes a new modification for the E-Bayesian method of estimation to introduce a new technique namely Quasi E-Bayesian method (or briefly QE-Bayesian). The suggested criteria built in replacing the likelihood function by the quasi likelihood function in the E-Bayesian technique. This study is devoted to evaluate the performance of the new method versus the quasi-Bayesian, quasi-hierarchical Bayesian and quasi-empirical Bayesian approaches in estimating the scale parameter of the Erlang distribution. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and four different asymmetric loss functions [Precautionary loss function (PLF), entropy loss function (ELF), Degroot loss function (DLF) and quadratic loss function (QLF)]. The properties of the QE-Bayesian estimates are introduced and the relations between the QE-Bayes and quasi-hierarchical Bayes estimates are discussed. Comparisons among all estimators are performed in terms of mean square error (MSE) via Monte Carlo simulation.

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21

Rahman, Md Habibur, and MK Roy. "Bayes Estimation under Conjugate Prior for the Case of Laplace Double Exponential Distribution." Chittagong University Journal of Science 40, no. 1 (June 28, 2018): 151–68. http://dx.doi.org/10.3329/cujs.v40i1.47921.

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The Bayesian estimation approach is a non-classical device in the estimation part of statistical inference which is very useful in real world situation. The main objective of this paper is to study the Bayes estimators of the parameter of Laplace double exponential distribution. In Bayesian estimation loss function, prior distribution and posterior distribution are the most important ingredients. In real life we try to minimize the loss and want to know some prior information about the problem to solve it accurately. The well known conjugate priors are considered for finding the Bayes estimator. In our study we have used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. The performance of the obtained estimators for different types of loss functions are then compared among themselves as well as with the classical maximum likelihood estimator (MLE). Mean Square Error (MSE) of the estimators are also computed and presented in graphs. The Chittagong Univ. J. Sci. 40 : 151-168, 2018

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22

Pecci, Filippo, Edo Abraham, and Ivan Stoianov. "Quadratic head loss approximations for optimisation problems in water supply networks." Journal of Hydroinformatics 19, no. 4 (April 17, 2017): 493–506. http://dx.doi.org/10.2166/hydro.2017.080.

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This paper presents a novel analysis of the accuracy of quadratic approximations for the Hazen–Williams (HW) head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the absolute and relative errors, respectively, from the original non-smooth HW head loss function over a range of flows. Since quadratic approximations are used to formulate head loss constraints for different optimisation problems, we are interested in quantifying and controlling their absolute errors, which affect the degree of constraint violations of feasible candidate solutions. We derive new exact analytical formulae for the absolute errors as a function of the approximation domain, pipe roughness and relative error tolerance. We investigate the efficacy of the proposed quadratic approximations in mathematical optimisation problems for advanced pressure control in an operational water supply network. We propose a strategy on how to choose the approximation domain for each pipe such that the optimisation results are sufficiently close to the exact hydraulically feasible solution space. By using simulations with multiple parameters, the approximation errors are shown to be consistent with our analytical predictions.

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23

Loganathan, A., S. Mari Chelvi, and M. Uma. "Bayes Estimation of Parameter in Inverse Maxwell Distribution under Weighted Quadratic Loss Function." International Journal of Scientific Research in Mathematical and Statistical Sciences 4, no. 5 (October 30, 2017): 13–16. http://dx.doi.org/10.26438/ijsrmss/v4i5.1316.

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24

Criticou, D., and D. Terzakis. "Shriknage estimators with general quadratic loss and differentiable or paratially differentiable shrinkage function." Stochastic Analysis and Applications 8, no. 2 (January 1990): 127–56. http://dx.doi.org/10.1080/07362999008809203.

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25

Dey, Sanku. "Minimax Estimation of the Parameter of the Rayleigh Distribution under Quadratic Loss Function." Data Science Journal 7 (2008): 23–30. http://dx.doi.org/10.2481/dsj.7.23.

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26

Koutsomanoli-Filippaki, Anastasia, Emmanuel Mamatzakis, and Christos Staikouras. "Banking inefficiency in Central and Eastern European countries under a quadratic loss function." Emerging Markets Review 10, no. 3 (September 2009): 167–78. http://dx.doi.org/10.1016/j.ememar.2009.02.004.

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27

Iliasu, G. B., A. A. Kogo, and M. K. Yakubu. "Optimization of mechanical properties of chitosan/phenol formaldehyde composite." Bayero Journal of Pure and Applied Sciences 11, no. 1 (November 5, 2018): 229–35. http://dx.doi.org/10.4314/bajopas.v11i1.39.

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The Frechet distribution which has a scale and shape parameters, has been found to have wide application in modelling extreme events such as radioactive emission, flood, rainfall, seismic analysis, wind speed, etc. In this research paper, the Bayesian analysis of scale parameter of Frechet distribution was considered. It is necessary to know the best combination of prior distribution and loss function for the parameter estimation. Posterior distribution was derived by uniform and Jeffrey’s prior under the square error, Precautionary, Quadratic and Weighted balance loss function. Bayes estimation and their corresponding risk was obtained by the above stated priors and loss function. Monte Carlo simulations was conducted to compare the performance of the estimators. It is evident that weighted balance loss function when used with uniform prior provides the least posterior risk.Keywords: Frechet Distribution, Non-Informative Prior, Bayesian Estimation, Loss Functions, Monte Carlo Simulations

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Nasir, Wajiha. "On estimation of Frechet distribution with known shape using Bayesian analysis under informative priors." International Journal of Scientific World 5, no. 2 (October 23, 2017): 141. http://dx.doi.org/10.14419/ijsw.v5i2.8371.

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In this study, Frechet distribution has been studied by using Bayesian analysis. Posterior distribution has been derived by using gamma and exponential. Bayes estimators and their posterior risks has been derived using five different loss functions. Elicitation of hyperparameters has been done by using prior predictive distributions. Simulation study is carried out to study the behavior of posterior distribution. Quasi quadratic loss function and exponential prior are found better among all.

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29

Cairns, Andrew. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time." ASTIN Bulletin 30, no. 1 (May 2000): 19–55. http://dx.doi.org/10.2143/ast.30.1.504625.

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AbstractThis paper discusses the modelling and control of pension funds.A continuous-time stochastic pension fund model is proposed in which there are n risky assets plus the risk-free asset as well as randomness in the level of benefit outgo. We consider Markov control strategies which optimise over the contribution rate and over the range of possible asset-allocation strategies.For a general (not necessarily quadratic) loss function it is shown that the optimal proportions of the fund invested in each of the risky assets remain constant relative to one another. Furthermore, the asset allocation strategy always lies on the capital market line familiar from modern portfolio theory.A general quadratic loss function is proposed which provides an explicit solution for the optimal contribution and asset-allocation strategies. It is noted that these solutions are not dependent on the level of uncertainty in the level of benefit outgo, suggesting that small schemes should operate in the same way as large ones. The optimal asset-allocation strategy, however, is found to be counterintuitive leading to some discussion of the form of the loss function. Power and exponential loss functions are then investigated and related problems discussed.The stationary distribution of the process is considered and optimal strategies compared with dynamic control strategies.Finally there is some discussion of the effects of constraints on contribution and asset-allocation strategies.

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30

Yu, Sheng-Hua. "The linear minimax estimator of stochastic regression coefficients and parameters under quadratic loss function." Statistics & Probability Letters 77, no. 1 (January 2007): 54–62. http://dx.doi.org/10.1016/j.spl.2006.05.011.

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31

Lin, Pi-Erh, and Amany M. Mousa. "Minimax estimation of independent normal means under a quadratic loss function with unknown weights." Communications in Statistics - Theory and Methods 15, no. 7 (January 1986): 2175–89. http://dx.doi.org/10.1080/03610928608829242.

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32

Koutsomanoli-Filippaki, Anastasia, and Emmanuel C. Mamatzakis. "Estimating the speed of adjustment of European banking efficiency under a quadratic loss function." Economic Modelling 27, no. 1 (January 2010): 1–11. http://dx.doi.org/10.1016/j.econmod.2009.07.006.

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33

PAKKALA, T. P. M., and M. A. RAHIM. "DETERMINATION OF AN OPTIMAL SETTING AND PRODUCTION RUN USING TAGUCHI'S LOSS FUNCTION." International Journal of Reliability, Quality and Safety Engineering 06, no. 04 (December 1999): 335–46. http://dx.doi.org/10.1142/s0218539399000310.

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This paper considers the problem of selecting an optimal setting of the process mean and an optimal production run for a continuous production process. The process is subject to gradual shifts in the process mean due to occurrences of some random shocks. The product output becomes nonconforming only when the process experiences a certain number of accumulated shocks. The changes in the process mean are assumed to follow a nonhomogeneous Poisson process. A quadratic loss function, which is a general form of Taguchi's loss function, is utilized for developing the economic model in determining an initial resetting process mean and an optimal production run. Some new results are derived and some interesting findings are reported.

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34

Ullah, Khalil, and Muhammad Aslam. "Bayesian Analysis of the Weibull Paired Comparison Model Using Numerical Approximation." Journal of Mathematics 2020 (December 14, 2020): 1–6. http://dx.doi.org/10.1155/2020/6628379.

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The method of paired comparisons (PC) is widely used to rank items using sensory evaluations. The PC models are developed to provide basis for such comparisons. In this study, the Weibull PC model is analyzed under the Bayesian paradigm using noninformative priors and different loss functions, namely, Squared Error Loss Function (SELF), Quadratic Loss Function (QLF), DeGroot Loss Function (DLF), and Precautionary Loss Function (PLF). Numerical approximation is used to illustrate the entire estimation procedure. A real dataset showing usage preferences for different cellphone brands, Huawei (HW), Samsung (SS), Oppo (OP), QMobile (QM), and Nokia (NK), is used. Quadrature method is used to evaluate the Bayes estimates, their posterior risks, preference probabilities, predictive probabilities, and posterior probabilities to establish and verify ranking order of the competing cellphone brands under study. The results show that the paired comparison model under the study using Bayesian approach involving various loss functions can offer mathematical approach to evaluate cellphone brand preferences. The ranking provided by the model is justifiable according to the usage preference for these cellphone brands. The ranking given by the model indicates that cellphone brand Samsung is preferred the most and QMobile is the least preferred. The plausibility of the model is also assessed using the Chi square test of goodness of fit.

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35

LEE, MIN-KOO, SANG-BOO KIM, HYUCK-MOO KWON, and SUNG HOON HONG. "ECONOMIC SELECTION OF MEAN VALUE FOR A FILLING PROCESS UNDER QUADRATIC QUALITY LOSS." International Journal of Reliability, Quality and Safety Engineering 11, no. 01 (March 2004): 81–90. http://dx.doi.org/10.1142/s021853930400135x.

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Consider a filling process where containers are filled with an important ingredient in a character. All containers are inspected, and the containers satisfying to meet the predetermined specification limits are sold in a regular market for a fixed price, and failing to meet them are emptied and refilled by the same filling process after some reprocessing. We assume that reprocessing cost is proportional to the quantity of the ingredients in a container that is not changed after reprocessing. An economic model is constructed on the basis of the selling price and the costs of production, inspection, reprocessing, and quality. We assume that the quality cost function is a quadratic function of the deviation from target and the quantity of the ingredients in a container is normally distributed with a known variance. Method for finding the optimum process mean is presented and a numerical example is given.

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36

Prabakaran, T. Edwin, and B. Chandrasekar. "Simultaneous Equivariant Estimation for Location - Scale Models with a Common Scale Parameter." Calcutta Statistical Association Bulletin 48, no. 3-4 (September 1998): 145–56. http://dx.doi.org/10.1177/0008068319980303.

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In this paper, we develop a procedure for simultaneous equivariant estimation of the pa rameters of location - scale models having a common scale parameter. Minimum risk equivariant (MRE) estimator is determined for any invariant loss function. MRE estimator is characterized with respect to a quadratic- type loss function (Zacks, 1971, p. 102) and its uniqueness is observed . Four optimality criteria for comparing vector equivariant estimators are considered and their equivalence is established .

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37

Feroz, Navid. "Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–21. http://dx.doi.org/10.1155/2014/519469.

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This paper is concerned with estimation of the parameter of Burr type VIII distribution under a Bayesian framework using censored samples. The Bayes estimators and associated risks have been derived under the assumption of five priors and three loss functions. The comparison among the performance of different estimators has been made in terms of posterior risks. A simulation study has been conducted in order to assess and compare the performance of different estimators. The study proposes the use of inverse Levy prior based on quadratic loss function for Bayes estimation of the said parameter.

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38

Lazović, Rade, and Ivana Mijatović. "Modified quadratic loss function for a trivariate response with the exact feasible region for parameters." Journal of Manufacturing Systems 31, no. 2 (April 2012): 177–83. http://dx.doi.org/10.1016/j.jmsy.2012.01.001.

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39

Chen, Chung-Ho, and Min-Tsai Lai. "Determining the optimum process mean based on quadratic quality loss function and rectifying inspection plan." European Journal of Operational Research 182, no. 2 (October 2007): 755–63. http://dx.doi.org/10.1016/j.ejor.2006.09.035.

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40

Huang, Guoping, Hui Wang, and Feiting Shi. "Coupling Effect of Salt Freeze-Thaw Cycles and Carbonation on the Mechanical Performance of Quick Hardening Sulphoaluminate Cement-Based Reactive Powder Concrete with Basalt Fibers." Coatings 11, no. 9 (September 20, 2021): 1142. http://dx.doi.org/10.3390/coatings11091142.

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The effect of salt freeze-thaw cycles coupled with carbonation on the mechanical performance of quick hardening sulphoaluminate cement-based reactive powder concrete combined with basalt fibers was investigated. The ratios of basalt fibers in sulphoaluminate cement-based reactive powder concrete (SAC-RPC) were 1%, 2%, 3% and 4% by the volume of concrete. The mechanical strengths (compressive strength, flexural strength and bonding strength) of SAC-RPC were investigated after curing for 5 h, 1 d, 14 d and 28 d, respectively. Meanwhile, the mechanical strengths of resultant concrete were detected, when different NaCl freeze-thaw cycles and carbonation were adopted. Results showed that the addition of basalt fibers could effectively improve the mechanical strengths, especially the flexural strength of SAC-RPC. The dosage of 3.0% was the threshold value affected mechanical strengths. The flexural, compressive and bonding strengths of SAC-RPC were higher than 8.53 MPa, 34 MPa and 3.21 MPa, respectively. The mass loss and mechanical strengths loss of SAC-RPC increased in the form of quadratic function with the increasing number of NaCl freeze-thaw cycles and varied in the form of quadratic decreasing function. Meanwhile, the effect of carbonation on the mechanical strengths of SAC-RPC can be ignored. Additionally, the coupling effect of salt freeze-thaw cycles and carbonation could accelerate the attenuation of concrete strength. The mechanical strengths loss demonstrated a decreased quadratic function with the increasing volume of basalt fibers.

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41

Sivak, Maria, and Vladimir Timofeev. "Building robust neural networks using different loss functions." Analysis and data processing systems, no. 2 (June 18, 2021): 67–82. http://dx.doi.org/10.17212/2782-2001-2021-2-67-82.

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The paper considers the problem of building robust neural networks using different robust loss functions. Applying such neural networks is reasonably when working with noisy data, and it can serve as an alternative to data preprocessing and to making neural network architecture more complex. In order to work adequately, the error back-propagation algorithm requires a loss function to be continuously or two-times differentiable. According to this requirement, two five robust loss functions were chosen (Andrews, Welsch, Huber, Ramsey and Fair). Using the above-mentioned functions in the error back-propagation algorithm instead of the quadratic one allows obtaining an entirely new class of neural networks. For investigating the properties of the built networks a number of computational experiments were carried out. Different values of outliers’ fraction and various numbers of epochs were considered. The first step included adjusting the obtained neural networks, which lead to choosing such values of internal loss function parameters that resulted in achieving the highest accuracy of a neural network. To determine the ranges of parameter values, a preliminary study was pursued. The results of the first stage allowed giving recommendations on choosing the best parameter values for each of the loss functions under study. The second stage dealt with comparing the investigated robust networks with each other and with the classical one. The analysis of the results shows that using the robust technique leads to a significant increase in neural network accuracy and in a learning rate.

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HELMES, K., and C. SRINIVASAN. "CHARACTERISATION OF LINEAR MINI-MAX ESTIMATORS FOR LOSS FUNCTIONS OF ARBITRARY POWER." International Game Theory Review 03, no. 02n03 (June 2001): 203–11. http://dx.doi.org/10.1142/s0219198901000397.

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Let Y(t), t∈[0,1], be a stochastic process modelled as dYt=θ(t)dt+dW(t), where W(t) denotes a standard Wiener process, and θ(t) is an unknown function assumed to belong to a given set Θ⊂L2[0,1]. We consider the problem of estimating the value ℒ(θ), where ℒ is a continuous linear function defined on Θ, using linear estimators of the form <m,y>=∫m(t)dY(t), m∈L2[0,1]. The distance between the quantity ℒ(θ) and the estimated value is measured by a loss function. In this paper, we consider the loss function to be an arbitrary even power function. We provide a characterisation of the best linear mini-max estimator for a general power function which implies the characterisation for two special cases which have previously been considered in the literature, viz. the case of a quadratic loss function and the case of a quartic loss function.

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Liu, Jin, Wei Wang, and Hongjun Song. "Optimization of Weighting Window Functions for SAR Imaging via QCQP Approach." Sensors 20, no. 2 (January 11, 2020): 419. http://dx.doi.org/10.3390/s20020419.

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Weighting window functions are commonly used in Synthetic Aperture Radar (SAR) imaging to suppress the high Peak SideLobe Ratio (PSLR) at the price of probable Signal-to-Noise Ratio (SNR) loss and mainlobe widening. In this paper, based on the method of designing a mismatched filter, we have proposed a Quadratically Constrained Quadratic Program (QCQP) approach, which is a convex that can be solved efficiently, to optimize the weighting window function with both amplitude and phase, expecting to offer better imaging performance, especially on PSLR, SNR loss, and mainlobe width. According to this approach and its modified form, we are able to design window functions to optimize the PSLR or the SNR loss under different kinds of flexible and practical constraints. Compared to the ordinary real-valued and symmetric window functions, like the Taylor window, the designed window functions are complex-valued and can be asymmetric. By using Synthetic Aperture Radar (SAR) point target imaging simulation, we show that the optimized weighting window function can clearly show the weak target hidden in the sidelobes of the strong target.

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Zhang, Heng, Xinxin Zhao, and Jianning Sun. "Optimal Clutch Pressure Control in Shifting Process of Automatic Transmission for Heavy-Duty Mining Trucks." Mathematical Problems in Engineering 2020 (October 10, 2020): 1–9. http://dx.doi.org/10.1155/2020/8618759.

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The optimal control of automatic transmission plays an important role in the shifting smoothness and fuel economy of heavy-duty mining trucks. In this paper, a dynamic model of the powertrain system is built to study the clutch pressure control during the shifting process. A linear-quadratic optimal regulator is used to achieve the optimum control pressure of clutches, where shifting jerk and clutch friction loss are chosen to a form quadratic performance index function. Besides, a detailed solution of the linear-quadratic problem with the disturbance matrix in the state equations is provided. This paper also carries out a software simulation and verification of the normal condition (no load without slope) and the extreme condition (full load with maximum slope). Compared with the preset reference trajectory control, the simulation results show that the proposed optimal clutch pressure control can effectively reduce jerk and friction loss during the shifting process and has good robustness to different operating conditions.

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Cheema, Ammara Nawaz, Muhammad Aslam, Ibrahim M. Almanjahie, and Ishfaq Ahmad. "Bayesian Modeling of 3-Component Mixture of Exponentiated Inverted Weibull Distribution under Noninformative Prior." Mathematical Problems in Engineering 2020 (July 29, 2020): 1–11. http://dx.doi.org/10.1155/2020/8765321.

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Bayesian study of 3-component mixture modeling of exponentiated inverted Weibull distribution under right type I censoring technique is conducted in this research work. The posterior distribution of the parameters is obtained assuming the noninformative (Jeffreys and uniform) priors. The different loss functions (squared error, quadratic, precautionary, and DeGroot loss function) are used to obtain the Bayes estimators and posterior risks. The performance of the Bayes estimators through posterior risks under the said loss functions is investigated through simulation process. Real data analysis of tensile strength of carbon fiber is also applied for 3 components to conclude the presentation of Bayes estimators. The limiting expressions are also elaborated for Bayes estimators and posterior risks in this study. The impact of some test termination times and sample sizes is reported on Bayes estimators.

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Nguyen, Thang Trung, Nguyen Vu Quynh, and Le Van Dai. "Improved Firefly Algorithm: A Novel Method for Optimal Operation of Thermal Generating Units." Complexity 2018 (July 9, 2018): 1–23. http://dx.doi.org/10.1155/2018/7267593.

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This paper presents a novel improved firefly algorithm (IFA) to deal the problem of the optimal operation of thermal generating units (OOTGU) with the purpose of reducing the total electricity generation fuel cost. The proposed IFA is developed based on combining three improvements. The first is to be based on the radius between two solutions, the second is updated step size for each considered solution based on different new equations, and the third is to slightly modify a formula producing new solutions by using normally distributed random numbers and canceling uniform random numbers of conventional firefly algorithm (FA). The effect of each proposed improvement on IFA is investigated by executing five benchmark functions and two different systems. The performance of IFA is investigated on six other study cases consisting of different types of objective function and complex level of constraints. The objective function considers single fuel with quadratic form and nonconvex form, and multifuels with the sum of several quadratic and nonconvex functions while a set of constraints taken into account are power loss, prohibited zone, ramp rate limit, spinning reserve, and all constraints in transmission power networks. The obtained results indicate the proposed improvements in terms of high optimal solution quality, stabilization of search ability, and fast convergence compared with FA. In addition, the comparisons with other methods also lead to a conclusion that the proposed method is a very promising optimization tool for systems with quadratic fuel cost function and with complicated constraints.

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Li, Zhenzhen, Jian-Feng Cai, and Ke Wei. "Toward the Optimal Construction of a Loss Function Without Spurious Local Minima for Solving Quadratic Equations." IEEE Transactions on Information Theory 66, no. 5 (May 2020): 3242–60. http://dx.doi.org/10.1109/tit.2019.2956922.

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CHO, BYUNG-RAE, WILLIAM G. FERRELL, and DELBERT L. KIMBLER. "DEVELOPMENT OF THE OPTIMUM PRODUCT SPECIFICATION FOR AN EXPONENTIAL-TYPE QUALITY CHARACTERISTIC." International Journal of Reliability, Quality and Safety Engineering 03, no. 03 (September 1996): 243–56. http://dx.doi.org/10.1142/s021853939600017x.

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This paper investigates the problem of determining the most economical product specification (upper specification limit) for an exponential-type quality characteristic using the concept of a truncated quadratic loss function within the framework of a screening inspection scheme. Implementing a tight limit on products may provide a high outgoing quality, but it creates a high rejection cost on the rejected products. In contrast, implementing a loose limit may reduce the rejection cost, but it can result in a low outgoing quality. An immediate problem is then how to trade off these conflicting cost criteria to determine the most economical upper specification limit. This important issue has neither been satisfactorily addressed or received much attention in the literature. This paper presents the concept of the truncated quadratic loss function, applies the concept to screening inspection problems, derives the truncated statistics of interest, and presents the optimization model of the most economical upper specification limit for an exponential-type quality characteristic. A numerical example is presented.

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Wang, Siyao, Xiaoming Tang, Li Deng, Hongchun Qu, Linfeng Tian, and Cheng Tan. "Predictive Control for Interval Type-2 Fuzzy System with Event-Triggered Scheme." Advances in Fuzzy Systems 2019 (July 8, 2019): 1–13. http://dx.doi.org/10.1155/2019/9365767.

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In this paper, a synthesis approach of model predictive control (MPC) is proposed for interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy system with quantization error, bounded disturbance, and data loss. The novelty lies in the following technical improvements. In order to reduce the redundant data transmission, an event-triggered communication scheme is applied to determine whether the control law should be transmitted into the communication network or not. The IT2 T-S fuzzy model is utilized to address the nonlinearity of plant with parameter uncertainties, which can be captured by the lower and upper membership functions. Furthermore, the phenomena of data loss and quantization error between the controller and the actuator are expressed as Markovian chain and sector-bound uncertainties. The synthesis approach of MPC is provided by solving an MPC optimization problem over an infinite horizon objective function which explicitly considers the input constraints. By applying the quadratic boundedness (QB) technique, the recursive feasibility and quadratic stability of closed-loop system can be guaranteed. A numerical simulation and comparison studies are proposed to illustrate the effectiveness of this approach.

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Li, Kai, and Zhen Lv. "Smooth twin bounded support vector machine with pinball loss." Applied Intelligence 51, no. 8 (January 9, 2021): 5489–505. http://dx.doi.org/10.1007/s10489-020-02085-5.

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AbstractThe twin support vector machine improves the classification performance of the support vector machine by solving two small quadratic programming problems. However, this method has the following defects: (1) For the twin support vector machine and some of its variants, the constructed models use a hinge loss function, which is sensitive to noise and unstable in resampling. (2) The models need to be converted from the original space to the dual space, and their time complexity is high. To further enhance the performance of the twin support vector machine, the pinball loss function is introduced into the twin bounded support vector machine, and the problem of the pinball loss function not being differentiable at zero is solved by constructing a smooth approximation function. Based on this, a smooth twin bounded support vector machine model with pinball loss is obtained. The model is solved iteratively in the original space using the Newton-Armijo method. A smooth twin bounded support vector machine algorithm with pinball loss is proposed, and theoretically the convergence of the iterative algorithm is proven. In the experiments, the proposed algorithm is validated on the UCI datasets and the artificial datasets. Furthermore, the performance of the presented algorithm is compared with those of other representative algorithms, thereby demonstrating the effectiveness of the proposed algorithm.

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