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A novel approach for non-normal multi-response optimisation problems

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2021年第23期59卷 7194-7215页

作者： Wang, Jianjun Tu, Yanan Ma, Yan Ouyang, Linhan Tu, Yiliu Nanjing Univ Sci & Technol Dept Management Sci & Engn Sch Econ & Management Nanjing Peoples R China Nanjing Univ Aeronaut & Astronaut Dept Management Sci & Engn Coll Econ & Management Nanjing Peoples R China Univ Calgary Dept Mech & Mfg Engn SCHULICH Sch Engn Univ Dr 2500 NW Calgary AB T2N 1N4 Canada

Various creative multi-response optimisation approaches have been developed in the literature. Most of these researches are based on the normality assumption of the response distribution. However, this assumption does not necessarily hold in some real cases, such as non-normal multiple responses. Also, the reproducibility of optimisation results does not hold in some practical applications due to the variability of predicted responses associated with model uncertainty. In this paper, a novel approach is proposed to address the issues for non-normal multi-response optimisation. The proposed method not only identifies significant effects for each response by incorporating factorial effect principles into the framework of the Bayesian generalised linear models (GLMs) but also takes into account the model uncertainty and the variability of predicted responses by using the Bayesian sampling technique and Pareto optimal strategy. Furthermore, the optimal parameter settings are found by using grey incidence analysis (GIA). Besides, two examples are used to illustrate the effectiveness of the proposed method. The results show that the proposed method not only effectively identify significant factors but also find more satisfactory parameter settings when the reliability and reproducibility of optimisation results are considered simultaneously.

关键词： Quality management non-normal multi-response generalized linear models Bayesian analysis factorial effect principle

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A Novel Two-Parameter Estimation Technique for Handling Multicollinearity in Inverse Gaussian Regression Model

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JOURNAL OF CHEMOMETRICS 2025年第5期39卷

作者： Riaz, Ishrat Sanaullah, Aamir Hasaballah, Mustafa M. Balogun, Oluwafemi Samson Bakr, Mahmoud E. COMSATS Univ Islamabad Lahore Campus Lahore Pakistan Marg Higher Inst Engn & Modern Technol Dept Basic Sci Cairo Egypt Univ Eastern Finland Dept Comp Kuopio Finland King Saud Univ Coll Sci Dept Stat & Operat Res Riyadh Saudi Arabia

This study focuses on the prevalent issue of multicollinearity in the inverse Gaussian regression model (IGRM), which arises when predictor variables have a high degree of correlation. The typical maximum likelihood estimator (MLE) proves to be highly unstable when dealing with linearly linked regressors. Eventually, the accuracy of the model may suffer because of inflated variances and inaccurate coefficient estimates. To improve parameter estimation accuracy and combat multicollinearity, this paper suggests an alternative biased estimator for the IGRM that integrates a two-parameter framework. This novel two-parameter estimator is a general estimator that takes the maximum likelihood, ridge, and Stein estimators as special cases. The theoretical characteristics of the estimator, including its bias and mean squared error (MSE), are develop and then go through a thorough theoretical comparison with the previous estimators in terms of the mean square error matrix (MMSE) criterion. Moreover, the optimal values of the biasing parameters for the advised estimator are also obtained. An extensive simulated study and real-world dataset are examined to assess the practical relevance of the proposed estimator. The empirical results show that, in comparison to conventional estimators, including MLE, ridge, and Stein estimators, the suggested estimator considerably lowers the MSE and improves the parameter estimation accuracy. These results illustrate the novel approach's potential for dealing with multicollinearity in IGRM. The continuous development of reliable estimating methods for generalized linear models (GLMs) is aided by these findings.

关键词： biasing parameters generalized linear models inverse Gaussian regression model mean square error multicollinearity two-parameter estimator

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A heteroscedastic Bayesian generalized logistic regression model with application to scaling problems

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CHAOS SOLITONS & FRACTALS 2024年 182卷

作者： Sutton, Jack Shahtahmassebi, Golnaz Hanley, Quentin S. V. Ribeiro, Haroldo Univ Derby Coll Sci & Engn Markeaton St Derby DE22 3AW England Nottingham Trent Univ Sch Sci & Technol Nottingham NG11 8NS England GH & Q Serv Ltd West Studios Sheffield Rd Chesterfield S41 7LL England Univ Estadual Maringa Dept Fis BR-87020900 Maringa PR Brazil

Power law scaling models have been used to understand the complexity of systems as diverse as cities, neurological activity, and rainfall and lightning. In the scaling framework, power laws and standard linear regression methods are widely used to estimate model parameters with assumed normality and fixed variance. generalized linear models (GLM) can accommodate a wider range of distributions where the chosen distribution must meet the assumptions of the data to prevent model bias. We present a widely applicable Bayesian generalized logistic regression (BGLR) framework to more flexibly model a continuous real response addressing skew and heteroscedasticity. The generalized Logistic Distribution (GLD) was selected to flexibly model skewed continuous data. This resulted in a nonlinear posterior distribution which may not have an analytical solution which can be solved numerically with Markov Chain Monte Carlo (MCMC) methods. We compared the BGLR model to standard and Bayesian normal models having fixed and varying variance when fitting power laws to 759 days of COVID-19 data. The BGLR yielded information beyond existing methods about the evolution of skew and skedasticity while revealing parameter bias of widely used methods. The BGLR flexibly modelled the complex characteristics necessary for an improved understanding of the propagation and dynamics of this infectious disease. The model is generally applicable and can be used as a template for modelling complexity with other distributions.

关键词： Bayesian inference generalized linear models generalized logistic distribution Markov chain Monte Carlo methods Power laws Nonlinear system

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Impact of season, cloud cover, and air pollution on different spectral regions of ultraviolet and visible incident solar radiation at the surface

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QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY 2021年第738期147卷 2834-2849页

作者： Musiolkova, Marie Huszar, Peter Navratil, Martin Spunda, Vladimir Czech Univ Life Sci Prague Fac Agrobiol Food & Nat Resources Dept Agroecol & Crop Prod Suchdol Czech Republic Charles Univ Prague Fac Math & Phys Dept Atmospher Phys Prague Czech Republic Univ Ostrava Fac Sci Dept Phys Ostrava Czech Republic

This study deals with the impact of season, cloud cover, and air pollution on spectral regions of incident solar radiation (UVB, UVA, photosynthetically active radiation (PAR) = Blue + Green + Red, 660, 730 nm) and their ratios (Blue/Red, Blue/PAR, Green/PAR, Red/PAR, 660/730 nm, UVB/UVA, UVB/PAR, and UVA/PAR) measured at three measuring stations at two locations in the City of Ostrava, Czech Republic. The mentioned spectral regions are crucial for plants because they influence photosynthesis and photomorphogenesis. However, there is still a lack of published information about the radiation regime in the plants' environment. The measured data underwent a quality check and were divided into 40 groups corresponding to different combinations of season, cloud cover, and air pollution level. Standard statistical characteristics of spectral regions and their ratios were calculated for each combination. generalized linear models were used to evaluate the effect of air pollutants on spectral regions of incident solar radiation. Average irradiance values in the spectral regions generally decreased with increasing air pollution on both cloudy and sunny days. A mostly decreasing trend of average values of ratios with increasing air pollution is found mainly on sunny days and, for some cases, even on cloudy days. Each ratio shows a specific patterns depending on the season and cloud cover. The generalized linear models confirm previously published results and underline that air pollution affects various spectral regions of incident solar radiation differently.

关键词： atmospheric pollution cloud cover Czech Republic generalized linear models Ostrava solar radiation

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RENT-Repeated Elastic Net Technique for Feature Selection

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IEEE ACCESS 2021年 9卷 152333-152346页

作者： Jenul, Anna Schrunner, Stefan Liland, Kristian Hovde Indahl, Ulf Geir Futsaether, Cecilia Marie Tomic, Oliver Norwegian Univ Life Sci Fac Sci & Technol N-1430 As Norway

Feature selection is an essential step in data science pipelines to reduce the complexity associated with large datasets. While much research on this topic focuses on optimizing predictive performance, few studies investigate stability in the context of the feature selection process. In this study, we present the Repeated Elastic Net Technique (RENT) for Feature Selection. RENT uses an ensemble of generalized linear models with elastic net regularization, each trained on distinct subsets of the training data. The feature selection is based on three criteria evaluating the weight distributions of features across all elementary models. This fact leads to the selection of features with high stability that improve the robustness of the final model. Furthermore, unlike established feature selectors, RENT provides valuable information for model interpretation concerning the identification of objects in the data that are difficult to predict during training. In our experiments, we benchmark RENT against six established feature selectors on eight multivariate datasets for binary classification and regression. In the experimental comparison, RENT shows a well-balanced trade-off between predictive performance and stability. Finally, we underline the additional interpretational value of RENT with an exploratory post-hoc analysis of a healthcare dataset.

关键词： Feature extraction Stability criteria Predictive models Training Training data Task analysis Data models Elastic net regularization exploratory analysis ensemble feature selection generalized linear models selection stability

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Model averaging in distributed machine learning: a case study with Apache Spark

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VLDB JOURNAL 2021年第4期30卷 693-712页

作者： Guo, Yunyan Zhang, Zhipeng Jiang, Jiawei Wu, Wentao Zhang, Ce Cui, Bin Li, Jianzhong Harbin Inst Technol Mass Data Comp Res Ctr Harbin 150001 Peoples R China Peking Univ Sch EECS Beijing 100871 Peoples R China Microsoft Res Redmond WA USA Swiss Fed Inst Technol Dept Comp Sci CH-8092 Zurich Switzerland

The increasing popularity of Apache Spark has attracted many users to put their data into its ecosystem. On the other hand, it has been witnessed in the literature that Spark is slow when it comes to distributed machine learning (ML). One resort is to switch to specialized systems such as parameter servers, which are claimed to have better performance. Nonetheless, users have to undergo the painful procedure of moving data into and out of Spark. In this paper, we investigate performance bottlenecks of MLlib (an official Spark package for ML) in detail, by focusing on analyzing its implementation of stochastic gradient descent (SGD)-the workhorse under the training of many ML models. We show that the performance inferiority of Spark is caused by implementation issues rather than fundamental flaws of the bulk synchronous parallel (BSP) model that governs Spark's execution: we can significantly improve Spark's performance by leveraging the well-known "model averaging" (MA) technique in distributed ML. Indeed, model averaging is not limited to SGD, and we further showcase an application of MA to training latent Dirichlet allocation (LDA) models within Spark. Our implementation is not intrusive and requires light development effort. Experimental evaluation results reveal that the MA-based versions of SGD and LDA can be orders of magnitude faster compared to their counterparts without using MA.

关键词： Distributed machine learning Apache Spark MLlib generalized linear models Latent Dirichlet allocation

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Modified ridge parameter estimators for log-gamma model: Monte Carlo evidence with a graphical investigation

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2021年第7期50卷 2168-2183页

作者： Kurtoglu, Fikriye Cukurova Univ Fac Sci & Letters Dept Stat TR-01330 Adana Turkey

In ordinary ridge regression, the estimation of the ridge parameter is a significant topic. This article generalizes some different methods for estimating the ridge parameter by considering the work of Kibria (2003), Khalaf and Shukur (2005), Alkhamisi, Khalaf, and Shukur (2006), Alkhamisi and Shukur (2008) and Muniz et al. (2012) in generalized linear models. The superiority of these estimators are assessed by the estimated mean squared error via Monte Carlo simulation study and real data set where the response follows gamma distribution with log link function. In this simulation study, it is chosen to vary the degree of correlation, the sample size, the number of explanatory variables and the different shape parameter for gamma response.

关键词： Ridge parameter estimator Log-gamma model generalized linear models Mean squared error

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generalized nonlinearity in animal ecology: Research, review, and recommendations

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ECOLOGY AND EVOLUTION 2024年第7期14卷 e11387页

作者： Heit, David R. Ortiz-Calo, Waldemar Poisson, Mairi K. P. Butler, Andrew R. Moll, Remington J. Univ New Hampshire Dept Nat Resources & Environm Durham NH 03824 USA Univ Montana WA Franke Coll Forestry Wildlife Biol Program Missoula MT USA

generalized linear models (GLMs) are an integral tool in ecology. Like general linear models, GLMs assume linearity, which entails a linear relationship between independent and dependent variables. However, because this assumption acts on the link rather than the natural scale in GLMs, it is more easily overlooked. We reviewed recent ecological literature to quantify the use of linearity. We then used two case studies to confront the linearity assumption via two GLMs fit to empirical data. In the first case study we compared GLMs to generalized additive models (GAMs) fit to mammal relative abundance data. In the second case study we tested for linearity in occupancy models using passerine point-count data. We reviewed 162 studies published in the last 5 years in five leading ecology journals and found less than 15% reported testing for linearity. These studies used transformations and GAMs more often than they reported a linearity test. In the first case study, GAMs strongly out-performed GLMs as measured by AIC in modeling relative abundance, and GAMs helped uncover nonlinear responses of carnivore species to landscape development. In the second case study, 14% of species-specific models failed a formal statistical test for linearity. We also found that differences between linear and nonlinear (i.e., those with a transformed independent variable) model predictions were similar for some species but not for others, with implications for inference and conservation decision-making. Our review suggests that reporting tests for linearity are rare in recent studies employing GLMs. Our case studies show how formally comparing models that allow for nonlinear relationships between the dependent and independent variables has the potential to impact inference, generate new hypotheses, and alter conservation implications. We conclude by suggesting that ecological studies report tests for linearity and use formal methods to address linearity assumption violations in GLMs. This p

关键词： additive models generalized linear models general liner models model assumptions regression

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Comparing Beta Regression and Quantile Regression Forests for Probabilistic Photovoltaic Energy Forecasting ⁎

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IFAC-PapersOnLine 2025年第1期59卷 325-330页

作者： Marco Capelletti Valentina Fogli Edoardo Santilli Matteo Gardini Riccardo Vignali Giuseppe De Nicolao Department of Electrical Computer and Biomedical Engineering University of Pavia Italy Global Quants & Risk Modeling Eni Plenitude S.p.A.

This work focuses on the analysis of probabilistic power curve models that link the energy production of a photovoltaic system with the irradiance forecasts of the weather provider. It is shown that the essential information is provided by global horizontal irradiance (GHI) forecasts, which can be used to obtain simple and meaningful probabilistic models using non-parametric (quantile Regression forests) and parametric (Beta regression) methods. The second step is the analysis of the monthly performance of power curve models, to understand whether their performance can improve by taking monthly variability into account.

关键词： Renewable energy forecasting Estimation learning Statistical data analysis Solar power forecasting generalized linear models Quantile regression forest

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Bayesian regression analysis of stutter in DNA mixtures

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第17期50卷 4066-4080页

作者： Alaeddini, Reza Yang, Mo Puza, Borek Decontta Co Ft Worth TX USA Dongbei Univ Finance & Econ Sch Finance Dalian 116025 Peoples R China Australian Natl Univ Res Sch Finance Actuarial Studies & Stat Canberra ACT Australia

Probabilistic genotyping methods use a hierarchical probability model in deconvolution of DNA mixtures. The parameters of the model, including the stutter which are required to calculate the expected values of peak heights, are estimated in the validation process. linear modeling of stutter, as a common artifact in DNA genotyping, has been reported previously. The typically right-skewed error distribution and non-negativeness of stutter to its allele peak heights ratios make generalized linear models preferable, especially Bayesian analogs, which allow even more flexibility. In this paper, we show how such models can be fitted and applied with the aid of Markov chain Monte Carlo methods.

关键词： Bayesian methods DNA genotyping generalized linear models Markov chain Monte Carlo methods stutter

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