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WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS 2012年第3期4卷 275-294页

作者： Su, Xiaogang Yan, Xin Tsai, Chih-Ling Univ Alabama Birmingham Sch Nursing Birmingham AL 35294 USA Univ Cent Florida Dept Stat Orlando FL USA Univ Calif Grad Sch Management Davis CA USA

linear regression plays a fundamental role in statistical modeling. This article provides a step-by-step coverage of linear models in the order of model specification, model estimation, statistical inference, variable selection, model diagnosis, and prediction. Computation issues in linear regression and intimately relevant extensions of linear models are also discussed. (C) 2012 Wiley Periodicals, Inc.

关键词： linear regression model diagnosis shrinkage statistical inference variable selection

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linear regression coupled Wasserstein generative adversarial network for direct demand modeling of ride-hailing trips in Chicago and Austin

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TRANSPORTATION LETTERS-THE INTERNATIONAL JOURNAL OF TRANSPORTATION RESEARCH 2025年第4期17卷 653-665页

作者： Rahman, Md Hishamur Abrar, Masnun Rifaat, Shakil Mohammad Univ Utah Dept Civil & Environm Engn Salt Lake City UT 84112 USA Int Univ Business Agr & Technol Dept Civil Engn Dhaka Bangladesh Tekken AML Abenikko JV Dept Document Control Dhaka Bangladesh Islamic Univ Technol Dept Civil & Environm Engn Gazipur Bangladesh

Accurate estimation of ride-hailing demand and understanding of its influencing factors are necessary for modern-day transportation planning. Although modern machine learning techniques improve the predictive accuracy of zone-to-zone direct demand models, they lack inference ability due to their complex model structure. Furthermore, zone-to-zone direct demand models suffer from limited sample size for machine learning due to fixed number of origin-destination (OD) pairs. To overcome these limitations, we propose a linear regression coupled Wasserstein generative adversarial network (LR-WGAN) for direct demand modeling of zone-to-zone ride-hailing trips that captures both linear explanatory components and non-linear patterns and improves the predictive accuracy by generating data to expand the OD sample size. The proposed LR-WGAN is found to significantly improve the predictive accuracy of OD ride-hailing demand in Chicago and Austin. Furthermore, the linear explanatory component of the model is utilized to draw inferences regarding the relationship between OD ride-hailing demand and predictor variables.

关键词： Direct demand modeling ride-hailing generative adversarial network linear regression forecasting inference transportation planning

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Online identification of knee point in conventional and accelerated aging lithium-ion batteries using linear regression and Bayesian inference methods

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APPLIED ENERGY 2025年 388卷

作者： Ni, Yulong Li, Xiaoyu Zhang, He Wang, Tiansi Song, Kai Zhu, Chunbo Xu, Jianing Harbin Inst Technol Sch Elect Engn & Automat Harbin 150001 Peoples R China Shenzhen Univ Coll Phys & Optoelect Engn Shenzhen 518060 Peoples R China Jiangsu Univ Sch Automot & Traff Engn Zhenjiang 212013 Peoples R China

Accurate online knee point identification is crucial for predictive maintenance and secondary utilization of batteries. The "knee point" refers to the point in the battery capacity degradation curve where the degradation rate changes from linear to non-linear, marking a critical transition indicating the onset of accelerated capacity loss. However, challenges such as incomplete monitoring data, prevalent noise, difficulty in extracting characteristic parameters, and capacity regeneration phenomena hinder precise, real-time knee point detection. This study integrates physical mechanism modeling, signal processing techniques, and statistical inference to propose a robust, efficient solution for knee point identification. The proposed method employs feature extraction based on capacity loss mechanism models, denoising using variational mode decomposition (VMD), and a hybrid framework that combines linear regression with Bayesian inference. This dynamic model updates boundary limits in real-time, enabling highly accurate knee point identification across two positive materials, lithium cobalt oxide (LCO) and lithium iron phosphate (LFP), under various operating conditions. Comprehensive evaluations show that the proposed method achieves accuracies exceeding 94 % for conventional aging batteries and 92 % for accelerated aging batteries, surpassing existing methods. Additionally, the method demonstrates resilience to noise interference and capacity regeneration phenomena, maintaining high accuracy even under complex conditions. These results suggest that the proposed method has broad adaptability, making it a valuable tool for real-time battery health monitoring and providing a solid foundation for future research on battery aging diagnostics.

关键词： Lithium-ion batteries Conventional aging Accelerated aging Knee point linear regression Bayesian inference method

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Random permutation-based linear regression for cancelable biometrics

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EXPERT SYSTEMS 2025年第2期42卷

作者： Singh, Onkar Jaiswal, Ajay Kumar, Nitin Kumar, Naveen Univ Delhi Shaheed Sukhdev Coll Business Studies Delhi India Univ Delhi Dept Comp Sci Delhi 110007 India Univ Delhi Dept Distance & Continuing Educ Campus Open Learning Delhi India Punjab Engn Coll Dept Comp Sci & Engn Chandigarh Punjab India

The security of biometric data in biometric-based authentication systems is a significant concern. Cancellable biometrics aim to generate templates that can be replaced by new templates if compromised. We propose a new approach for generating cancellable biometric templates based on linear regression with random permutation. Our approach generates a virtual image for every biometric image by applying linear regression. In the next step, the cancellable biometric template is produced by randomly permuting each virtual image depending on a key assigned to each individual. If the template is compromised, it can be cancelled, and a new template can be generated by altering the key. Our method has shown superior performance compared to existing random permutation-based methods in terms of authentication accuracy across six databases, encompassing face, iris, and ear, even when dealing with low-resolution images. It performed well on challenging databases like UBIRIS and Georgia Tech, demonstrating the robustness of the proposed approach.

关键词： cancellable biometric linear regression random permutation template generation

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Magneto Inductive (MI) Channel Variables Prediction Through Machine Learning linear regression Method, for Underwater and Underground WSNs

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IEEE ACCESS 2025年 13卷 33124-33137页

作者： Muhammad, Aman Li, Fuzhong Mohsan, Syed Agha Hassnain Khan, Zahid Ullah Khan, Waqar Khan, Sajid Ullah Han, Ziqi Khan, Faheem Shanxi Agr Univ Coll Agr Engn Jinzhong 030801 Peoples R China Shanxi Agr Univ Sch Software Jinzhong 030801 Peoples R China Zhejiang Univ Ocean Coll Zhoushan 310027 Zhejiang Peoples R China Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Peoples R China Fuzhou Univ Int Studies & Trade Sch Big Data Fuzhou 350200 Fujian Peoples R China Prince Sattam bin Abdulaziz Univ Coll Comp Engn & Sci Dept Informat Syst Al Kharj 16278 Saudi Arabia Univ Engn & Technol Peshawar Dept Elect Engn Peshawar 610636 Pakistan

In today's digital era, where information flows seamlessly and is readily available and accessible. However, these information and communication systems are highly dependent on the robustness and adaptability of communication links, which must endure the dynamic and often unpredictable changes occurring in the communication environment, especially in underwater and underground communication. As technology advances and demands for reliable data transfer grows, the resilience of these links becomes increasingly critical to ensure an uninterrupted access to information. For this we will be analyzing a new paradigm in Wireless Sensor Networks (WSNs), i.e. Magneto Inductive (MI) communication. Which has the capability to provide robustness to the communication link as well as the security of the information can also be controlled, by utilizing the directionality factor of the created magnetic flux around the MI tri-directional (MI-TD) coils. In this study we will examine MI communication variable factors, which have effects on the output of the MI channel's response, such as frequency of applied excitation current, number of turns, radius of the communicating coils, and changing communication distance between nodes. Than we will use a linear regression machine learning (ML) model to predict the values of the aforementioned variables, which will help to predict the MI channel's response in the form of Path loss/Bit Error Rate (BER). The model that we have created for the prediction purpose, archives an estimation accuracy of 92%.

关键词： Coils Wireless sensor networks Magnetic flux Magnetic fields Wireless communication Magnetic field measurement Receivers Predictive models Media Magnetic domains Magneto inductive communication machine learning linear regression information security magnetic flux magneto inductive channel wireless sensor networks

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Bayes Optimal Learning in High-Dimensional linear regression With Network Side Information

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IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第1期71卷 565-591页

作者： Nandy, Sagnik Sen, Subhabrata Univ Chicago Dept Stat Chicago IL 60637 USA Harvard Univ Dept Stat Cambridge MA 02138 USA

Supervised learning problems with side information in the form of a network arise frequently in applications in genomics, proteomics and neuroscience. For example, in genetic applications, the network side information can accurately capture background biological information on the intricate relations among the relevant genes. In this paper, we initiate a study of Bayes optimal learning in high-dimensional linear regression with network side information. To this end, we first introduce a simple generative model (called the Reg-Graph model) which posits a joint distribution for the supervised data and the observed network through a common set of latent parameters. Next, we introduce an iterative algorithm based on Approximate Message Passing (AMP) which is provably Bayes optimal under very general conditions. In addition, we characterize the limiting mutual information between the latent signal and the data observed, and thus precisely quantify the statistical impact of the network side information. Finally, supporting numerical experiments suggest that the introduced algorithm has excellent performance in finite samples.

关键词： Bayes methods Message passing Mutual information Signal processing algorithms Numerical models Limiting Data models Approximation algorithms Slabs Iterative methods linear regression random networks approximate message passing mutual information variable selection

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Segmentation and calculation of splashes area during fish feeding using deep learning and linear regression

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COMPUTERS AND ELECTRONICS IN AGRICULTURE 2025年 234卷

作者： Qian, Liwen Yu, Guoyan Liu, Haochun He, Zijian Guangdong Ocean Univ Sch Mech Engn Zhanjiang 524088 Guangdong Peoples R China Guangdong Ocean Univ Guangdong Marine Equipment & Mfg Engn Technol Res Zhanjiang 524088 Guangdong Peoples R China

Evaluating the feeding intensity of fish in large deep-sea cages is crucial for improving feed utilization efficiency and reducing aquaculture costs. During feeding operations, fish engage in intense feeding competition and jumping behaviors, creating splashes of varying sizes that indirectly reflect their hunger intensity. This study focuses on the splashes generated by golden pompano during feeding and introduces a splash area estimation model, SSS-YOLOv8n-seg-DI, which combines linear regression and deep learning, providing foundational data for non-invasive appetite analysis. Firstly, the model employs the StarNet network and a self-designed SCD-Head shared convolutional detection head to make the YOLOv8n-seg network more lightweight, resulting in the SSSYOLOv8n-seg model. This modification improves accuracy while reducing parameters and FLOPs by 53.99 % and 32.50 %, respectively. Secondly, to reduce equipment costs, this paper utilizes a binocular camera and proposes a target area calculation model, DI, based on linear regression, which calculates the target area using the depth information provided by the camera. Ultimately, the combined SSS-YOLOv8n-seg-DI model is capable of segmenting and calculating the splash area generated by fish during feeding, providing foundational data for appetite analysis and adjusting subsequent feeding quantities. Results from marine experiments show that the calculated splash area achieved an R2 of 0.931, with a mean absolute error (MAE) of 0.813 m2 and a root mean square error (RMSE) of 0.869 m2. The experimental outcomes demonstrate that the model exhibits strong robustness, meeting the requirements for splash area calculation in complex environments.

关键词： Feeding intensity of fish Binocular camera Deep learning linear regression

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Uncertainty analysis of linear and non-linear regression models in the modeling of water quality in the Caspian Sea basin: Application of Monte-Carlo method

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ECOLOGICAL INDICATORS 2025年 170卷

作者： Masteali, Sahar Heidari Bayat, Mahmoud Bettinger, Pete Ghorbanpour, Mansour Univ Tehran Fac Nat Resources Dept Environm Tehran Iran Educ & Extens Org AREEO Res Inst Forests & Rangelands Agr Res Tehran Iran Univ Georgia Sch Forestry & Nat Resources Athens GA 30602 USA Arak Univ Fac Agr & Nat Resources Dept Med Plants Arak *** Iran

The assessment of uncertainty in water quality prediction models is crucial for understanding the reliability of these models. This research focuses on the southern basin area of the Caspian Sea in Iran, where there have been limited studies on uncertainty analysis in water quality models. First, a forest layer was extracted from land cover map and 25 large watersheds were selected. River water quality was then assessed from the perspective of 8 landscape connectivity metrics and 12 graph theory indices. We developed predictive models using stepwise linear regression, power, exponential, and logarithmic models to locate the best model form for each water quality parameter (dependent variable) we examined. The goal of this study was to analyze the uncertainty in both linear and non-linear water quality regression models for this region. The researchers used a Monte Carlo simulation method, which is a common approach to investigate uncertainty. First, they determined the best distribution of the independent variables in the regression models using the Kolmogorov-Smirnov goodness of fit test. Then, they generated 15,000 random data points based on the characteristics of the identified variable distributions. In the third stage, new regression models were created using the data from the previous stages. Probability density functions related to the output of the models were developed, and uncertainty analysis was conducted based on the behavior of the models. The results indicated that the CO3 model had the lowest uncertainty bandwidth and the highest R2 among other models. Additionally, the K models had less bandwidth than the other models developed. The research results showed that more than 70% of the models produced results within an acceptable range of uncertainty. Furthermore, the normalized RMSE (NRMSE) values associated with the models were all in the range of 0 to 30%, which is considered acceptable. These outcomes suggest that landscape indicators and graph the

关键词： Uncertainty linear regression Non-linear regression Landscape Water quality

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Factors Affecting Student Academic Performance: A Combined Factor Analysis of Mixed Data and Multiple linear regression Analysis

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IEEE ACCESS 2025年 13卷 15946-15964页

作者： El Jihaoui, Mohamed Abra, Oum El Kheir Mansouri, Khalifa Univ Hassan II Casablanca Modeling & Simulat Intelligent Ind Syst Lab M2S2I ENSET Mohammedia Casablanca 20000 Morocco Reg Ctr Educ & Training Profess Rabat 11000 Morocco

Understanding student academic performance is a cornerstone for developing sustainable educational practices that benefit students, teachers, policymakers, and society. This analysis directly impacts students' ability to engage in and promote sustainable practices, thereby shaping their future academic success. While many studies focus on predicting student performance based on a set of features, our study takes an approach by reducing these features into factors and analyzing their impact. We aim to identify the factors influencing student performance within the middle school education system using a combined approach of Factor Analysis for Mixed Data (FAMD) and Multiple linear regression (MLR). Our analysis is based on a robust and reliable large dataset of 1,073,450 observations, encompassing qualitative and quantitative features. FAMD analysis identified four underlying factors: prior academic performance, academic delay, socioeconomic status, and class environment;all these factors have good to excellent reliability, with Cronbach's Alpha values ranging from 0.809 to 0.930. Feeding these factors into the MLR produces a robust model that explains 88.53% of the variance in the CGPA, indicating a strong fit. Prior Academic Performance factor emerges as the most powerful predictor, accounting for 76.6% of the explained variance. Academic Delay follows, explaining 14.34% of the variance. Socioeconomic Status contributes 6.02%, and Class Environment adds 3.03%, reflecting smaller but meaningful impacts. All predictors are statistically significant (p <0.001), confirming their critical roles in influencing student performance (CGPA). The insights gained from this study are critically important in the field of education. They enable teachers and educational leaders to identify at-risk students early and develop targeted interventions that address the factors influencing their performance. This approach aims to enhance learning outcomes, improve educational practices, a

关键词： Education Predictive models Data mining Machine learning Accuracy linear regression Data models Prediction algorithms Analytical models Random forests Factors analysis factor analysis for mixed data FAMD student performance multiple linear regression prediction

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Representation Transfer Learning via Multiple Pre-Trained Models for linear regression

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2025年第1期19卷 208-220页

作者： Singh, Navjot Diggavi, Suhas Univ Calif Los Angeles Dept Elect & Comp Engn Los Angeles CA 90025 USA

In this paper, we consider the problem of learning a linear regression model on a data domain of interest (target) given few samples. To aid learning, we are provided with a set of pre-trained regression models that are trained on potentially different data domains (sources). Assuming a representation structure for the data generating linear models at the sources and the target domains, we propose a representation transfer based learning method for constructing the target model. The proposed scheme is comprised of two phases: (i) utilizing the different source representations to construct a representation that is adapted to the target data, and (ii) using the obtained model as an initialization to a fine-tuning procedure that re-trains the entire (over-parameterized) regression model on the target data. For each phase of the training method, we provide excess risk bounds for the learned model compared to the true data generating target model. The derived bounds show a gain in sample complexity for our proposed method compared to the baseline method of not leveraging source representations when achieving the same excess risk, therefore, theoretically demonstrating the effectiveness of transfer learning for linear regression.

关键词： Data models Adaptation models Training Transfer learning Vectors linear regression Analytical models Few shot learning Context modeling Complexity theory Machine learing: Transfer learning few shot learning representation learning

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