Iteratively Reweighted Least Squares Research Articles

An evaluation of computational methods for aggregate data meta-analyses of diagnostic test accuracy studies

BackgroundA Generalized Linear Mixed Model (GLMM) is recommended to meta-analyze diagnostic test accuracy studies (DTAs) based on aggregate or individual participant data. Since a GLMM does not have a closed-form likelihood function or parameter solutions, computational methods are conventionally used to approximate the likelihoods and obtain parameter estimates. The most commonly used computational methods are the Iteratively Reweighted Least Squares (IRLS), the Laplace approximation (LA), and the Adaptive Gauss-Hermite quadrature (AGHQ). Despite being widely used, it has not been clear how these computational methods compare and perform in the context of an aggregate data meta-analysis (ADMA) of DTAs.MethodsWe compared and evaluated the performance of three commonly used computational methods for GLMM - the IRLS, the LA, and the AGHQ, via a comprehensive simulation study and real-life data examples, in the context of an ADMA of DTAs. By varying several parameters in our simulations, we assessed the performance of the three methods in terms of bias, root mean squared error, confidence interval (CI) width, coverage of the 95% CI, convergence rate, and computational speed.ResultsFor most of the scenarios, especially when the meta-analytic data were not sparse (i.e., there were no or negligible studies with perfect diagnosis), the three computational methods were comparable for the estimation of sensitivity and specificity. However, the LA had the largest bias and root mean squared error for pooled sensitivity and specificity when the meta-analytic data were sparse. Moreover, the AGHQ took a longer computational time to converge relative to the other two methods, although it had the best convergence rate.ConclusionsWe recommend practitioners and researchers carefully choose an appropriate computational algorithm when fitting a GLMM to an ADMA of DTAs. We do not recommend the LA for sparse meta-analytic data sets. However, either the AGHQ or the IRLS can be used regardless of the characteristics of the meta-analytic data.

3D high-resolution Radon transform based on strong sparse LP‒1 norm and its applications

Abstract Multiple reflections are among the most challenging noises to suppress in seismic data, as they differ from effective waves only in terms of apparent velocity. Besides, the Radon transform, an essential technique for attenuating multiple reflections, has been widely incorporated into various commercial software packages. Thus, this study introduces a 3D Radon transform method based on the LP‒1 norm to enhance sparsity-constraining capability in the transform domain, leveraging high-resolution Radon transform techniques. Specifically, an iteratively reweighted least squares (IRLS) algorithm is employed to obtain the transformed data in the Radon domain. Given that the LP‒1 norm is applied to seismic data processing for the first time, this paper theoretically demonstrates its powerful sparsity-constraining capability. Indeed, the proposed strategy enhances energy concentration in the Radon transform domain, better-separating primaries from multiples and ultimately suppressing the multiples. Both model tests and real data indicate that the 3D Radon transform constrained by the LP‒1 norm outperforms existing high-resolution Radon transform methods with sparsity constraints regarding energy concentration and effectiveness in multiple reflection attenuation.

The global effects of digestive system cancers worldwide on the COVID-19 pandemic by negative binomial (mixed) regression models

In this study, the main goal is to determine statistically significant relationships between the biggest epidemic problem of last years as the COVID-19 pandemic and digestive system cancers belonging to 168 countries worldwide using generalized linear mixed model (GLMM) and its special case as generalized linear model (GLM) approaches, and to obtain global inferences that will shed light on this pandemic. For this goal, the response variable is “total cases of the COVID-19 pandemic per 100,000 people” until January 14, 2022. The explanatory variables are total number of people suffering from colon and rectum, stomach, lip and oral cavity, esophageal, and nasopharynx cancers belonging to 2019, respectively. In this study, the negative binomial (NB) regression model in GLM using iteratively reweighted least squares (IRLS) algorithm and the NB mixed regression model in GLMM with “countries” taken as “random effects” using Adaptive Gauss-Hermite Quadrature (AGHQ) approximation method at 1, 2, 10, and 20 quadrature points are used for modelling the COVID-19 pandemic and digestive systems cancer data. In this study, by using information criteria, the NB mixed regression model in GLMM under log-link function with 168 countries taken as random effects using AGHQ method at 20 quadrature point is detected as the most appropriate model for the global COVID-19 pandemic and digestive system cancers data.

Solving Maxmin Optimization Problems via Population Games

Population games are games with a finite set of available strategies and an infinite number of players, in which the reward for choosing a given strategy is a function of the distribution of players over strategies. The paper shows that, in a certain class of maxmin optimization problems, it is possible to associate a population game to a given maxmin problem in such a way that solutions to the optimization problem are found from Nash equilibria of the associated game. Iterative solution methods for maxmin optimization problems can then be derived from systems of differential equations whose trajectories are known to converge to Nash equilibria. In particular, we use a discrete-time version of the celebrated replicator equation of evolutionary game theory, also known in machine learning as the exponential multiplicative weights algorithm. The resulting algorithm can be viewed as a generalization of the Iteratively Reweighted Least Squares (IRLS) method, which is well known in numerical analysis as a useful technique for solving Chebyshev function approximation problems on a finite grid. Examples are provided to show the use of the generalized IRLS method in collective investment and in decision making under model uncertainty.

L1-norm optimisation of rank deficient GNSS networks by an improved Grey Wolf method

An improved grey wolf optimization (GWO) is proposed for direct L1-norm optimization in rank deficient GNSS networks to detect outliers since the standard GWO and the global optimization (GO) algorithms cannot deal with such problems. In contrast to the traditional method for L1-norm minimization which is solved by a cumbersome search of linear programming (LP) problem, in this algorithm, one only requires to input the target function. Furthermore, it has a greater ability to detect gross errors of observables with low reliability compared to traditional methods such as LP. Moreover, it does not consider the correct observables as blunders in contrast to some algorithms such as the iteratively reweighted least-squares (IRLS) method, which may consider them as outliers. The numerical results of real and simulated GNSS networks approve the efficiency of the new algorithm.

Fully automated structured light scanning for high-fidelity 3D reconstruction via graph optimization.

Convenient and high-fidelity 3D model reconstruction is crucial for industries like manufacturing, medicine and archaeology. Current scanning approaches struggle with high manual costs and the accumulation of errors in large-scale modeling. This paper is dedicated to achieving industrial-grade seamless and high-fidelity 3D reconstruction with minimal manual intervention. The innovative method proposed transforms the multi-frame registration into a graph optimization problem, addressing the issue of error accumulation encountered in frame-by-frame registration. Initially, a global consistency cost is established based on point cloud cross-multipath registration, followed by using the geometric and color differences of corresponding points as dynamic nonlinear weights. Finally, the iteratively reweighted least squares (IRLS) method is adopted to perform the bundle adjustment (BA) optimization of all poses. Significantly enhances registration accuracy and robustness under the premise of maintaining near real-time efficiency. Additionally, for generating watertight, seamless surface models, a local-to-global transitioning strategy for multiframe fusion is introduced. This method facilitates efficient correction of normal vector consistency, addressing mesh discontinuities in surface reconstruction resulting from normal flips. To validate our algorithm, we designed a 3D reconstruction platform enabling spatial viewpoint transformations. We collected extensive real and simulated model data. These datasets were rigorously evaluated against advanced methods, roving the effectiveness of our approach. Our data and implementation is made available on GitHub for community development.

Analyzing Motorcycle Accident Frequency Using Generalized Poisson Distributions

Motorcycle accidents in East Java are more common than accidents in other modes of transportation. In addition to the many motorcycle users today, human, environmental, and road factors are considered the highest causes of these accidents. The study's goal is to find the best model of the Generalized Poisson Family Distribution (GPR), namely Lagrangian Poisson Regression (LPR) and to construct a model that will quantify the frequency of motorcycle accidents in East Java. Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) criteria are the model comparison methods used in this research. The selection was also made based on the model's exponential coefficient with a 95% CI to further deepen the selection results obtained. In addition, the paired samples test was performed to determine the degree of dissimilarity between the outcomes produced by the developed model and the actual data. The best performance model is applied to identify the characteristics or factors highly involved in motorcycle accidents. The research uses secondary data from related agencies, namely the East Java Regional Police, especially the traffic accident unit, and East Java BPS, for 38 cities and districts in 2021. The numerical optimization method used is the iteratively reweighted least squares (IRLS) algorithm, assisted by R Studio software. The study findings show that LPR is the most efficient and exact approach for modeling the frequency of motorcycle accidents. Meanwhile, the percentage of teenagers (X1), the frequency of motorized vehicles (X3), and the average annual rainfall (X5) have a considerable impact on accident occurrence. This research has an important contribution, especially in the field of transportation modeling and designing appropriate strategies to reduce the frequency of motorcycle accidents.

An errors-unidentified hand-eye calibration method via robot relocalization and iterative combinatorial refinement

The accuracy of hand-eye calibration is easily affected by robot kinematic error, measurement error, random error, etc., and can be to a certain extent enhanced by the complicated error identification. To address this problem, we propose a novel errors-unidentified hand-eye calibration method. A relocalization-based hand-eye calibration is implemented to overcome the challenge from robot kinematics at first owing to the high robot relocalization accuracy. The tool center point (TCP) coordinates are then obtained based on an iterative reweighted least squares (IRLS) spherical fitting algorithm. An iterative combinatorial refinement algorithm is finally presented to search the solutions in the form of permutation and combination when solving the rigid transformation matrix. Experiments on criterion sphere and blade demonstrate that by converting the hand-eye matrix solving problem into a point set matching problem, the accuracy of the proposed method is enhanced by 60% on average compared with three state-of-the-art hand-eye calibration methods.

Relationship Between World Happiness Index, Hoefstede Cultural Dimensions And Government Education Spending

The author analyzes the interplay between the World Happiness Index and a nuanced array of seven variables in this research. Specifically, the focus extends to the Hofstede Cultural Dimensions, encompassing six distinct facets and the financial allocations dedicated to government education spending. The author starts with a literature survey on the profound domains of happiness and wellbeing. Building upon this foundation, the author posits the Hofstede Cultural Dimensions and Government Education Expenditures as prospective variables that may yield a discernible influence on the World Happiness Index. A dataset spanning 58 countries and analytical methodologies of Ordinary Least Squares (OLS) regression and Iteratively Reweighted Least Squares (IRLS) regression are used to test this conjecture. The outcome of this study reveals compelling insights into the association between the World Happiness Index and the identified variables. The results underscore a discernible relationship between the World Happiness Index and specific dimensions of cultural orientation, such as individualism, long-term orientation, and indulgence. Furthermore, the study reveals that government investment in education is another factor influencing the overarching landscape of happiness. These findings transcend mere statistical findings; they serve as beacons of knowledge with far-reaching implications for education policymakers, educators, and individuals interested in understanding the complexities of cultural variations, educational dynamics, and overall wellbeing. The implications of this research can offer relevant information to those who navigate the intricate intersections of cultural diversity, education policy, and the pursuit of societal happiness, such as education policymakers, educators and anyone interested in the issues of cultural differences, education, and wellbeing.

An improved parameter estimation of HFM signals based on IRLS linear fitting of extracted group delay

To address the issue of robust parameter estimation of hyperbolic frequency modulated (HFM) signals under low signal-to-noise ratios (SNRs), an improved algorithm based on iteratively reweighted least squares (IRLS) linear fitting of extracted group delay is proposed. The algorithm includes three main steps. First, a novel method for estimating the frequency distribution range (FDR) of an HFM signal is presented, which involves analyzing the transient features of the amplitude spectrum (AS). Second, the spectrum phase (SP) is unwrapped in the estimated FDR to extract the group delay (GD) of the HFM signal. Last, parameter estimation of the HFM signal is achieved by fitting the GD, which is a linear function of the reciprocal of the frequency, using the IRLS linear fitting method. The simulation results have shown that for SNR ≥ -14 dB, the normalized root mean square errors (NRMSEs) estimated by the proposed estimator are 1.5 dB lower than those estimated by the spectrum phase unwrapping (SPU) estimator, including the starting frequency and period slope. Furthermore, experimental results based on sea trial data have also verified the validity and feasibility of the proposed estimator.

Formula omitted]-norm minimization for outlier-resistant elliptic positioning in [formula omitted]-stable impulsive interference

This short communication considers the problem of robust elliptic positioning (EP) in α-stable impulsive interference based on the ℓp-norm minimization criterion. We start with converting the associated nonconvex optimization task into the well-established ℓp-minimization framework of iteratively reweighted least squares (IRLS). While the effect of p is taken into account by a weight update step in each IRLS iteration, we employ an assortment of surrogate functions, in order to effectively handle the location update subproblem using the majorization–minimization technique. The superiority of our proposal over a number of existing EP methods in terms of localization accuracy in α-stable impulsive noise is demonstrated via numerical simulations.

Iteratively Reweighted Least Squares Method for Estimating Polyserial and Polychoric Correlation Coefficients

An iteratively reweighted least squares (IRLS) method is proposed for the estimation of polyserial and polychoric correlation coefficients in this article. It calculates the slopes in a series of weighted linear regression models fitting on conditional expected values. For polyserial correlation, conditional expectations of the latent predictor is derived from the observed ordinal categorical variable, and the regression coefficient is obtained with the weighted least squares method. In estimating polychoric correlation coefficient, conditional expectations of the response variable and the predictor are updated in turns. Standard errors of the estimators are obtained using the delta method based on data summaries instead of the whole data. Conditional univariate normal distribution is exploited and a single integral is numerically evaluated in the proposed algorithm, comparing to the double integral computed numerically based on the bivariate normal distribution in the traditional maximum likelihood (ML) approaches. This renders the new algorithm very fast in the estimation of both polyserial and polychoric correlation coefficients. Thorough simulation studies are conducted to compare the performances of the proposed method with the classical ML methods. Real data analyses illustrate the advantage of the new method in computing speed. Supplementary materials for this article are available online.

Mixture extreme learning machine algorithm for robust regression

The extreme learning machine (ELM) is a well-known approach for training single hidden layer feedforward neural networks (SLFNs) in machine learning. However, ELM is most effective when used for regression on datasets with simple Gaussian distributed error because it often employs a squared loss in its objective function. In contrast, real-world data is often collected from unpredictable and diverse contexts, which may contain complex noise that cannot be characterized by a single distribution. To address this challenge, we propose a robust mixture ELM algorithm, called Mixture-ELM, that enhances modeling capability and resilience to both Gaussian and non-Gaussian noise. The Mixture-ELM algorithm uses an adjusted objective function that blends Gaussian and Laplacian distributions to approximate any continuous distribution and match the noise. The Gaussian mixture accurately models the residual distribution, while the inclusion of the Laplacian distribution addresses the limitations of the Gaussian distribution in identifying outliers. We derive a solution to the novel objective function using the expectation maximization (EM) and iteratively reweighted least squares (IRLS) algorithms. We evaluate the effectiveness of the algorithm through numerical simulation and experiments on benchmark datasets, thereby demonstrating its superiority over other state-of-the-art machine learning methods in terms of robustness and generalization.

Multispectral and Hyperspectral Image Fusion Based on Joint-Structured Sparse Block-Term Tensor Decomposition

Multispectral and hyperspectral image fusion (MHF) aims to reconstruct high-resolution hyperspectral images by fusing spatial and spectral information. Unlike the traditional canonical polyadic decomposition and Tucker decomposition models, the block-term tensor decomposition model is able to improve the quality of fused images using known endmember and abundance information. This paper presents an improved hyperspectral image fusion algorithm. Firstly, the two abundance matrices are combined into a single bulk matrix to promote structural sparsity by introducing the L2,1-norm to eliminate the scaling effects present in the model. Secondly, the counter-scaling effect is eliminated by adding the L2-norm to the endmember matrix. Finally, the chunk matrix and the endmember matrix are coupled together, and the matrix is reorganized by adding the L2,1-norm to the matrix to facilitate chunk elimination and solved using an extended iterative reweighted least squares (IRLS) method, focusing on the problem of the inability to accurately estimate the tensor rank in the chunk-term tensor decomposition model and the noise/artifact problem arising from overestimation of rank. Experiments are conducted on standard and local datasets, and the fusion results are compared and analyzed in four ways: visual result analysis, metric evaluation, time of the algorithm, and classification results, and the experimental results show that the performance of the proposed method is better than the existing methods. An extensive performance evaluation of the algorithms is performed by conducting experiments on different datasets. The experimental results show that the proposed algorithm achieves significant improvements in terms of reconstruction error, signal-to-noise ratio, and image quality compared with the existing methods. Especially in the case of a low signal-to-noise ratio, the proposed algorithm shows stronger robustness and accuracy. These results show that the proposed algorithm has significant advantages in dealing with multispectral high-resolution hyperspectral data.

A robust lp‐norm localization of moving targets in distributed multiple‐input multiple‐output radar with measurement outliers

AbstractThe Gaussian noise model and estimators based on least squares (LS) are widely used in target localisation with distributed multiple‐input multiple‐output (MIMO) radar because of their computational efficiency. However, the accuracy of existing LS‐based target localisation algorithms deteriorates sharply in the presence of outliers in the measurements. Thus, a robust solution is developed based on the ‐norm minimisation criterion and iteratively reweighted least squares (IRLS) for locating a moving target with impulse noise using the angle of arrival (AOA), time delay (TD), and Doppler shift (DS) measurements. First, the AOA, TD, and DS measurement noise models are developed based on the α‐stable distribution. Then, the localisation problem is transformed into an ‐norm minimisation problem by linearising the AOA, TD, and DS measurement equations. Finally, the ‐norm minimisation problem is solved using an IRLS method to obtain the target position and estimate the velocity. Moreover, the optimum of the norm order (p) and the Cramér–Rao lower bound for the target position and velocity estimation are derived under α‐stable distributed measurement noise. The simulation results demonstrate that the developed algorithm offers higher accurascy and robustness than the existing ones in the presence of measurement outliers.

Low-Rank and Row-Sparse Decomposition for Joint DOA Estimation and Distorted Sensor Detection

Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. We consider an array model within which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array model, the problem of joint direction-of-arrival (DOA) estimation and distorted sensor detection is formulated under the framework of low-rank and row-sparse decomposition. We derive an iteratively reweighted least squares (IRLS) algorithm to solve the resulting problem. The convergence property of the IRLS algorithm is analyzed by means of the monotonicity and boundedness of the objective function. Extensive simulations are conducted regarding parameter selection, convergence speed, computational complexity, and performances of DOA estimation as well as distorted sensor detection. Even though the IRLS algorithm is slightly worse than the alternating direction method of multipliers in detecting the distorted sensors, the results show that our approach outperforms several state-of-the-art techniques in terms of convergence speed, computational cost, and DOA estimation performance.

EHP VALUE OF MINI LNG SHIP WITH FORM FACTOR FROM PROHASKA AND IRLS METHOD USING SHIP RESISTANCE TESTING DATA

The ship model test was believed to be one of the effective methods for figuring out the boundaries and reliability of the ship's horsepower. The ship's form factor determines a full-scale ship's effective horsepower. Determination of the form factor value can be done experimentally through the Prohaska method. The new method proposed in this study is employed the regression Iteratively Reweighted Least Squares (IRLS) method by utilizing the principle dimension of the ship, such as LWL, B, CB, CP, CM, WSA, T, ∆. etc. The Indonesian Hydrodynamics Laboratory has a database of ships with various principle dimensions which have undergone the towing model test. Through the database, the form factor can be predicted with the IRLS method. The method is then verified and validated with the Prohaska method. The result shows a good agreement with the Prohaska method. The obtained results from the IRLS method also show that the EHP & Resistance calculations are identical with old fashion Prohaska methods. The residual bias factor established by the IRLS method was verified in comparison to the value of the form factor generated by the Prohaska method. Comparison between the two methods results in a small error.

3-D Crosswell electromagnetic inversion based on IRLS norm sparse optimization algorithms

Due to the complexity of underground reservoir distribution and the non-uniqueness of geophysical inverse problems, there is still a lack of practical and effective cross-well electromagnetic inversion methods. Our goal is to develop an efficient method to reduce the non-uniqueness of the physical property model recovered in the inversion. Based on a defined framework, we propose a 3-D crosswell electromagnetic sparse inversion based on iterative reweighted least squares (IRLS) method. We perform the inversion using a hybrid norm formulation, where the lp-norm (0 ≤ p ≤ 1) sparse optimization problem can be transformed into a series of weighted l2-norm optimization problems. Compared with the traditional norm inversion method, the sparse inversion method can make more effective use of the known physical information and obtain more accurate abnormal body position and shape. Finally, the effectiveness of sparse inversion method is verified by model test and inversion of measured data in mining area.

Iteratively reweighted least square for kernel expectile regression with random features

To overcome the computational burden of quadratic programming in kernel expectile regression (KER), iteratively reweighted least square (IRLS) technique was introduced in literature, resulting in IRLS-KER. However, for nonlinear models, IRLS-KER involves operations with matrices and vectors of the same size as the training set. Thus, as the training set becomes large, nonlinear IRLS-KER needs a long training time and large memory. To further alleviate the training cost, this paper projects the original data into a low-dimensional space via random Fourier feature. The inner product of the random Fourier features of two data points is approximately the same as the kernel function evaluated at these two data points. Hence, it is possible to use a linear model in the new low-dimensional space to approximate the original nonlinear model, and consequently, the time/memory efficient linear training algorithms could be applied. This paper applies the idea of random Fourier features to IRLS-KER, and our testing results on simulated and real-world datasets show that, the introduction of random Fourier features makes IRLS-KER achieve similar prediction accuracy as the original nonlinear version with substantially higher time efficiency.

Distributed iterative reweighted least squares algorithm for high-resolution finite-frequency traveltime velocity inversion using VSP data

Seismic traveltime between a source-receiver pair is a finite-frequency phenomenon. The velocity information at all points inside the first Fresnel zone is contained inside the traveltime. Therefore, finite-frequency traveltime velocity inversion (FFTVI) is able to invert velocity with finer structures than that can be obtained by ray-based tomography. Since FFTVI is a global inversion, its cost is lower than full waveform inversion. The implementation in this paper mainly focuses on the numerical aspects of FFTVI. We analyze the characteristics of FFTVI from the computational point of view. A parallel version, Iterative Reweighted Least Squares (IRLS) is designed for solving a large linear system in the memories of computer clusters. This implementation not only yields the accurate inversion of velocity at arbitrary grids and with an arbitrary acquisition geometry, but also is able to mitigate the impacts of traveltime picks with large uncertainties. The proposed workflow and parallel algorithm are demonstrated on synthetic VSP examples designed from a land project.