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The widespread use of maximum Jeffreys’-prior penalized likelihood in binomial-response generalized linear models, and in logistic regression, in particular, are supported by the results of Kosmidis and Firth (Biometrika 108:71–82, 2021. ), who show that the resulting estimates are always finite-valued, even in cases where the maximum likelihood estimates are not, which is a practical issue regardless of the size of the data set. In logistic regression, the implied adjusted score equations are formally bias-reducing in asymptotic frameworks with a fixed number of parameters and appear to deliver a substantial reduction in the persistent bias of the maximum likelihood estimator in high-dimensional settings where the number of parameters grows asymptotically as a proportion of the number of observations. In this work, we develop and present two new variants of iteratively reweighted least squares for estimating generalized linear models with adjusted score equations for mean bias reduction and maximization of the likelihood penalized by a positive power of the Jeffreys-prior penalty, which eliminate the requirement of storing O(n) quantities in memory, and can operate with data sets that exceed computer memory or even hard drive capacity. We achieve that through incremental QR decompositions, which enable IWLS iterations to have access only to data chunks of predetermined size. Both procedures can also be readily adapted to fit generalized linear models when distinct parts of the data is stored across different sites and, due to privacy concerns, cannot be fully transferred across sites. We assess the procedures through a real-data application with millions of observations. [ABSTRACT FROM AUTHOR]

AbstractThe primary choice to summarize a finite collection of random objects is by using measures of central tendency, such as mean and median. In the field of optimal transport, the Wasserstein barycenter corresponds to the Fréchet or geometric mean of a set of probability measures, which is defined as a minimizer of the sum of squared distances to each element in a given set with respect to the Wasserstein distance of order 2. We introduce the Wasserstein median as a robust alternative to the Wasserstein barycenter. The Wasserstein median corresponds to the Fréchet median under the 2-Wasserstein metric. The existence and consistency of the Wasserstein median are first established, along with its robustness property. In addition, we present a general computational pipeline that employs any recognized algorithms for the Wasserstein barycenter in an iterative fashion and demonstrate its convergence. The utility of the Wasserstein median as a robust measure of central tendency is demonstrated using real and simulated data. [ABSTRACT FROM AUTHOR]

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. Also, 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 |${L_{p - 1}}$| norm to enhance sparsity-constraining capability in the transform domain, leveraging high-resolution radon transform techniques. Specifically, an iteratively reweighted least-squares algorithm is employed to obtain the transformed data in the radon domain. Given that the |${L_{p - 1}}$| norm was first applied to the Radon transform in seismic data processing methods, 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 |${L_{p - 1}}$| norm outperforms existing high-resolution radon transform methods with sparsity constraints regarding energy concentration and effectiveness in multiple reflection attenuation. [ABSTRACT FROM AUTHOR]

AbstractMultivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this article a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach. [ABSTRACT FROM AUTHOR]

Image processing on surfaces has gotten increasing interest in recent years, and denoising is a basic problem in image processing. In this paper, we extend non-Lipschitz variational methods for 2D image denoising, including TVp, to image denoising on surfaces. We establish a lower bound for nonzero gradients of the recovered image, implying the advantage of the models in recovering piecewise constant images. A new iteratively reweighted least squares algorithm with the thresholding and support shrinking strategy is proposed. The global convergence of the algorithm is established under the assumption that the object function is a Kurdyka-Łojasiewicz function. Numerical examples are given to show good performance of the algorithm. [ABSTRACT FROM AUTHOR]

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. for this article are available online. [ABSTRACT FROM AUTHOR]

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 L 2 , 1 -norm to eliminate the scaling effects present in the model. Secondly, the counter-scaling effect is eliminated by adding the L 2 -norm to the endmember matrix. Finally, the chunk matrix and the endmember matrix are coupled together, and the matrix is reorganized by adding the L 2 , 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. [ABSTRACT FROM AUTHOR]

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.

This article examines wording effects when positive and negative worded items are included in psychological assessment. Wordings effects have been analyzed in the literature using statistical approaches based on population homogeneity assumptions (i.e. CFA, SEM), commonly adopting the bifactor model to separate trait variance and wording effects. This article presents an alternative approach by explicitly modeling population heterogeneity through a latent profile model, based on the idea that a subset of individuals exhibits wording effects. This kind of mixture model allows simultaneously to classify respondents, substantively characterize the differences in their response profiles, and report respondents' results in a comparable manner. Using the Rosenberg's self-esteem scale data from the LISS Panel (N = 6,762) in three studies, we identify a subgroup of participants who respond differentially according to item-wording and examine the impact of its responses in the estimation of the RSES measurement model, in terms of global and individual fit, under one-factor and bifactor models. The results of these analyses support the interpretation of wording effects in terms of a theoretically-proposed differential pattern of response to positively and negatively worded items, introducing a valuable tool for examining the artifactual or substantive interpretations of such wording effects. [ABSTRACT FROM AUTHOR]

We present a connection between two dynamical systems arising in entirely different contexts: the Iteratively Reweighted Least Squares (IRLS) algorithm used in compressed sensing and sparse recovery to find a minimum ℓ 1 -norm solution in an affine space, and the dynamics of a slime mold (Physarum polycephalum) that finds the shortest path in a maze. We elucidate this connection by presenting a new dynamical system – Meta-Algorithm – and showing that the IRLS algorithms and the slime mold dynamics can both be obtained by specializing it to disjoint sets of variables. Subsequently, and building on work on slime mold dynamics for finding shortest paths, we prove convergence and obtain complexity bounds for the Meta-Algorithm that can be viewed as a "damped" version of the IRLS algorithm. A consequence of this latter result is a slime mold dynamics to solve the undirected transshipment problem that computes a (1 + ε) - approximate solution in time polynomial in the size of the input graph, maximum edge cost, and 1 ε – a problem that was left open by the work of (Bonifaci V et al. [10] Physarum can compute shortest paths. Kyoto, Japan, pp. 233–240). [ABSTRACT FROM AUTHOR]

The main objective of this paper is to discuss selected computational aspects of robust estimation in the linear model with the emphasis on R-estimators. We focus on numerical algorithms and computational efficiency rather than on statistical properties. In addition, we formulate some algorithmic properties that a “good” method for R-estimators is expected to satisfy and show how to satisfy them using the currently available algorithms. We illustrate both good and bad properties of the existing algorithms. We propose two-stage methods to minimize the effect of the bad properties. Finally we justify a challenge for new approaches based on interior-point methods in optimization. [ABSTRACT FROM AUTHOR]

The precise stellar object identification is one of the major research fields in astronomy. In astronomical images, the 2D Gaussian function provides a good approximation of stellar objects. This paper proposes a robust method for the estimation of the 2D Gaussian profiles in astronomical images when the stellar components are overlapped. The proposed method efficiently separates the regions of interest of close components without knowing neither their exact number nor accurate center positions. Therefore, fainter objects can be identified, and outliers can be detected. The proposed method is an iteratively reweighted least squares method where weights are updated in each step using a robust measure of residual error dispersion. Soft thresholding based on robust statistics increases the accuracy of the estimated 2D profile parameters and efficiently solves the problem of outliers. The comparison of the proposed method with the conventional least squares method showed a significant modeling gain for one particular set of contributing factors; the difference of magnitudes of close objects, their center-to-center distance, and the widths of their semiaxes relative to the imaging system resolution.

Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-smooth regularization terms (e.g., total variation). Such regularization methods can be treated as iteratively reweighted least squares problems (IRLS), which are usually solved by the repeated application of a Krylov projection method. This approach gives rise to an inner–outer iterative scheme where the outer iterations update the weights and the inner iterations solve a least squares problem with fixed weights. Recently, flexible or generalized Krylov solvers, which avoid inner–outer iterations by incorporating iteration-dependent weights within a single approximation subspace for the solution, have been devised to efficiently handle IRLS problems. Indeed, substantial computational savings are generally possible by avoiding the repeated application of a traditional Krylov solver. This paper aims to extend the available flexible Krylov algorithms in order to handle a variety of edge-enhancing regularization terms, with computationally convenient adaptive regularization parameter choice. In order to tackle both square and rectangular linear systems, flexible Krylov methods based on the so-called flexible Golub–Kahan decomposition are considered. Some theoretical results are presented (including a convergence proof) and numerical comparisons with other edge-enhancing solvers show that the new methods compute solutions of similar or better quality, with increased speedup. [ABSTRACT FROM AUTHOR]

In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise. [ABSTRACT FROM AUTHOR]

We propose a novel differentiable reformulation of the linearly-constrained ℓ 1 minimization problem, also known as the basis pursuit problem. The reformulation is inspired by the Laplacian paradigm of network theory and leads to a new family of gradient-based methods for the solution of ℓ 1 minimization problems. We analyze the iteration complexity of a natural solution approach to the reformulation, based on a multiplicative weights update scheme, as well as the iteration complexity of an accelerated gradient scheme. The results can be seen as bounds on the complexity of iteratively reweighted least squares (IRLS) type methods of basis pursuit. [ABSTRACT FROM AUTHOR]

Least squares kernel-based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine (ELM) are popular techniques. However, the noise sensitivity is a major bottleneck. To address this issue, a generalized loss function, called ℓ s -loss, is proposed in this paper. With the support of novel loss function, two kernel-based regressors are constructed by replacing the ℓ 2 -loss in LS-SVR and ELM with the proposed ℓ s -loss for better noise robustness. Important properties of ℓ s -loss, including robustness, asymmetry and asymptotic approximation behaviors, are verified theoretically. Moreover, iteratively reweighted least squares are utilized to optimize and interpret the proposed methods from a weighted viewpoint. The convergence of the proposal is proved, and detailed analyses of robustness are given. Experiments on both artificial and benchmark datasets confirm the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

• The proposed method of estimating the bandwidth by using the transient features of the amplitude spectrum can be extended and generalized to other FM signals. • The proposed method based on the IRLS linear fitting can reduce the influence of consecutive outliers and improve the robustness. • The proposed method involving the criterion of continuity to eliminate the isolated outliers is also appropriate to the fitting of other curves with little change trend. To address the issue of robust parameter estimation of hyperbolic frequency modulated (HFM) signals under low signal-to-noise ratios (SNR s), 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 (NRMSE s) 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. [ABSTRACT FROM AUTHOR]

Generalised additive models (GAMs) provide flexible models for a wide array of data sources. In the past, improvements of GAM estimation have focused on the smoothers used in the local scoring algorithm used for estimation, but poor prediction for non-Gaussian data motivates the need for robust estimation of GAMs. In this paper, rank-based estimation, as a robust and efficient alternative to the likelihood-based estimation of GAMs, is proposed. It is shown that rank GAM estimators can be obtained through iteratively reweighted likelihood-based GAM estimation which we call the iterated regularised rank quasi-likelihood (IRRQL). Simulation experiments support the use of rank-based GAM estimation for heavy-tailed or contaminated sources of data. [ABSTRACT FROM AUTHOR]

Uniformly Spaced Antenna Array (USAA) with large radiating elements is characterized with complex feed network as well as high sidelobes level (SLL) leading to interference and power wastage. To solve these problems, research works have been carried out using different methodologies, to synthesize sparse Randomly Spaced Antenna Array (RSAA) to reconstruct the desired radiation pattern using fewer radiating elements and suppressed SLL. In this paper, a deterministic Iteratively Reweighted Least Squares (IRLS) algorithm based on the concept of compressed sensing was used to achieve better sparsity through thinning. The SLL was also suppressed using Convex Technique (CT). The performance of the synthesized array was evaluated in terms of sparsity and SLL. Simulation results showed that it has a higher sparsity of 12 elements with SLL of -39.44dB which are 14.29% and 28.72% improvements, respectively compared to previous research work with 14 elements and SLL of -30.64dB. [ABSTRACT FROM AUTHOR]

In wafer test, the probe mark center shall be close to the pad center as much as possible. But the traditional probe-to-pad alignment (PTPA) process cannot always meet the requirements. So a novel automatic error correction approach was developed in this paper to improve the PTPA process. The approach is based on a classic two dimension rigid motion model and enhanced by integrating an iteratively reweighted least squares algorithm. The singular value decomposition method is also used to seek the solutions. Using the probe mark and pad geometric information, it first best fits the probe mark centers to the targets, then it expands the minimum probe mark to pad edge clearance to the largest. The experiments proved its good feasibility, accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. 10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple observables measured contemporaneously. The proposed approaches allow for the modeling of both auto- and cross-correlations through a vector-autoregressive (VAR) process, where the components of the white-noise input vector are modeled at every time instance either as stochastically independent t-distributed (herein called “stochastic model A”) or as multivariate t-distributed random variables (herein called “stochastic model B”). Both stochastic models are complementary in the sense that the former allows for group-specific degrees of freedom (df) of the t-distributions (thus, sensor-component-specific tail or outlier characteristics) but not for correlations within each white-noise vector, whereas the latter allows for such correlations but not for different dfs. Within the observation equations, nonlinear (differentiable) regression models are generally allowed for. Two different generalized expectation maximization (GEM) algorithms are derived to estimate the regression model parameters jointly with the VAR coefficients, the variance components (in case of stochastic model A) or the cofactor matrix (for stochastic model B), and the df(s). To enable the validation of the fitted VAR model and the selection of the best model order, the multivariate portmanteau test and Akaike’s information criterion are applied. The performance of the algorithms and of the white noise test is evaluated by means of Monte Carlo simulations. Furthermore, the suitability of one of the proposed models and the corresponding GEM algorithm is investigated within a case study involving the multivariate modeling and adjustment of time-series data at four GPS stations in the EUREF Permanent Network (EPN). [ABSTRACT FROM AUTHOR]

This paper presents a method to reduce noise and refine detail features of a scene based on an iteratively reweighted least squares method. The performance of the proposed filter, called the iteratively reweighted least squares filter (IRLSF), was compared with the state-of-the-art filters by checking their ability to recover simulated edge models under various degrees of noise contamination. The results of the simulation comparison show that IRLSF is superior to the other filters in terms of its ability to recover the original edge models. To apply IRLSF to real images of a scene captured by a camera, a procedure composed of corner detection, least squares matching, bilinear resampling, and iteratively reweighted least squares is proposed. The experimental results show that IRLSF produces mean images that are effectively denoised, and that its accuracy is less than one half of grey-level-quantization-unit of test images captured by a commercial camera. [ABSTRACT FROM AUTHOR]

Dynamic treatment regimes (DTRs) aim to formalize personalized medicine by tailoring treatment decisions to individual patient characteristics. G‐estimation for DTR identification targets the parameters of a structural nested mean model, known as the blip function, from which the optimal DTR is derived. Despite its potential, G‐estimation has not seen widespread use in the literature, owing in part to its often complex presentation and implementation, but also due to the necessity for correct specification of the blip. Using a quadratic approximation approach inspired by iteratively reweighted least squares, we derive a quasi‐likelihood function for G‐estimation within the DTR framework, and show how it can be used to form an information criterion for blip model selection. We outline the theoretical properties of this model selection criterion and demonstrate its application in a variety of simulation studies as well as in data from the Sequenced Treatment Alternatives to Relieve Depression study. [ABSTRACT FROM AUTHOR]

Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-smooth regularization terms (e.g., total variation). Such regularization methods can be treated as iteratively reweighted least squares problems (IRLS), which are usually solved by the repeated application of a Krylov projection method. This approach gives rise to an inner–outer iterative scheme where the outer iterations update the weights and the inner iterations solve a least squares problem with fixed weights. Recently, flexible or generalized Krylov solvers, which avoid inner–outer iterations by incorporating iteration-dependent weights within a single approximation subspace for the solution, have been devised to efficiently handle IRLS problems. Indeed, substantial computational savings are generally possible by avoiding the repeated application of a traditional Krylov solver. This paper aims to extend the available flexible Krylov algorithms in order to handle a variety of edge-enhancing regularization terms, with computationally convenient adaptive regularization parameter choice. In order to tackle both square and rectangular linear systems, flexible Krylov methods based on the so-called flexible Golub–Kahan decomposition are considered. Some theoretical results are presented (including a convergence proof) and numerical comparisons with other edge-enhancing solvers show that the new methods compute solutions of similar or better quality, with increased speedup.

As an extension of the widely used ℓr-minimization with 0 < r ≤ 1, a new non-convex weighted ℓr − ℓ1 minimization method is proposed for compressive sensing. The theoretical recovery results based on restricted isometry property and q-ratio constrained minimal singular values are established. An algorithm that integrates the iteratively reweighted least squares algorithm and the difference of convex functions algorithm is given to approximately solve this non-convex problem. Numerical experiments are presented to illustrate our results.

The prediction of the heating and cooling loads of a building is an essential aspect in studies involving the analysis of energy consumption in buildings. An accurate estimation of heating and cooling load leads to better management of energy related tasks and progressing towards an energy efficient building. With increasing global energy demands and buildings being major energy consuming entities, there is renewed interest in studying the energy performance of buildings. Alternative technologies like Artificial Intelligence (AI) techniques are being widely used in energy studies involving buildings. This paper presents a review of research in the area of forecasting the heating and cooling load of buildings using AI techniques. The results discussed in this paper demonstrate the use of AI techniques in the estimation of the thermal loads of buildings. An accurate prediction of the heating and cooling loads of buildings is necessary for forecasting the energy expenditure in buildings. It can also help in the design and construction of energy efficient buildings. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to solve the problem of multicollinearity that affects the estimation of logistic regression model by introducing first-order approximated jackknifed ridge logistic estimator which is more efficient than the first-order approximated maximum likelihood estimator and has smaller variance than the first-order approximated jackknife ridge logistic estimator. Comparisons of the first-order approximated jackknifed ridge logistic estimator to the first-order approximated maximum likelihood, first-order approximated ridge, first-order approximated r-k class and principal components logistic regression estimators according to the bias, covariance and mean square error criteria are done. Three different estimators for the ridge parameter are also proposed. A real data set is used to see the performance of the first-order approximated jackknifed ridge logistic estimator over the first-order approximated maximum likelihood, first-order approximated ridge logistic, first-order approximated r-k class and first-order approximated principal components logistic regression estimators. Finally, two simulation studies are conducted in order to show the performance of the first-order approximated jackknife ridge logistic estimator. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new estimation method for binary quantile regression and variable selection which can be implemented by an iteratively reweighted least square approach. In contrast to existing approaches, this method is computationally simple, guaranteed to converge to a unique solution and implemented with standard software packages. We demonstrate our methods using Monte-Carlo experiments and then we apply the proposed method to the widely used work trip mode choice dataset. The results indicate that the proposed estimators work well in finite samples. [ABSTRACT FROM AUTHOR]

W artykule przedstawiono empiryczne porównanie trzech dobrze znanych M - estymatorów (Huber’a, Tukey’a oraz Hampel’a) jak również kilku nowych. Nowe estymatory motywowane były funkcjami wagowymi wykorzystywanymi w teorii wielomianów ortogonalnych, estymacji jądrowej oraz jeden motywowany przez funkcję gęstości „półokręgu” Wigner’a. Każdy z estymatorów został użyty do wykrywania obserwacji odstających w skażonych zbiorach danych. Obliczenia wykonano za pomocą „reważonej” metody najmniejszych kwadratów. Ze względu na fakt, iż wariancja resztowa (używana w konstrukcji macierzy kowariancyjnych) nie jest odpornym estymatorem skali, w testach wykorzystano również odporne miary takie jak: rozstęp ćwiartkowy oraz znormalizowane odchylenie medianowe. Testy wykonano na prostej sieci niwelacyjnej w dużej ilości wariantów ukazujących dobre i złe strony M - estymacji. Nowe estymatory zostały wyposażone w teoretyczne stałe odcinania zapewniające 95% efektywność względem standaryzowanego rozkładu normalnego. Kwestia rozwijania metod bazujących na stałych odcinania pochodzących z danych została również pokrótce poruszona.

We propose a new iteratively reweighted least squares (IRLS) algorithm for the recovery of a matrix X ε Cd1xd2 of rank r min(1, d2) from incomplete linear observations, solving a sequence of low complexity linear problems. The easily implementable algorithm, which we call harmonic mean iteratively reweighted least squares (HM-IRLS), optimizes a non-convex Schatten-p quasi-norm penalization to promote low-rankness and carries three major strengths, in particular for the matrix completion setting. First, we observe a remarkable global convergence behavior of the algorithm's iterates to the low-rank matrix for relevant, interesting cases, for which any other state-of-the-art optimization approach fails the recovery. Secondly, HM-IRLS exhibits an empirical recovery probability close to 1 even for a number of measurements very close to the theoretical lower bound r(d1+d2-r), i.e., already for significantly fewer linear observations than any other tractable approach in the literature. Thirdly, HM-IRLS exhibits a locally superlinear rate of convergence (of order 2 - p) if the linear observations fulfill a suitable null space property. While for the first two properties we have so far only strong empirical evidence, we prove the third property as our main theoretical result. [ABSTRACT FROM AUTHOR]

We introduce a convex approach for mixed linear regression over d features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $$\mathbb {R}^{d}$$ for each data point. These estimates can then be clustered using, for example, k -means. For problems with two or more mixture classes, we prove that the convex program exactly recovers all of the mixture components in the noiseless setting under technical conditions that include a well-separation assumption on the data. Under these assumptions, recovery is possible if each class has at least d -independent measurements. We also explore an iteratively reweighted least squares implementation of this method on real and synthetic data. [ABSTRACT FROM AUTHOR]

This work presents a fast and non-convex algorithm for robust subspace recovery. The datasets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space and a possibly large portion of outliers that do not lie nearby this subspace. The proposed algorithm, which we refer to as fast median subspace (FMS), is designed to robustly determine the underlying subspace of such datasets, while having lower computational complexity than existing accurate methods. We prove convergence of the FMS iterates to a stationary point. Further, under two special models of data, FMS converges to a point which is near to the global minimum with overwhelming probability. Under these models, we show that the iteration complexity is globally sublinear and locally r-linear. For one of the models, these results hold for any fixed fraction of outliers (< 1). Numerical experiments on synthetic and real data demonstrate its competitive speed and accuracy. [ABSTRACT FROM AUTHOR]

In structural equation models, outliers could result in inaccurate parameter estimates and misleading fit statistics when using traditional methods. To robustly estimate structural equation models, iteratively reweighted least squares (IRLS; Yuan & Bentler, 2000) has been proposed, but not thoroughly examined. We explore the large-sample properties of IRLS and its effect on parameter recovery, model fit, and aberrant data identification. A parametric bootstrap technique is proposed to determine the tuning parameters of IRLS, which results in improved Type I error rates in aberrant data identification, for data sets generated from homogenous populations. Scenarios concerning (a) simulated data, (b) contaminated data, and (c) a real data set are studied. Results indicate good parameter recovery, model fit, and aberrant data identification when noisy observations are drawn from a real data set, but lackluster parameter recovery and identification of aberrant data when the noise is parametrically structured. Practical implications and further research are discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust and efficient relative rotation averaging in the context of large-scale Structure from Motion. Relative rotation averaging finds global or absolute rotations for a set of cameras from a set of observed relative rotations between pairs of cameras. We propose a generalized framework of relative rotation averaging that can use different robust loss functions and jointly optimizes for all the unknown camera rotations. Our method uses a quasi-Newton optimization which results in an efficient iteratively reweighted least squares (IRLS) formulation that works in the Lie algebra of the 3D rotation group. We demonstrate the performance of our approach on a number of large-scale data sets. We show that our method outperforms existing methods in the literature both in terms of speed and accuracy. [ABSTRACT FROM PUBLISHER]

In this paper, data-driven adaptive fractional order proportional integral (AFOPI) control is presented for permanent magnet synchronous motor (PMSM) servo system perturbed by measurement noise and data dropouts. The proposed method directly exploits the closed-loop process data for the AFOPI controller design under unknown noise distribution and data missing probability. Firstly, the proposed method constructs the AFOPI controller tuning problem as a parameter identification problem using the modified l p norm virtual reference feedback tuning (VRFT). Then, iteratively reweighted least squares is integrated into the l p norm VRFT to give a consistent compensation solution for the AFOPI controller. The measurement noise and data dropouts are estimated and eliminated by feedback compensation periodically, so that the AFOPI controller is updated online to accommodate the time-varying operating conditions. Moreover, the convergence and stability are guaranteed by mathematical analysis. Finally, the effectiveness of the proposed method is demonstrated both on simulations and experiments implemented on a practical PMSM servo system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a linear regression time series model of possibly outlier-afflicted observations and autocorrelated random deviations. This colored noise is represented by a covariance-stationary autoregressive (AR) process, in which the independent error components follow a scaled (Student’s) t-distribution. This error model allows for the stochastic modeling of multiple outliers and for an adaptive robust maximum likelihood (ML) estimation of the unknown regression and AR coefficients, the scale parameter, and the degree of freedom of the t-distribution. This approach is meant to be an extension of known estimators, which tend to focus only on the regression model, or on the AR error model, or on normally distributed errors. For the purpose of ML estimation, we derive an expectation conditional maximization either algorithm, which leads to an easy-to-implement version of iteratively reweighted least squares. The estimation performance of the algorithm is evaluated via Monte Carlo simulations for a Fourier as well as a spline model in connection with AR colored noise models of different orders and with three different sampling distributions generating the white noise components. We apply the algorithm to a vibration dataset recorded by a high-accuracy, single-axis accelerometer, focusing on the evaluation of the estimated AR colored noise model. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of the reconstructed data, we propose three algorithms based on iteratively reweighted least squares. We first develop an exact reweighted algorithm. Next, an approximate version is developed based on eigenpair approximation when the algorithm is near convergent. Finally, the approximate version is extended based on stochastic singular value decomposition. We provide convergence analyses, and compare their performance against benchmark algorithms in the literature. The computational experiment shows that the proposed algorithms consistently perform the best and the scalability is improved as we use eigenpair approximation and stochastic singular value decomposition. [ABSTRACT FROM AUTHOR]

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite precision arithmetic) the exact solution after a finite number of iterations. It is thus well suited for many types of inverse problems. On the other hand, the method requires the computation of the gradient. Here difficulty can arise, since the functional of interest to the given inverse problem may not be differentiable. In this paper, we review two approaches to deal with this situation: iteratively reweighted least squares and convolution smoothing. We apply the methods to a more generalized, two parameter penalty functional. We show advantages of the proposed algorithms using examples from a geotomographical application and for synthetically constructed multi-scale reconstruction and regularization parameter estimation. [ABSTRACT FROM AUTHOR]