Power Divergence Research Articles

Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence

In this paper, we propose a method for optimizing the parameter values in iterative reconstruction algorithms that include adjustable parameters in order to optimize the reconstruction performance. Specifically, we focus on the power divergence-based expectation-maximization algorithm, which includes two power indices as adjustable parameters. Through numerical and physical experiments, we demonstrate that optimizing the evaluation function based on the extended power-divergence and weighted extended power-divergence measures yields high-quality image reconstruction. Notably, the optimal parameter values derived from the proposed method produce reconstruction results comparable to those obtained using the true image, even when using distance functions based on differences between forward projection data and measured projection data, as verified by numerical experiments. These results suggest that the proposed method effectively improves reconstruction quality without the need for machine-learning techniques in parameter selection. Our findings also indicate that this approach is useful for enhancing the performance of iterative reconstruction algorithms, especially in medical imaging, where high-accuracy reconstruction under noisy conditions is required.

The Most Powerful Member of the Power-Divergence Family for the Independence Model in Contingency Tables

The family of power-divergence (PD) test statistic contains many well-known test statistics used in the analysis of the contingency tables under the independence model. In this work, we compare the various test statistics for the independence model. The type-I and type-II errors of the test statistics are obtained and compared via simulation study considering the different degree of freedoms and sample sizes. According to the simulation results, we recommend the PD(0.4) test statistic for the small sample size based on its power and type-I error rates. Two applications are given to demonstrate the usefulness of the PD(0.4) test statistic over the chi-square test statistic {contingency tables}.

Atlantic Blue Marlin, Boops, Chironex Fleckeri, and General Practitioner – Sick Person Optimization Algorithms mization Algorithms

In this paper Atlantic blue marlin (ABM) optimization algorithm, Boops optimization (BO) algorithm, Chironex fleckeri Search Optimization (CSO) algorithm, General practitioner -Sick person (PS) optimization algorithm are applied for solving factual power loss reduction problem. The regular actions of Atlantic blue marlin are emulated to design the Atlantic blue marlin (ABM) optimization algorithm and populace in the examination space is capriciously stimulated. Boops optimization (BO) algorithm is designed by imitating the actions of Boops. Boops possess the obliging stalking physiognomies. As a cluster they stalk the quarry by forming the key and subordinate clusters CSO is based on the drive and search behaviour of Chironex fleckeri. Obviously Chironex fleckeri will exploit the limbs to paralyze the pray by injecting the rancour. In real time world a General practitioner will treat the Sick person with various procedures and it has been imitated to model the Projected PS algorithm. In general people will be inoculated and then with respect to disorder and disease- medical treatment will be given by medicines. Inoculation, medicine and operation are the procedures have been considered as the phases of the projected PS algorithm. Atlantic blue marlin (ABM) optimization algorithm, Boops optimization (BO) algorithm, Chironex fleckeri Search Optimization (CSO) algorithm, General practitioner -Sick person (PS) optimization algorithm validated in IEEE 57, 300 systems and 220 KV network. Factual power loss lessening, power divergence restraining, and power constancy index amplification has been attained.

Iterative Tomographic Image Reconstruction Algorithm Based on Extended Power Divergence by Dynamic Parameter Tuning.

Computed tomography (CT) imaging plays a crucial role in various medical applications, but noise in projection data can significantly degrade image quality and hinder diagnosis accuracy. Iterative algorithms for tomographic image reconstruction outperform transform methods, especially in scenarios with severe noise in projections. In this paper, we propose a method to dynamically adjust two parameters included in the iterative rules during the reconstruction process. The algorithm, named the parameter-extended expectation-maximization based on power divergence (PXEM), aims to minimize the weighted extended power divergence between the measured and forward projections at each iteration. Our numerical and physical experiments showed that PXEM surpassed conventional methods such as maximum-likelihood expectation-maximization (MLEM), particularly in noisy scenarios. PXEM combines the noise suppression capabilities of power divergence-based expectation-maximization with static parameters at every iteration and the edge preservation properties of MLEM. The experimental results demonstrated significant improvements in image quality in metrics such as the structural similarity index measure and peak signal-to-noise ratio. PXEM improves CT image reconstruction quality under high noise conditions through enhanced optimization techniques.

Robust inference methods for meta-analysis involving influential outlying studies.

Meta-analysis is an essential tool to comprehensively synthesize and quantitatively evaluate results of multiple clinical studies in evidence-based medicine. In many meta-analyses, the characteristics of some studies might markedly differ from those of the others, and these outlying studies can generate biases and potentially yield misleading results. In this article, we provide effective robust statistical inference methods using generalized likelihoods based on the density power divergence. The robust inference methods are designed to adjust the influences of outliers through the use of modified estimating equations based on a robust criterion, even when multiple and serious influential outliers are present. We provide the robust estimators, statistical tests, and confidence intervals via the generalized likelihoods for the fixed-effect and random-effects models of meta-analysis. We also assess the contribution rates of individual studies to the robust overall estimators that indicate how the influences of outlying studies are adjusted. Through simulations and applications to two recently published systematic reviews, we demonstrate that the overall conclusions and interpretations of meta-analyses can be markedly changed if the robust inference methods are applied and that only the conventional inference methods might produce misleading evidence. These methods would be recommended to be used at least as a sensitivity analysis method in the practice of meta-analysis. We have also developed an R package, robustmeta, that implements the robust inference methods.

An index for measuring degree of departure from symmetry for ordinal square contingency tables

AbstractFor the analysis of square contingency tables with the same row and column ordinal classifications, this study proposes an index for measuring the degree of departure from the symmetry model using new cumulative probabilities. The proposed index is constructed based on the Cressie and Read’s power divergence, or the weighted average of the Patil and Taillie’s diversity index. This study derives a plug-in estimator of the proposed index and an approximate confidence interval for the proposed index. The estimator of the proposed index is expected to reduce the bias more than the estimator of the existing index, even when the sample size is not large. The proposed index is identical to the existing index under the conditional symmetry model. Therefore, assuming the probability structure in which the conditional symmetry model holds, the performances of plug-in estimators of the proposed and existing indexes can be simply compared. Through numerical examples and real data analysis, the usefulness of the proposed index compared to the existing index is demonstrated.

Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory

In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the first-principle calculation of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD using the formulation of large momentum effective theory. We provide appropriate RI′-type conditions that address the power and logarithmic divergences, as well as the mixing among staple operators of different Dirac structures, using a number of different possible projectors. A variant of RI′, including calculations of rectangular Wilson loops, which cancel the pinch-pole singularities of the staple operators at infinite length and reduce residual power divergences, is also employed. We calculate at one-loop order the conversion matrix, which relates the quasi-TMDPDFs in the RI′-type schemes to the reference scheme MS¯ for arbitrary values of the renormalization momentum scale and of the dimensions of the staple. Published by the American Physical Society 2024

Parton distributions from boosted fields in the Coulomb gauge

We propose a new method to calculate parton distribution functions (PDFs) from lattice correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used gauge-invariant Wilson-line operators, these correlations greatly simplify the renormalization thanks to the absence of linear power divergence. Additionally, they enable access to larger off-axis momenta under preserved 3D rotational symmetry, as well as enhanced long-range precision that facilitates the Fourier transform. We verify the factorization formula that relates this new observable to the quark PDF at one-loop order in perturbation theory. Moreover, through a lattice calculation of the pion valence quark PDF, we demonstrate the aforementioned advantage and features of the Coulomb gauge correlation and show that it yields consistent results with the gauge-invariant method. This opens the door to a more efficient way to calculate parton physics on the lattice. Published by the American Physical Society 2024

Robust and efficient estimation in ordinal response models using the density power divergence

In real life, we frequently encounter ordinal variables depending upon independent covariates. The latent linear regression model is useful for modelling such data. One can find the model's parameters' maximum likelihood estimate (MLE). Though noted for its optimum properties, a small proportion of outliers may destabilize the MLE. This paper uses the minimum density power divergence estimate (MDPDE) as a robust alternative. The roles of different link functions are analysed in this context. We discuss their asymptotic properties in this setup. Unlike the MLE, the MDPDEs are robust for– lower values of the gross error sensitivity, and very high breakdown point. Also, the slope’s MDPDEs never implode. In simulation studies for pure data, MDPDEs perform almost as good as the MLE. However, the MDPDEs outperform the MLE in data contamination. Moreover, MDPDEs are very competitive with the other robust alternatives. Finally, this article is wrapped up with a real-data example.

Minimum density power divergence estimation for the generalized exponential distribution

Statistical modeling of rainfall data is an active research area in agro-meteorology. The most common models fitted to such datasets are exponential, gamma, log-normal, and Weibull distributions. As an alternative to some of these models, the generalized exponential (GE) distribution was proposed by Gupta and Kundu (2001a). Rainfall (specifically for short periods) datasets often include outliers, and thus, a proper robust parameter estimation procedure is necessary. Here, we use the popular minimum density power divergence estimation (MDPDE) procedure developed by Basu et al. (1998) for estimating the GE parameters. We derive the analytical expressions for the estimating equations and asymptotic distributions. We analytically compare MDPDE with maximum likelihood estimation in terms of robustness, through an influence function analysis. Besides, we study the asymptotic relative efficiency of MDPDE analytically for different parameter settings. We apply the proposed technique to some simulated datasets and two rainfall datasets from Texas, United States. The results indicate superior performance of MDPDE compared to the other existing estimation techniques in most of the scenarios.

Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals

AbstractRecently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal‐Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one‐shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence‐based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald‐type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi‐criteria‐based optimal design. Population‐based heuristic algorithm nondominated sorting‐based multiobjective Genetic algorithm is exploited to solve this optimization problem.

From lab to life: Decoding the predictive power of present bias on adolescent self-control behaviors

This research examines the external validity of laboratory-measured preferences, specifically present bias, in predicting real-life adolescent behaviors. Rooted in the broader debate in experimental economics, we investigate the transferability of lab results, especially in relation to self-control manifestations. Engaging approximately 200 adolescents aged 14 to 19, we assessed present bias through standard intertemporal monetary decisions in a lab setting. Our findings indicate a divergence in the predictive power of laboratory observations. In health-related behaviors, significant correlations were observed between laboratory measurements and BMI, but not with exercise frequency. Meanwhile, academic behaviors such as attendance in self-study courses and late homework submissions were strongly associated. This study sheds light on the nuanced applicability of laboratory-derived preferences in real-world contexts, emphasizing the need for domain-specific considerations.

Poisson and Gaussian approximations of the power divergence family of statistics

Poisson and Gaussian approximations of the power divergence family of statistics

Robust and adaptive functional logistic regression

A novel family of robust estimators for the functional logistic regression model is introduced and studied. The estimators are based on the concept of density power divergence between densities and may be formed with any combination of lower rank approximations and penalties, as the need arises. Uniform convergence and high rates of convergence with respect to the commonly used prediction error are established under general assumptions. Importantly, these assumptions permit random tuning parameters thereby allowing for the robustness of the estimators to adapt to the data. This leads to estimators with high efficiency in clean data and a high degree of resistance towards atypical observations. The highly competitive practical performance of the proposed family of estimators is illustrated on a simulation study and a real data example involving gait analysis and which includes atypical observations.

Robust small area estimation for unit level model with density power divergence.

Unit level model is one of the classical models in small area estimation, which plays an important role with unit information data. Empirical Bayesian(EB) estimation, as the optimal estimation under normal assumption, is the most commonly used parameter estimation method in unit level model. However, this kind of method is sensitive to outliers, and EB estimation will lead to considerable inflation of the mean square error(MSE) when there are outliers in the responses yij. In this study, we propose a robust estimation method for the unit-level model with outliers based on the minimum density power divergence. Firstly, by introducing the minimum density power divergence function, we give the estimation equation of the parameters of the unit level model, and obtain the asymptotic distribution of the robust parameters. Considering the existence of tuning parameters in the robust estimator, an optimal parameter selection algorithm is proposed. Secondly, empirical Bayesian predictors of unit and area mean in finite populations are given, and the MSE of the proposed robust estimators of small area means is given by bootstrap method. Finally, we verify the superior performance of our proposed method through simulation data and real data. Through comparison, our proposed method can can solve the outlier situation better.

Robust estimation for general integer-valued autoregressive models based on the exponential-polynomial divergence

In this study, we develop a robust estimator for integer-valued one-parameter exponential family autoregressive models, named general integer-valued autoregressive models. This model accommodates a broad class of integer-valued time series models. In particular, we propose a robust estimation method that minimizes the exponential-polynomial divergence (EPD) belonging to the Brègman divergence family. EPD subsumes the density power divergence (DPD), which has been extensively studied by many authors for the past decades. Under regularity conditions, the minimum EPD estimator (MEPDE) is shown to be consistent and asymptotically normal. Comparing the performance of MEPDE with the minimum DPD estimator, we substantiate the validity of MEPDE through a simulation study and real data analysis.

Robust Clustering with Normal Mixture Models: A Pseudo [formula omitted]-Likelihood Approach

As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust alternative to the ordinary likelihood approach for this estimation problem is proposed which performs simultaneous estimation and data clustering and leads to subsequent anomaly detection. To invoke robustness, the methodology based on the minimization of the density power divergence (or alternatively, the maximization of the β-likelihood) is utilized under suitable constraints. An iteratively reweighted least squares approach has been followed in order to compute the proposed estimators for the component means (or equivalently cluster centers) and component dispersion matrices which leads to simultaneous data clustering. Some exploratory techniques are also suggested for anomaly detection, a problem of great importance in the domain of statistics and machine learning. The proposed method is validated with simulation studies under different set-ups; it performs competitively or better compared to the popular existing methods like K-medoids, TCLUST, trimmed K-means and MCLUST, especially when the mixture components (i.e., the clusters) share regions with significant overlap or outlying clusters exist with small but non-negligible weights (particularly in higher dimensions). Two real datasets are also used to illustrate the performance of the newly proposed method in comparison with others along with an application in image processing. The proposed method detects the clusters with lower misclassification rates and successfully points out the outlying (anomalous) observations from these datasets.

Analysis of one-shot device testing data under logistic-exponential lifetime distribution with an application to SEER gallbladder cancer data

In the literature, the reliability analysis of one-shot devices is found under accelerated life testing in the presence of various stress factors. The application of one-shot devices can be extended to the bio-medical field, where we often evidence that inflicted with a certain disease, survival time would be under different stress factors like environmental stress, co-morbidity, the severity of disease etc. This work is concerned with a one-shot device data analysis and applies it to SEER gallbladder cancer data. The two-parameter logistic-exponential distribution is applied as a lifetime distribution. For robust parameter estimation, weighted minimum density power divergence estimators (WMDPDE) is obtained along with the conventional maximum likelihood estimators (MLE). The asymptotic behaviour of the WMDPDE and the robust test statistic based on the density power divergence measure are also studied. The performances of estimators are evaluated through extensive simulation experiments. Later those developments are applied to SEER gallbladder cancer data. Citing the importance of knowing exactly when to inspect the one-shot devices put to the test, a search for optimum inspection times is performed. This optimization is designed to minimize a defined cost function which strikes a trade-off between the precision of the estimation and experimental cost. The search is accomplished through the population-based heuristic optimization method genetic algorithm.

Robust adaptive variable selection in ultra-high dimensional linear regression models

We consider the problem of simultaneous variable selection and parameter estimation in an ultra-high dimensional linear regression model. The adaptive penalty functions are used in this regard to achieve the oracle variable selection property with simpler assumptions and lesser computational burden. Noting the non-robust nature of the usual adaptive procedures (e.g. adaptive LASSO) based on the squared error loss function against data contamination, quite frequent with modern large-scale data sets (e.g. noisy gene expression data, spectra and spectral data), in this paper, we present a new adaptive regularization procedure using a robust loss function based on the density power divergence (DPD) measure under a general class of error distributions. We theoretically prove that the proposed adaptive DPD-LASSO estimator of the regression coefficients is highly robust, consistent, asymptotically normal and leads to robust oracle-consistent variable selection under easily verifiable assumptions. Numerical illustrations are provided for the mostly used normal and heavy-tailed error densities. Finally, the proposal is applied to analyse an interesting spectral dataset, in the field of chemometrics, regarding the electron-probe X-ray microanalysis (EPXMA) of archaeological glass vessels from the 16th and 17th centuries.

Density Power Divergence Estimator for General Integer-Valued Time Series with Exogenous Covariates

Density Power Divergence Estimator for General Integer-Valued Time Series with Exogenous Covariates