Kernel Estimation Method Research Articles

Enhanced QSVM with elitist non‐dominated sorting genetic optimisation algorithm for breast cancer diagnosis

AbstractMachine learning has emerged as a promising method for predicting breast cancer using quantum computation techniques. Quantum machine learning algorithms, such as quantum support vector machines (QSVMs), are demonstrating superior efficiency and economy in tackling complex problems compared to traditional machine learning methods. When compared with classical support vector machine, the quantum machine produces remarkably accurate results. The suggested quantum SVM model in this study effectively resolved the binary classification problem for diagnosing malignant breast cancer. This work introduces an enhanced approach to breast cancer diagnosis by integrating QSVM with elitist non‐dominated sorting genetic optimization (ENSGA), leveraging the strengths of both techniques to achieve more accurate and efficient classification results. ENSGA plays a crucial role in optimising QSVM parameters, ensuring that the model attains the best possible classification accuracy while considering multiple objectives simultaneously. Moreover, the quantum kernel estimation method demonstrated exceptional performance by achieving high accuracy within an impressive execution time of 0.14 in the IBM QSVM simulator. The seamless integration of quantum computation techniques with optimisation strategies such as ENSGA highlights the potential of quantum machine learning in revolutionising the field of healthcare, particularly in the domain of breast cancer diagnosis.

Evaluation of the Performance of Kernel Non-parametric Regression and Ordinary Least Squares Regression

Researchers need to understand the differences between parametric and nonparametric regression models and how they work with available information about the relationship between response and explanatory variables and the distribution of random errors. This paper proposes a new nonparametric regression function for the kernel and employs it with the Nadaraya-Watson kernel estimator method and the Gaussian kernel function. The proposed kernel function (AMS) is then compared to the Gaussian kernel and the traditional parametric method, the ordinary least squares method (OLS). The objective of this study is to examine the effectiveness of nonparametric regression and identify the best-performing model when employing the Nadaraya-Watson kernel estimator method with the proposed kernel function (AMS), the Gaussian kernel, and the ordinary least squares (OLS) method. Additionally, it determines which method yields the most accurate results when analyzing nonparametric regression models and provides valuable insights for practitioners looking to apply these techniques in real-world scenarios. However, criteria such as generalized cross-validation (GCV), mean square error (MSE), and coefficient determination are used to select the most efficient estimated model. Simulated data was used to evaluate the performance and efficiency of estimators using different sample sizes. The results favorable the simulation illustrate that the Nadaraya-Watson kernel estimator using the proposed kernel function (AMS) exhibited favorable and superior performance compared to other methods. The coefficients of determination indicate that the highest values attained were 98%, 99%, and 99%. The proposed function (AMS) yielded the lowest MSE and GCV values across all samples. Therefore, this suggests that the model can generate precise predictions and enhance the performance of the focused data.

Automatic beam optimization method for scanning electron microscopy based on electron beam Kernel estimation

Scanning Electron Microscopy (SEM) leverages electron wavelengths for nanoscale imaging, necessitating precise parameter adjustments like focus, stigmator, and aperture alignment. However, traditional methods depend on skilled personnel and are time-consuming. Existing auto-focus and auto-stigmation techniques face challenges due to interdependent nature of these parameters and sample diversity. We propose a beam kernel estimation method to independently optimize SEM parameters, regardless of sample variations. Our approach untangles parameter influences, enabling concurrent optimization of focus, stigmator x, y, and aperture-align x, y. It achieves robust performance, with average errors of 1.00 μm for focus, 0.30% for stigmators, and 0.79% for aperture alignment, surpassing sharpness-based approach with its average errors of 6.42 μm for focus and 2.32% for stigmators and lacking in aperture-align capabilities. Our approach addresses SEM parameter interplay via blind deconvolution, facilitating rapid and automated optimization, thereby enhancing precision, efficiency, and applicability across scientific and industrial domains.

Single Image Integrated Deblurring Algorithm in Non-Uniform Environment

Motion blurriness in an image caused by camera shake during exposure is unavoidable. It could lead to information loss and degradation in the image quality. Therefore, many researchers are dedicated to developing image deblurring techniques to recover clear images from blurred images. During the deblurring process, structural edges in images play a vital part in estimating the blur kernels. For images with rich textures, fine-scale edges become more apparent. This will cause vagueness in the image’s structural edges and affect the accuracy of the kernel estimation process. In this study, we propose a single-image motion deblurring by kernel estimation method combined with L0-Regularized Intensity and Gradient Prior, and enhanced Scale Aware Smoothing methods. Two types of non-uniform datasets are used, which are real and synthetic. While synthetic datasets are utilized to assess the consistency in performance across real and synthetic images, real datasets are used to portray the level of detail and variation of actual blurred images. The dataset is divided into five categories (people, nature, manmade, text, and night light). Two image quality metrics were selected: full-reference assessment, including learned perceptual image patch similarity (LPIPS), peak signal-to-noise ratio (PSNR), and structural similarity indexing method (SSIM) for synthetic datasets, and no-reference assessments, including blind/reference-less image spatial quality (BRISQUE), natural image quality evaluator (NIQE) and perception-based image quality evaluator (PIQE) for real datasets. According to the findings, the fusion method performs best in the text category, followed by manmade and in nature, then night light and poor in people. The proposed method not only removes fine-scale edges and preserves the boundary sharpness, but also improved the estimated blur kernel.

Optimal smoothing parameter selection in single-index model derivative estimation

. Single-index model is one of the most popular semiparametric models in applied econometrics. Estimation of the derivative function is often of crucial importance, as studying “marginal effects” serves as a cornerstone of microeconomics. A prerequisite for the successful application of nonparametric/semiparametric kernel estimation methods is to select smoothing parameters properly to balance the estimation squared bias and variance. Henderson et al. (2015) propose a novel method for selecting the smoothing parameters optimally for derivative function estimation. However, their method suffers from the “curse of diemnsionality” problem in a multivariate nonparametric regression model. In this article, we extend the work of Henderson et al. (2015) to estimation of the derivative function of a single-index model. Specifically, we propose a data-driven method to select smoothing parameters optimally for single-index model derivative function estimation. We also derive the asymptotic distribution of the resulting local linear estimator of the derivative function. Both simulations and empirical applications show that the proposed method works well in practice.

Insight into soft chemometric computational learning for modelling oily-wastewater separation efficiency and permeate flux of polypyrrole-decorated ceramic-polymeric membranes

Reliable modeling of oily wastewater emphasizes the paramount importance of sustainable and health-conscious wastewater management practices, which directly aligns with the Sustainable Development Goals (SDG) while also meeting the guidelines of the World Health Organization (WHO). This research explores the efficiency of utilizing polypyrrole-coated ceramic-polymeric membranes to model oily wastewater separation efficiency (SE) and permeate flux (PF) based on established experimental procedures. In this area, computational simulation still needs to be explored. The study developed predictive regression models, including robust linear regression (RLR), stepwise linear regression (SWR) and linear regression (LR) for the ceramic-polymeric porous membrane, aiming to interpret its complex performance across diverse conditions and, thus, develop its utility in oily wastewater treatment applications. Subsequently, a novel, simple average ensemble paradigm was explored to reduce errors and improve prediction skills. Prior to the development of the model, stability and reliability analysis of the data was conducted based on Philip Perron tests with the Bartlett kernel estimation method. The accuracy of the SE exhibited a high consistency, averaging 99.92% with minimal variability (standard deviation of 0.026%), potentially simplifying its prediction compared to PF. The modes were validated and evaluated using metrics like MAE, RMSE, Speed, and MSE, in addition to 2D graphical and cumulative distribution function graphs. The LR model emerged as the best with the lowest RMSE =0.21951, indicating superior prediction accuracy, followed closely by RLR with an RMSE = 0.22359. SWLR, while having the highest RMSE = 0.34573, marked its dominance in prediction speed with 110 observations per second. Notably, the RLR model justified a reduction in error by approximately 35.29% compared to SWLR. Moreover, the training efficiency of the LR model exceeded, demanding a mere 2.9252 s, marking a reduction of about 32.54% compared to SWLR. The improved simple ensemble learning proved merit over the three models regarding error accuracy. This study emphasizes the essential role of soft-computing learning in optimizing the design and performance of ceramic-polymeric membranes.

Unfolded deep kernel estimation-attention UNet-based retinal image segmentation

Retinal vessel segmentation is a critical process in the automated inquiry of fundus images to screen and diagnose diabetic retinopathy. It is a widespread complication of diabetes that causes sudden vision loss. Automated retinal vessel segmentation can help to detect these changes more accurately and quickly than manual evaluation by an ophthalmologist. The proposed approach aims to precisely segregate blood vessels in retinal images while shortening the complication and computational value of the segmentation procedure. This can help to improve the accuracy and reliability of retinal image analysis and assist in diagnosing various eye diseases. Attention U-Net is an essential architecture in retinal image segmentation in diabetic retinopathy that obtained promising results in improving the segmentation accuracy especially in the situation where the training data and ground truth are limited. This approach involves U-Net with an attention mechanism to mainly focus on applicable regions of the input image along with the unfolded deep kernel estimation (UDKE) method to enhance the effective performance of semantic segmentation models. Extensive experiments were carried out on STARE, DRIVE, and CHASE_DB datasets, and the proposed method achieved good performance compared to existing methods.

A Method for Predicting the Macro Environment of Enterprise Management Based on Linear Models

Aiming at interval data, this paper combines the additive model on the basis of the partial linear model and introduces the sliding window model, and proposes an additive linear model based on the midpoint and range of each window of the sliding window mode. This model combines the advantages of semi-parametric regression and sliding window model, and avoids the dimensional disaster. In addition, the model determines the number of phases of the sliding window according to the cross-entropy criterion, and gives an iterative algorithm for estimating model parameters and unknown function based on the least square method and kernel estimation method. In the empirical analysis, several financial indicators are introduced to predict the law of macroeconomic development. The results show that the improved model is better than the traditional regression model.

Kernel adaptive memory network for blind video super-resolution

Although recent video super-resolution (VSR) works show remarkable restoration performance for low-resolution (LR) video downscaled by a fixed known blur kernel, blind VSR suffers from severe performance degradation when the blur kernel is unknown. To alleviate this problem, blur kernel estimation methods have been proposed for VSR. However, existing VSR models must be trained separately with each LR dataset downscaled using all possible blur kernels. This is a time-consuming and memory-consuming task. To address these issues, we propose a kernel adaptive memory network for a blind VSR (KeMoVSR). The KeMoVSR mainly consists of a dual regression blur kernel estimator and a kernel adaptive VSR. The proposed blur kernel estimator predicts the parametric and non-parametric blur kernels by exploiting the blur kernel variation. Due to the blur kernel variation, the proposed kernel estimator can consider the temporal consistency of the blur kernel variation in adjacent frames, which leads to accurate blur kernel estimation in LR video frames. The proposed kernel adaptive VSR modulates the VSR weights according to the shape of the blur kernel by weight modulation layers. By integrating the proposed methods based on the memory network, we propose the KeMoVSR, which performs VSR by adaptively modulating the VSR weights using the blur kernel parameters as keys and values in memory networks. Experiments show that the KeMoVSR achieves superior performance compared to other blind VSR approaches. The KeMoVSR provides effective memory utilization that is appropriate for real-world scenarios. The code is available at https://github.com/dbseorms16/KeMoVSR.

A study on optimal share pledge rate based on bilateral risk-CVaR of pledgee

This paper proposes the optimal pledge rate model based on the pledgee's bilateral risk-CVaR and dual-objective planning. First, a bilateral risk-CVaR model is constructed, for which a nonparametric kernel estimation method is presented, with a comparative analysis of the efficient frontier for “mean-variance”, “mean-CVaR”, and “mean-bilateral risk CVaR”. Second, it establishes a dual-objective planning model by the objectives of bilateral risk-CVaR and expected return of the pledgee, and accordingly develops an optimal pledge rate model combined with objective deviation, priority factor, and entropy method. Finally, the relationships between the pledge rate, the number of pledged shares, and the expected return are explored through simulation. The results illustrate that: (i) There are sequential inclusion relationships between the “mean-bilateral risk CVaR”, the “mean-CVaR” considering only the downside risk, and the “mean-variance” efficient sets of share pledge rate. (ii) As the number of shares increases, the pledgee's expected return also rises, and its sensitivity to the pledge rate grows. (iii) When the pledgee's expected return fixes, the number of pledged shares and the pledge rate have a U-shaped relationship. As it increases, the number of pledged shares rises, but the variation range of the pledge rate gradually decreases, and the pledgor's default risk declines.

Blind Text Image Deblurring Algorithm Based on Multi-Scale Fusion and Sparse Priors

The goal of blind text image deblurring is to obtain a clean text image from the given blurry text image without knowing the blur kernel. Sparsity-based methods have been shown their effectiveness in various blind text image deblurring models. However, the blur kernel estimation methods based on sparse priors lack of the consideration for the brightness information about the blur kernel, which will affect the restoration effect of the blur kernel. Besides, previous methods seldom apply sparse priors to both spatial domain and transform domain information. We propose a novel blind text image deblurring model based on multi-scale fusion and sparse priors. Besides the sparse gradient prior on the latent clean text image, we add the sparse prior on the high-frequency wavelet coefficients of the latent text image, which will better constrain the solution space and obtain good clean images. The semi-quadratic splitting method is used to alternately optimize the blur kernel and the latent clean image. Meanwhile, we consider the influence of the brightness feature of the restored blur kernel. By multi-scale fusion technique on the basis of Laplacian weight and saliency weight, we fuse the computed blur kernels in three channels to improve the quality of blur kernel. The experimental results show that our algorithm has good results in the restoration of blur kernels and text images.

Kernel density estimation for undirected dyadic data

We study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables defined for all n≡defN2 unordered pairs of agents/nodes in a weighted network of order N). These random variables satisfy a local dependence property: any random variables in the network that share one or two indices may be dependent, while those sharing no indices in common are independent. In this setting, we show that density functions may be estimated by an application of the kernel estimation method of Rosenblatt (1956) and Parzen (1962). We suggest an estimate of their asymptotic variances inspired by a combination of (i) Newey’s (1994) method of variance estimation for kernel estimators in the “monadic” setting and (ii) a variance estimator for the (estimated) density of a simple network first suggested by Holland and Leinhardt (1976). More unusual are the rates of convergence and asymptotic (normal) distributions of our dyadic density estimates. Specifically, we show that they converge at the same rate as the (unconditional) dyadic sample mean: the square root of the number, N, of nodes. This differs from the results for nonparametric estimation of densities and regression functions for monadic data, which generally have a slower rate of convergence than their corresponding sample mean.

Motion Video Image Based on Sensor and Multiprocessing Technology in Track and Field Sports

In order to use motion video image processing technology to better guide and evaluate athletes’ technical and tactical ability, this paper first constructed a motion video image acquisition system. Secondly, a fuzzy kernel estimation method for uniform linear motion based on cepstrum property is proposed. Then, the motion blur areas to be processed are selected, and only these areas are deblurred. Finally, the effective removal of local motion blur is realized, and a clear scene image is obtained. Then, the maximum value of the total entropy of the image is calculated by using the information entropy theory, and the particle swarm optimization algorithm is introduced to find the maximum threshold of image segmentation. Finally, small wave optical flow estimation algorithm and rectangular window scanning algorithm across scales of motion image target detection algorithm are proposed, to not only solve the traditional optical flow estimation for fast moving object detection accuracy but also improve the efficiency of the optical flow computation. Compared to many kinds of algorithms, this paper proposed an algorithm that can improve the accuracy of moving target detection and measurement accuracy. And, the detection accuracy of the proposed algorithm is up to 86.5%. The estimated accuracy was as high as 65%. The segmentation accuracy is up to 95%.

Asymptotically Minimax Goodness-of-fit Testing for Single-index Models

In the context of non parametric multivariate regression model, we are interested in goodness-of-fit testing for the single-index models. These models are dimension reduction models and are therefore useful in multidimensional nonparametric statistics because of the well-known phenomenon called the curse of dimensionality. Fan and Li [5] have proposed the first consistent test for goodness-of-fit testing of the single-index by using nonparametric kernel estimation method and a central limit theorem for degenerate <img src=image/13427297_05.gif>-statistics of order higher than two. Since then, the minimax properties of this test have not been investigated. Following this work, we use here the asymptotic minimax approach. We are interested in finding the asymptotic minimax rate of testing <img src=image/13427297_01.gif> which gives the minimal distance between the null and alternative hypotheses such that a successful testing is possible. We propose a test procedure of level <img src=image/13427297_02.gif> which can tend to zero when the sample size tends to infinity. We have established the minimax asymptotic properties of our test procedure by showing that it reaches the asymptotic minimax rate <img src=image/13427297_01.gif> for the dimension <img src=image/13427297_03.gif> and there is no test of level <img src=image/13427297_02.gif> reaching this rate for <img src=image/13427297_04.gif>. Because of its minimax asymptotic properties, our test is able to distinguish the null hypothesis of the closest possible alternative. The results obtained were possible thanks to a large deviation result that we established for a degenerate U-statistic of order two appearing in our decision variable.

Application of normalized SPH method to inviscid fluid flows with large deformation of free surface

A new normalized smoothed particle hydrodynamics (SPH) method has been presented recently and applied to transient solid mechanics problems of small deformation. The method can overcome boundary deficiency of the conventional SPH method without troublesome inversion of corrective matrix and provide convenience for treating boundary conditions. In this paper, a formulation of the normalized SPH method is derived for modeling inviscid fluid flows with large deformation of free surface. The treatment of dynamic free surface boundary conditions in the present method is addressed and theoretically compared with that in the conventional SPH method. A method based on kernel estimation is proposed for calculation of boundary summation and compared with the method based on α-shape. The normalized SPH method is applied to modeling inviscid free surface flows. Numerical results demonstrate that the present method is capable of modeling large deformation of free surface and can produce higher accuracy than the conventional SPH method, especially at boundary regions. The newly developed kernel estimation method for the calculation of boundary summation is more efficient than the α-shape-based method, and makes the computational efficiency of the normalized SPH method close to the conventional SPH method. To simulate violent free surface flows, a particle shifting technique is introduced in the present method. With this technique, the method is applied to simulating extremely large deformation, fragmentation and reconnection of free surface.

On the nonparametric estimation of the conditional hazard estimator in a single functional index

Abstract This paper deals with the conditional hazard estimator of a real response where the variable is given a functional random variable (i.e it takes values in an infinite-dimensional space). Specifically, we focus on the functional index model. This approach offers a good compromise between nonparametric and parametric models. The principle aim is to prove the asymptotic normality of the proposed estimator under general conditions and in cases where the variables satisfy the strong mixing dependency. This was achieved by means of the kernel estimator method, based on a single-index structure. Finally, a simulation of our methodology shows that it is efficient for large sample sizes.

Analysis of Information Search around the Time of Childbirth: Estimating Probability Distributions of Search Dates via Mathematical Optimization

Many mothers have considerable anxiety about pregnancy, childbirth, and childcare. For such mothers, searching for information on the Internet is an effective means of dissolving their anxieties. We consider the problem of estimating, for each search word, a distribution of search dates with respect to children’s birth dates. Most of the empirical distributions have unimodal or bimodal shapes, and some of them are asymmetric about extremal points and rise or fall sharply. We propose nonparametric estimation methods based on mathematical optimization models for such probability distributions. Our unimodal and bimodal optimization models automatically estimate the optimal extremal points and can be extended to multimodal distributions. These models are formulated as mixed-integer convex quadratic optimization problems, which can be solved exactly using optimization software. Experimental results using real-world and synthetic datasets demonstrate that our methods are effective by comparison to conventional moving average and kernel estimation methods.

A multiobjective prediction model with incremental learning ability by developing a multi-source filter neural network for the electrolytic aluminium process

Improving current efficiency and reducing energy consumption are two important technical goals of the electrolytic aluminum process (EAP). However, because the process involves complex noise characteristics (i.e., unknown types, redundant distributions and variable forms), it is very difficult to accurately develop a multiobjective prediction model. To overcome this problem, in this paper, a novel framework of multiobjective incremental learning based on a multi-source filter neural network (MSFNN) is presented. The proposed framework first presents a “multi-source filter” (MSF) technique that utilizes the mean and variance in the unscented Kalman filter (UKF) to guide the importance function of the particle filter (PF) based on a density kernel estimation method. Then, the MSF is embedded in the mutated neural network to adjust weights in real time. Third, weights are calculated and normalized by a modified importance function, which is the basis for further optimizing a secondary sampling based on sampling importance resampling (SIR). Finally, the incremental learning model with two objectives (i.e., process power consumption and current efficiency) based on the MSFNN in the EAP is established. The presented framework has been verified by the real-world EAP and some closely related methods. All test results indicate that the MSFNN’s relative prediction errors of the above two objectives are controlled within 0.51% and 0.38%, respectively and prove that MSFNN has significant competitive advantages over other recent filtering network models. Successfully establishment of the proposed framework provides a model foundation for multiobjective optimization problems in the EAP.

Does the Chinese labour force make sufficient efforts? Empirical evidence using non‐parametric analysis

AbstractIn this study, we construct an incentive model under which the optimal wage incentive scheme is a linear contract. This linear incentive contract can induce truth telling by workers about their inefficiency types and promote optimal efforts by them. We use the non‐parametric kernel estimation method to estimate the model primitives to analyse the insufficient efforts in the Chinese labour market. The empirical results based on data collected from the China Health and Nutrition Survey show that efficient male workers in white‐collar occupations do not exert sufficient efforts in the Chinese labour market. And wages for male workers in white‐collar occupations are undervalued.

Kernel regression estimation for LTRC and associated data

This paper focuses on nonparametric regression modeling of time-series and incomplete observations. In this sense, the observations are subject to both left truncation and right censoring (LTRC) and satisfy an association dependency. Using the well-known kernel estimation method, we establish the strong uniform consistency with a rate of the kernel estimator proposed in this paper. Simulation studies are conducted to assess the impact of both incompleteness and association dependency on the estimation.