Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

Enhanced kernel minimum squared error algorithm and its application in face recognition

To improve the classification performance of the kernel minimum squared error（ KMSE）, an enhanced KMSE algorithm（ EKMSE） is proposed. It redefines the regular objective function by introducing a novel class label definition, and the relative class label matrix can be adaptively adjusted to the kernel matrix.Compared with the common methods, the newobjective function can enlarge the distance between different classes, which therefore yields better recognition rates. In addition, an iteration parameter searching technique is adopted to improve the computational efficiency. The extensive experiments on FERET and GT face databases illustrate the feasibility and efficiency of the proposed EKMSE. It outperforms the original MSE, KMSE,some KMSE improvement methods, and even the sparse representation-based techniques in face recognition, such as collaborate representation classification（ CRC）.

Low Complexity Minimum Mean Square Error Channel Estimation for Adaptive Coding and Modulation Systems

Performance of the Adaptive Coding and Modulation(ACM) strongly depends on the retrieved Channel State Information(CSI),which can be obtained using the channel estimation techniques relying on pilot symbol transmission.Earlier analysis of methods of pilot-aided channel estimation for ACM systems were relatively little.In this paper,we investigate the performance of CSI prediction using the Minimum Mean Square Error(MMSE)channel estimator for an ACM system.To solve the two problems of MMSE:high computational operations and oversimplified assumption,we then propose the Low-Complexity schemes(LC-MMSE and Recursion LC-MMSE(R-LC-MMSE)).Computational complexity and Mean Square Error(MSE) are presented to evaluate the efficiency of the proposed algorithm.Both analysis and numerical results show that LC-MMSE performs close to the wellknown MMSE estimator with much lower complexity and R-LC-MMSE improves the application of MMSE estimation to specific circumstances.

Adaptive control of machining process based on extended entropy square error and wavelet neural network

Combining information entropy and wavelet analysis with neural network,an adaptive control system and an adaptive control algorithm are presented for machining process based on extended entropy square error(EESE)and wavelet neural network(WNN).Extended entropy square error function is defined and its availability is proved theoretically.Replacing the mean square error criterion of BP algorithm with the EESE criterion,the proposed system is then applied to the on-line control of the cutting force with variable cutting parameters by searching adaptively wavelet base function and self adjusting scaling parameter,translating parameter of the wavelet and neural network weights.Simulation results show that the designed system is of fast response,non-overshoot and it is more effective than the conventional adaptive control of machining process based on the neural network.The suggested algorithm can adaptively adjust the feed rate on-line till achieving a constant cutting force approaching the reference force in varied cutting conditions,thus improving the machining efficiency and protecting the tool.

融合IMR-WGAN的时序数据修复方法

工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小迭代修复和改进WGAN混合模型的时序数据修复方法.首先,在预处理阶段,保留异常数据,进行信息标注等处理,从而充分挖掘异常值与真实值之间的特征约束.其次,在噪声模块提出了近邻参数裁剪规则,用于修正最小迭代修复公式生成的噪声向量.将其传递至模拟分布模块的生成器中,同时设计了一个动态时间注意力网络层,用于提取时序特征权重并与门控循环单元串联组合捕捉不同步长的特征依赖,并引入递归多步预测原理共同提升模型的表达能力;在判别器中设计了Abnormal and Truth奖励机制和Weighted Mean Square Error损失函数共同反向优化生成器修复数据的细节和质量.最后,在公开数据集和真实数据集上的实验结果表明,该方法的修复准确度与模型稳定性显著优于现有方法.

A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network

The purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission model(FDTM)in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network(LM-NN)technique.The fractional dengue transmission model(FDTM)consists of 12 compartments.The human population is divided into four compartments;susceptible humans(S_(h)),exposed humans(E_(h)),infectious humans(I_(h)),and recovered humans(R_(h)).Wolbachia-infected and Wolbachia-uninfected mosquito population is also divided into four compartments:aquatic(eggs,larvae,pupae),susceptible,exposed,and infectious.We investigated three different cases of vertical transmission probability(η),namely when Wolbachia-free mosquitoes persist only(η=0.6),when both types of mosquitoes persist(η=0.8),and when Wolbachia-carrying mosquitoes persist only(η=1).The objective of this study is to investigate the effectiveness of Wolbachia in reducing dengue and presenting the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three different cases of the fractional order derivatives(α=0.4,0.6,0.8).LM-NN approach includes a training,validation,and testing procedure to minimize the mean square error(MSE)values using the reference dataset(obtained by solving the model using the Adams-Bashforth-Moulton method(ABM).The distribution of data is 80% data for training,10% for validation,and,10% for testing purpose)results.A comprehensive investigation is accessible to observe the competence,precision,capacity,and efficiency of the suggested LM-NN approach by executing the MSE,state transitions findings,and regression analysis.The effectiveness of the LM-NN approach for solving the FDTM is demonstrated by the overlap of the findings with trustworthy measures,which achieves a precision of up to 10^(-4).

Performance Analysis of ZF and RZF in Low-Resolution ADC/DAC Massive MIMO Systems

Large number of antennas and higher bandwidth usage in massive multiple-input-multipleoutput(MIMO)systems create immense burden on receiver in terms of higher power consumption.The power consumption at the receiver radio frequency(RF)circuits can be significantly reduced by the application of analog-to-digital converter(ADC)of low resolution.In this paper we investigate bandwidth efficiency(BE)of massive MIMO with perfect channel state information(CSI)by applying low resolution ADCs with Rician fadings.We start our analysis by deriving the additive quantization noise model,which helps to understand the effects of ADC resolution on BE by keeping the power constraint at the receiver in radar.We also investigate deeply the effects of using higher bit rates and the number of BS antennas on bandwidth efficiency(BE)of the system.We emphasize that good bandwidth efficiency can be achieved by even using low resolution ADC by using regularized zero-forcing(RZF)combining algorithm.We also provide a generic analysis of energy efficiency(EE)with different options of bits by calculating the energy efficiencies(EE)using the achievable rates.We emphasize that satisfactory BE can be achieved by even using low-resolution ADC/DAC in massive MIMO.

Low-complexity signal detection for massive MIMO systems via trace iterative method

Linear minimum mean square error(MMSE)detection has been shown to achieve near-optimal performance for massive multiple-input multiple-output(MIMO)systems but inevitably involves complicated matrix inversion,which entails high complexity.To avoid the exact matrix inversion,a considerable number of implicit and explicit approximate matrix inversion based detection methods is proposed.By combining the advantages of both the explicit and the implicit matrix inversion,this paper introduces a new low-complexity signal detection algorithm.Firstly,the relationship between implicit and explicit techniques is analyzed.Then,an enhanced Newton iteration method is introduced to realize an approximate MMSE detection for massive MIMO uplink systems.The proposed improved Newton iteration significantly reduces the complexity of conventional Newton iteration.However,its complexity is still high for higher iterations.Thus,it is applied only for first two iterations.For subsequent iterations,we propose a novel trace iterative method(TIM)based low-complexity algorithm,which has significantly lower complexity than higher Newton iterations.Convergence guarantees of the proposed detector are also provided.Numerical simulations verify that the proposed detector exhibits significant performance enhancement over recently reported iterative detectors and achieves close-to-MMSE performance while retaining the low-complexity advantage for systems with hundreds of antennas.

Comparative Analysis of Machine Learning Models for Stock Price Prediction: Leveraging LSTM for Real-Time Forecasting

The research focuses on improving predictive accuracy in the financial sector through the exploration of machine learning algorithms for stock price prediction. The research follows an organized process combining Agile Scrum and the Obtain, Scrub, Explore, Model, and iNterpret (OSEMN) methodology. Six machine learning models, namely Linear Forecast, Naive Forecast, Simple Moving Average with weekly window (SMA 5), Simple Moving Average with monthly window (SMA 20), Autoregressive Integrated Moving Average (ARIMA), and Long Short-Term Memory (LSTM), are compared and evaluated through Mean Absolute Error (MAE), with the LSTM model performing the best, showcasing its potential for practical financial applications. A Django web application “Predict It” is developed to implement the LSTM model. Ethical concerns related to predictive modeling in finance are addressed. Data quality, algorithm choice, feature engineering, and preprocessing techniques are emphasized for better model performance. The research acknowledges limitations and suggests future research directions, aiming to equip investors and financial professionals with reliable predictive models for dynamic markets.

A Novel Approach for Developing a Linear Regression Model within Logistic Cluster Using Scikit-Learn

Due to the rapid development of logistic industry, transportation cost is also increasing, and finding trends in transportation activities will impact positively in investment in transportation infrastructure. There is limited literature and data-driven analysis about trends in transportation mode. This thesis delves into the operational challenges of vehicle performance management within logistics clusters, a critical aspect of efficient supply chain operations. It aims to address the issues faced by logistics organizations in optimizing their vehicle fleets’ performance, essential for seamless logistics operations. The study’s core design involves the development of a predictive logistics model based on regression, focused on forecasting, and evaluating vehicle performance in logistics clusters. It encompasses a comprehensive literature review, research methodology, data sources, variables, feature engineering, and model training and evaluation and F-test analysis was done to identify and verify the relationships between attributes and the target variable. The findings highlight the model’s efficacy, with a low mean squared error (MSE) value of 3.42, indicating its accuracy in predicting performance metrics. The high R-squared (R2) score of 0.921 emphasizes its ability to capture relationships between input characteristics and performance metrics. The model’s training and testing accuracy further attest to its reliability and generalization capabilities. In interpretation, this research underscores the practical significance of the findings. The regression-based model provides a practical solution for the logistics industry, enabling informed decisions regarding resource allocation, maintenance planning, and delivery route optimization. This contributes to enhanced overall logistics performance and customer service. By addressing performance gaps and embracing modern logistics technologies, the study supports the ongoing evolution of vehicle performance management in logistics clusters, fostering increased competitiveness and sustainability in the logistics sector.

Adaptive Linear Filtering Design with Minimum Symbol Error Probability Criterion

Adaptive digital filtering has traditionally been developed based on the minimum mean square error （MMSE） criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate （MSER） criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.

Using self-location to calibrate the errors of observer positions for source localization

The uncertainty of observers＇ positions can lead to significantly degrading in source localization accuracy. This pa-per proposes a method of using self-location for calibrating the positions of observer stations in source localization to reduce the errors of the observer positions and improve the accuracy of the source localization. The relative distance measurements of the two coordinative observers are used for the linear minimum mean square error （LMMSE） estimator. The results of computer si-mulations prove the feasibility and effectiveness of the proposed method. With the general estimation errors of observers＇ positions, the MSE of the source localization with self-location calibration, which is significantly lower than that without self-location calibra-tion, is approximating to the Cramer-Rao lower bound （CRLB）.

Efficient Mean Estimation in Log-normal Linear Models with First-order Correlated Errors

In this paper, we propose a log-normal linear model whose errors are first-order correlated, and suggest a two-stage method for the efficient estimation of the conditional mean of the response variable at the original scale. We obtain two estimators which minimize the asymptotic mean squared error （MM） and the asymptotic bias （MB）, respectively. Both the estimators are very easy to implement, and simulation studies show that they are perform better.

LOW COMPLEXITY LMMSE TURBO EQUALIZATION FOR COMBINED ERROR CONTROL CODED AND LINEARLY PRECODED OFDM

The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing （OFDM） system with combined error control coding and linear precoding. While previous literatures employed linear precodcr of small size for complexity reasons, this paper proposes to use a linear precoder of size larger than or equal to the maximum length of the equivalent discrete-time channel in order to achieve full frequency diversity and reduce complexities of the error control coder/decoder. Also a low complexity Linear Minimum Mean Square Error （LMMSE） turbo equalizer is derived for the receiver. Through simulation and performance analysis, it is shown that the performance of the proposed scheme over frequency selective fading channel reaches the matched filter bound; compared with the same coded OFDM without linear precoding, the proposed scheme shows an Signal-to-Noise Ratio （SNR） improvement of at least 6dB at a bit error rate of 10 6 over a multipath channel with exponential power delay profile. Convergence behavior of the proposed scheme with turbo equalization using various type of linear precoder/transformer, various interleaver size and error control coder of various constraint length is also investigated.

THE INEFFICIENCY OF THE LEAST SQUARES ESTIMATOR AND ITS BOUND

It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.

Performance of cumulant-based rank reduction estimator in presence of unexpected modeling errors

Compared with the rank reduction estimator(RARE) based on second-order statistics(called SOS-RARE), the RARE based on fourth-order cumulants(referred to as FOC-RARE) can handle more sources and restrain the negative impacts of the Gaussian colored noise. However, the unexpected modeling errors appearing in practice are known to significantly degrade the performance of the RARE. Therefore, the direction-of-arrival(DOA) estimation performance of the FOC-RARE is quantitatively derived. The explicit expression for direction-finding(DF) error is derived via the first-order perturbation analysis, and then the theoretical formula for the mean square error(MSE) is given. Simulation results demonstrate the validation of the theoretical analysis and reveal that the FOC-RARE is more robust to the unexpected modeling errors than the SOS-RARE.

A Modified Regression Estimator for Single Phase Sampling in the Presence of Observational Errors

In this paper, a regression method of estimation has been used to derive the mean estimate of the survey variable using simple random sampling without replacement in the presence of observational errors. Two covariates were used and a case where the observational errors were in both the survey variable and the covariates was considered. The inclusion of observational errors was due to the fact that data collected through surveys are often not free from errors that occur during observation. These errors can occur due to over-reporting, under-reporting, memory failure by the respondents or use of imprecise tools of data collection. The expression of mean squared error (MSE) based on the obtained estimator has been derived to the first degree of approximation. The results of a simulation study show that the derived modified regression mean estimator under observational errors is more efficient than the mean per unit estimator and some other existing estimators. The proposed estimator can therefore be used in estimating a finite population mean, while considering observational errors that may occur during a study.

A Novel Adaptive Kalman Filter Based on Credibility Measure

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications,due to the fact that the covariances of noises are not exactly known.Our previous work reveals that in such scenario the filter calculated mean square errors(FMSE)and the true mean square errors(TMSE)become inconsistent,while FMSE and TMSE are consistent in the Kalman filter with accurate models.This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters.Obviously,it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models.Aiming at this,the concept of credibility is adopted to discuss the inconsistency problem in this paper.In order to formulate the degree of the credibility,a trust factor is constructed based on the FMSE and the TMSE.However,the trust factor can not be directly computed since the TMSE cannot be found for practical applications.Based on the definition of trust factor,the estimation of the trust factor is successfully modified to online estimation of the TMSE.More importantly,a necessary and sufficient condition is found,which turns out to be the basis for better design of Kalman filters with high performance.Accordingly,beyond trust factor estimation with Sage-Husa technique(TFE-SHT),three novel trust factor estimation methods,which are directly numerical solving method(TFE-DNS),the particle swarm optimization method(PSO)and expectation maximization-particle swarm optimization method(EM-PSO)are proposed.The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance.Meanwhile,the proposed EMPSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online.

A Robust Asynchrophasor in PMU Using Second-Order Kalman Filter

Phasor Measurement Units(PMUs)provide Global Positioning System(GPS)time-stamped synchronized measurements of voltage and current with the phase angle of the system at certain points along with the grid system.Those synchronized data measurements are extracted in the form of amplitude and phase from various locations of the power grid to monitor and control the power system condition.A PMU device is a crucial part of the power equipment in terms of the cost and operative point of view.However,such ongoing development and improvement to PMUs’principal work are essential to the network operators to enhance the grid quality and the operating expenses.This paper introduces a proposed method that led to lowcost and less complex techniques to optimize the performance of PMU using Second-Order Kalman Filter.It is based on the Asyncrhophasor technique resulting in a phase error minimization when receiving the signal from an access point or from the main access point.The MATLAB model has been created to implement the proposed method in the presence of Gaussian and non-Gaussian.The results have shown the proposed method which is Second-Order Kalman Filter outperforms the existing model.The results were tested usingMean Square Error(MSE).The proposed Second-Order Kalman Filter method has been replaced with a synchronization unit into thePMUstructure to clarify the significance of the proposed new PMU.

Energy Efficient and Intelligent Mosquito Repellent Fuzzy Control System

Mosquitoes are of great concern for occasionally carrying noxious diseases(dengue,malaria,zika,and yellow fever).To control mosquitoes,it is very crucial to effectively monitor their behavioral trends and presence.Traditional mosquito repellent works by heating small pads soaked in repellant,which then diffuses a protected area around you,a great alternative to spraying yourself with insecticide.But they have limitations,including the range,turning them on manually,and then waiting for the protection to kick in when the mosquitoes may find you.This research aims to design a fuzzy-based controller to solve the above issues by automatically determining a mosquito repellent’s speed and active time.The speed and active time depend on the repellent cartridge and the number of mosquitoes.The Mamdani model is used in the proposed fuzzy system(FS).The FS consists of identifying unambiguous inputs,a fuzzification process,rule evaluation,and a defuzzification process to produce unambiguous outputs.The input variables used are the repellent cartridge and the number of mosquitoes,and the speed of mosquito repellent is used as the output variable.The whole FS is designed and simulated using MATLAB Simulink R2016b.The proposed FS is executed and verified utilizing a microcontroller using its pulse width modulation capability.Different simulations of the proposed model are performed in many nonlinear processes.Then,a comparative analysis of the outcomes under similar conditions confirms the higher accuracy of the FS,yielding a maximum relative error of 10%.The experimental outcomes show that the root mean square error is reduced by 67.68%,and the mean absolute percentage error is reduced by 52.46%.Using a fuzzy-based mosquito repellent can help maintain the speed of mosquito repellent and control the energy used by the mosquito repellent.