Total Mean Square Error Research Articles

Collaboration of IoT devices in smart home scenarios: algorithm research based on graph neural networks and federated learning

Traditional IoT device collaboration is usually static and cannot adjust the collaboration mode between devices according to various changes, which limits work efficiency. To this end, an IoT device collaboration optimization algorithm based on graph neural network and federated learning is studied. This method abstracts various IoT device nodes and their communication relationships into graph structured data for storage, and then uses federated learning to train the graph convolutional network with graph structured data. The obtained model can be used to optimize the collaboration mode of IoT devices. During the training process, the total average MSE (mean square error) between the output and the label of the graph convolutional network model based on federated learning is 0.968; the total standard deviation of MSE is 0.0353; the total time from training to model convergence is 435.82 s, of which data transmission time accounts for 27.1% and model training time accounts for 72.9%. In a 2-h practical experiment, the graph convolutional network model based on federated learning was used to optimize the collaboration mode of smart homes, achieving a target environment residence time of 87 min and a total power consumption reduction of 0.69 kW·h. The results show that this method can effectively optimize the collaboration efficiency of IoT devices, reduce training time and network overhead, but it fails to improve the prediction accuracy of the model and may also lead to a decrease in stability.

Research on the Three-Level Integrated Environmental Evaluation Model for Multi-Greenhouse Potatoes

Aiming at the problems of large error and redundancy in the multi-node data acquisition of multi-greenhouse photo growth environmental information, a three-level fusion algorithm based on adaptive weighting, an LMBP network, and an improved D-S theory is proposed. The box-and-line graph method recognizes the original data and then replaces it based on the mean value method; the air temperature, humidity, and light intensity measurements are unbiased estimations of the true value to be estimated, so the first level of fusion chooses the adaptive weighted average algorithm to find the optimal weights of each sensor under the condition of minimizing the total mean-square error and obtains the optimal estimation of the weights of the homogeneous sensors of a greenhouse. The Levenberg–Marquardt algorithm was chosen for the second level of fusion to optimize the weight modification of the BP neural network, i.e., the LMBP network, and the three environmental factors corresponding to “suitable”, “uncertain” and “unsuitable” potato growth environments were trained for the three environmental factors in the reproductive periods. The output of the hidden layer was converted into probability by the Softmax function. The third level is based on the global fusion of evidence theory (also known as D-S theory), and the network output is used as evidence to obtain a consistent description of the multi-greenhouse potato cultivation environment and the overall scheduling of farming activities, which better solves the problem of the difficulty in obtaining basic probability assignments in the evidence theory; in the case of a conflict between the evidence, the BPA of the conflicting evidence is reallocated, i.e., the D-S theory is improved. Example validation shows that the total mean square error of the adaptive weighted fusion value is smaller than the variance of each sensor estimation, and sensors with lower variance are assigned lower weights, which makes the fusion result not have a large deviation due to the failure of individual sensors; when the fusion result of a greenhouse feature level is “unsuitable”, the fusion result of each data level is considered comprehensively, and the remote control agency makes a decision, which makes full use of the complementary nature of multi-sensor information resources and solves the problem of fusion of multi-source environmental information and the problem of combining conflicting environmental evaluation factors. Compared with the traditional D-S theory, the improved D-S theory reduces the probability of the “uncertainty” index in the fusion result again. The three-level fusion algorithm in this paper does not sacrifice data accuracy and greatly reduces the noise and redundancy of the original data, laying a foundation for big data analysis.

RIS-Aided MIMO Systems With Hardware Impairments: Robust Beamforming Design and Analysis

Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.

Exploration of the Relationships between Men's Healthy Life Expectancy in Japan and Regional Variables by Integrating Statistical Learning Methods.

A quantitative understanding of the relationship between comprehensive health levels, such as healthy life expectancy and their related factors, through a highly explanatory model is important in both health research and health policy making. In this study, we developed a regression model that combines multiple linear regression and a random forest model, exploring the relationship between men's healthy life expectancy in Japan and regional variables from open sources at the city level as an illustrative case. Optimization of node-splitting in each decision tree was based on the total mean-squared error of multiple regression models in binary-split child nodes. Variations of standardized partial regression coefficients for each city were obtained as the ensemble of multiple trees and visualized on scatter plots. By considering them, interaction terms with piecewise linear functions were exploratorily introduced into a final multiple regression model. The plots showed that the relationship between the healthy life expectancy and the explanatory variables could differ depending on the cities' characteristics. The procedure implemented here was suggested as a useful exploratory method for flexibly implementing interactions in multiple regression models while maintaining interpretability.

Parameter estimation of a model using maximum likelihood function and Bayesian analysis through moment of order statistics

Due to advancements in Bayesian modeling, the likelihood-free posterior estimate is now feasible. These estimation methods are crucial for a deeper understanding of simulation-based systems since it might be difficult, if not impossible, to estimate probability values. This compares the effectiveness of such updated estimate approaches to earlier maximum likelihood forecasting models and offers some adjustments to maximum likelihood estimation for estimating the parameters of the Bayesian analysis in this work. Recent improvements in Bayesian modeling have made it feasible to obtain the likelihood-free posterior estimate. These estimate methods are essential for evaluating simulation-based theories since it might be difficult, if not impossible, to determine probability values. Simulation-based concepts such as the Leaky Competing Accumulator (LCA) theory and Feed-Forward Inhibition (FFI) theory have not yet benefited from Bayesian techniques. As assessment criteria, total relative deviation (TRD), total mean square error (TMSE), and Stein Loss Function (SLF) are used. Maximum likelihood (ML) estimates are modified because the original statistic's Cumulative Distribution Function (CDF) is better than traditional ML estimations and other modified estimators emphasize average and coefficient variability. Prior estimator performance was unaffected by response rate or real parameter settings. These systems have not been formally evaluated by the Bayesian factor.

A Framework for Hardware Impairments-Aware Multi-Antenna Transceiver Design in IoT Systems via Majorization–Minimization

In view of the nonideality of communication links in the Internet of Things (IoT) originating from transceiver hardware impairments, in this article, we introduce a general framework for hardware impairments-aware multiantenna transceiver design, which considers different availabilities of CSI at the transmitter (CSIT) and the receiver (CSIR). The well-known Kronecker model is applied to characterize stochastic channel state information (CSI) errors. For each case, we aim to minimize the (average) total mean square error (MSE) of all data streams subject to the practical per-antenna power constraints. To address the nonconvexity of the formulated problem, we propose an efficient majorization–minimization (MM)-based iterative algorithm to transform the original problem into a series of convex subproblems with semiclosed-form optimal solutions. For low-complexity implementation, we also develop an alternative scheme for directly finding a high-quality suboptimal solution by considering both worst case hardware impairments and worst case CSI errors. In particular, since an explicit expression of the average total MSE for the perfect CSIR and imperfect CSIT case is hard to derive, we instead optimize its effective upper and lower bounds. The prospective applications of our work in the two currently popular multiple-input–multiple-output (MIMO) IoT scenarios are then discussed. Furthermore, we fundamentally reveal the MSE floor effect caused by both hardware distortion and CSI imperfection in the high-SNR regime. Numerical results illustrate the excellent average total MSE and average bit error rate (BER) performance of our proposed algorithms over the adopted benchmark schemes.

Twilight of Human Judgment

Twilight of Human Judgment

Weather Radar Echo Extrapolation Method Based on Deep Learning

In order to forecast some high intensity and rapidly changing phenomena, such as thunderstorms, heavy rain, and hail within 2 h, and reduce the influence brought by destructive weathers, this paper proposes a weather radar echo extrapolation method based on deep learning. The proposed method includes the design and combination of the data preprocessing, convolutional long short-term memory (Conv-LSTM) neuron and encoder–decoder model. We collect eleven thousand weather radar echo data in high spatiotemporal resolution, these data are then preprocessed before they enter the neural network for training to improve the data’s quality and make the training better. Next, the neuron integrates the structure and the advantages of convolutional neural network (CNN) and long short-term memory (LSTM), called Conv-LSTM, is applied to solve the problem that the full-connection LSTM (FC-LSTM) cannot extract the spatial information of input data. This operation replaced the full-connection structure in the input-to-state and state-to-state parts so that the Conv-LSTM can extract the information from other dimensions. Meanwhile, the encoder–decoder model is adopted due to the size difference of the input and output data to combine with the Conv-LSTM neuron. In the neural network training, mean square error (MSE) loss function weighted according to the rate of rainfall is added. Finally, the matrix “point-to-point” test method, including the probability of detection (POD), critical success index (CSI), false alarm ratio (FAR) and spatial test method contiguous rain areas (CRA), is used to examine the radar echo extrapolation’s results. Under the threshold of 30 dBZ, at the time of 1 h, we achieved 0.60 (POD), 0.42 (CSI) and 0.51 (FAR), compared with 0.42, 0.28 and 0.58 for the CTREC algorithm, and 0.30, 0.24 and 0.71 for the TITAN algorithm. Meanwhile, at the time of 1 h, we achieved 1.35 (total MSE ) compared with 3.26 for the CTREC algorithm and 3.05 for the TITAN algorithm. The results demonstrate that the radar echo extrapolation method based on deep learning is obviously more accurate and stable than traditional radar echo extrapolation methods in near weather forecasting.

Efficiency Comparisons of Robust and Non-Robust Estimators for Seemingly Unrelated Regressions Model

This paper studies and reviews several procedures for developing robust regression estimators of the seemingly unrelated regressions (SUR) model, when the variables are affected by outliers. To compare the robust estimators (M-estimation, S-estimation, and MM-estimation) with non-robust (traditional maximum likelihood and feasible generalized least squares) estimators of this model with outliers, the Monte Carlo simulation study has been performed. The simulation factors of our study are the number of equations in the system, the number of observations, the contemporaneous correlation among equations, the number of regression parameters, and the percentages of outliers in the dataset. The simulation results showed that, based on total mean squared error (TMSE), total mean absolute error (TMAE) and relative absolute bias (RAB) criteria, robust estimators give better performance than non-robust estimators; specifically, the MM-estimator is more efficient than other estimators. While when the dataset does not contain outliers, the results showed that the unbiased SUR estimator (feasible generalized least squares estimator) is more efficient than other estimators.

A gear fault diagnosis method based on improved accommodative random weighting algorithm and BB-1D-TP

As an essential component of a gearbox, gears can damage a structure or even an entire gear transmission system in case of failures. As a result, advanced fault diagnosis methods are crucial to system's operation. Currently, single-signal-driven gear fault diagnosis techniques have been applied in many fields, but multipath noise and single-sensor sampling errors inevitably affected the accuracy of diagnosis. This paper proposes a gear fault diagnosis method based on a novel accommodative random weighting theory and a balanced binary one dimension ternary pattern (BB-1D-TP) model. It can accurately diagnose the types of gear failures under the circumstances of multiple channels and strong background noise. The novel accommodative random weighting algorithm reduces the total mean-square error (MSE) by adaptively adjusting the proportional connection between a measured value at a present state and a historical state. Then the balanced binary algorithm extracts texture features of fault signals for signal enhancement. In the end, the classification is done by using Support Vector Machine (SVM) method. The result of experiments demonstrated that the method in this article effectively improves accuracy and efficiency of gear fault identification.

MSE-Based Joint Transceiver and Passive Beamforming Designs for Intelligent Reflecting Surface-Aided MIMO Systems

In this letter, novel schemes for joint transceiver and passive beamforming design in an intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) system are developed. Specifically, active beamformer at the BS, passive beamfomer at the IRS, and receive filter at the user are jointly optimized based on two realistic mean square error (MSE) criteria for signal estimation: (i) total MSE minimization and (ii) maximum per-stream MSE minimization. To tackle these challenging nonconvex problems effectively, two efficient iterative algorithms are proposed for both MSE criteria, in which the receive filter, active and passive beamformers are designed in alternating manner through solving the corresponding convex subproblems, respectively. Numerical results demonstrate better performance of the proposed schemes compared to baseline schemes in terms of the MSE and error rate performance.

An Improved Assessment Method and Its Application to the Latest IMERG Rainfall Product in Mainland China

Quantification of uncertainties associated with satellite precipitation products is a prior requirement for their better applications in earth science studies. An improved scheme is developed in this study to decompose mean bias error (MBE) and mean square error (MSE) into three components, i.e., MBE and MSE associated hits, missed precipitation, and false alarms, respectively, which are weighted by their relative frequencies of occurrence (RFO). The trend of total MBE or MSE is then naturally decomposed into six components according to the chain rule for derivatives. Quantitative estimation of individual contributions to total MBE and MSE is finally derived. The method is applied to validation of Integrated MultisatellitE Retrievals for GPM (IMERG) in Mainland China. MBE associated with false alarms is an important driver for total MBE, while MSE associated with hits accounts for more than 85% of MSE, except in inland semi-arid area. The RFO of false alarms increases, whereas the RFO of missed precipitation decreases. Both factors lead in part to a growing trend for total MBE. Detection of precipitation should be improved in the IMERG algorithm. More specifically, the priority should be to reduce false alarms.

Gift of gab: Probing the limits of dynamic concentration-sensing across a network of communicating cells

Many systems in biology and beyond employ collaborative, collective communication strategies for improved efficiency and adaptive benefit. One such paradigm of particular interest is the community estimation of a dynamic signal, when, for example, an epithelial tissue of cells must decide whether to react to a given dynamic external concentration of stress signaling molecules. At the level of dynamic cellular communication, however, it remains unknown what effect, if any, arises from communication beyond the mean field level. What are the limits and benefits to communication across a network of neighbor interactions? What is the role of Poissonian vs. super Poissonian dynamics in such a setting? How does the particular topology of connections impact the collective estimation and that of the individual participating cells? In this letter we construct a robust and general framework of signal estimation over continuous time Markov chains in order to address and answer these questions. Our results show that in the case of Possonian estimators, the communication solely enhances convergence speed of the Mean Squared Error (MSE) of the estimators to their steady-state values while leaving these values unchanged. However, in the super-Poissonian regime, MSE of estimators significantly decreases by increasing the number of neighbors. Surprisingly, in this case, the clustering coefficient of an estimator does not enhance its MSE while reducing total MSE of the population.

Dissecting Performances of PERSIANN-CDR Precipitation Product over Huai River Basin, China

Satellite-based precipitation products, especially those with high temporal and spatial resolution, constitute a potential alternative to sparse rain gauge networks for multidisciplinary research and applications. In this study, the validation of the 30-year Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Climate Data Record (PERSIANN-CDR) daily precipitation dataset was conducted over the Huai River Basin (HRB) of China. Based on daily precipitation data from 182 rain gauges, several continuous and categorical validation statistics combined with bias and error decomposition techniques were employed to quantitatively dissect the PERSIANN-CDR performance on daily, monthly, and annual scales. With and without consideration of non-rainfall data, this product reproduces adequate climatologic precipitation characteristics in the HRB, such as intra-annual cycles and spatial distributions. Bias analyses show that PERSIANN-CDR overestimates daily, monthly, and annual precipitation with a regional mean percent total bias of 11%. This is related closely to the larger positive false bias on the daily scale, while the negative non-false bias comes from a large underestimation of high percentile data despite overestimating lower percentile data. The systematic sub-component (error from high precipitation), which is independent of timescale, mainly leads to the PERSIANN-CDR total Mean-Square-Error (TMSE). Moreover, the daily TMSE is attributed to non-false error. The correlation coefficient (R) and Kling–Gupta Efficiency (KGE) respectively suggest that this product can well capture the temporal variability of precipitation and has a moderate-to-high overall performance skill in reproducing precipitation. The corresponding capabilities increase from the daily to annual scale, but decrease with the specified precipitation thresholds. Overall, the PERSIANN-CDR product has good (poor) performance in detecting daily low (high) rainfall events on the basis of Probability of Detection, and it has a False Alarm Ratio of above 50% for each precipitation threshold. The Equitable Threat Score and Heidke Skill Score both suggest that PERSIANN-CDR has a certain ability to detect precipitation between the second and eighth percentiles. According to the Hanssen–Kuipers Discriminant, this product can generally discriminate rainfall events between two thresholds. The Frequency Bias Index indicates an overestimation (underestimation) of precipitation totals in thresholds below (above) the seventh percentile. Also, continuous and categorical statistics for each month show evident intra-annual fluctuations. In brief, the comprehensive dissection of PERSIANN-CDR performance reported herein facilitates a valuable reference for decision-makers seeking to mitigate the adverse impacts of water deficit in the HRB and algorithm improvements in this product.

An Evaluation of the Impact of Multicollinearity on the Performance of Various Robust Regression Methods

Objectives: To examine the performance of several regression methods comprising of Ordinary Least Square (OLS), and certain robust methods including; M-regression, Least Median of Squared (LMS), Least Trimmed Square (LTS), MMestimation and S-estimation, under fluctuating levels of collinearity, using the criterion, Total Absolute Deviation (TAB) and Total Mean Square Error (TMSE) with some graphical tools. Methods/Statistical Analysis: Robust Regression methods insure good performance even in case the fundamental assumption of normality is not satisfied. The presence of multicollinearity affects the results of robust regression methods and marks them unsatisfactory. A quantitative evaluation of these techniques is provided by using the criterion, TAB and TMSE. Results are summarised by using box plot of absolute bias, along with the graphs of TAB, and TMSE. Findings: The results show that for minor levels of collinearity the effect is low and similar, but at greater levels of collinearity the effect is high and performance wise all the methods give quite incompatible results. It is also illustrated that greater magnitude of collinearity along with higher percentages of outliers ranks the underlying methods quite differently, resulting in MM-estimation method to be the most unpleasant. Conclusion: While applying any statistical method it is necessary to consider all the assumption underlying that method as well as every aspect of our data to avoid misleading results. It is illustrated that MM-estimation method although a best candidate for higher percentages of outliers alone, become the most unpleasant, by a simultaneous interruption of high level of collinearity, hence robust ridge techniques need to be adopted. Keywords: Multicollinearity, Ordinary Least Squares, Outliers, Robust Regression Methods

Prototype Filter Design to Minimize Stopband Energy With Constraint on Channel Estimation Performance for OQAM/FBMC Systems

In this paper, we propose a prototype filter design method to minimize the stopband energy of the filter with guaranteed time-domain channel estimation performance for offset quadrature amplitude modulation based filter bank multicarrier (OQAM/FBMC) systems. First, we analytically derive the total mean squared error (MSE) of estimated channel impulse response with two channel estimation schemes, i.e., the linear minimum mean square error and weighted least square, where the impact of intrinsic interference from data symbols is taken into account. Then, we formulate an optimization problem of filter coefficients to minimize the stopband energy with constraint on the total MSE. By exploiting the Heisenberg–Gabor uncertainty principle, the original optimization problem is transformed into an equality-constrained one. Finally, we employ the Lagrange multiplier method to solve the transformed problem and obtain the filter coefficients with the Newton’s method. Simulation results demonstrate that the proposed filter outperforms the isotropic orthogonal transform algorithm and extended Gaussian function filters considering both the MSE and stopband energy performances.

Training Power Allocation Based on MSE-Minimization for Multi-Relay Amplify-and-Forward Cooperation in Wireless Sensor Networks

In this paper, a training scheme for multi-relay clustered wireless sensor networks is proposed for the destination cluster head node to estimate the individual source-relay and relay-destination channels. Compared with an existing training scheme, the proposed one has shown improved efficiency with reduced power and computation time in the training of the source relay channels. Furthermore, the training power allocation problem is analyzed. Based on minimizing the total mean-square-error (MSE) of all channel estimates, two approximate solutions for the power allocation among all network nodes and all training links are derived. The first solution is adaptive to the instantaneous relay-destination channel estimates, thus requires feedback from the destination during the training process. The other solution depends on channel variances only and has lower complexity in implementation. Simulation results demonstrate that the proposed training scheme and power allocation solutions obtain lower total MSE and higher network throughput than existing schemes.

Robust Iterative Distributed Minimum Total MSE Algorithm for Secure Communications in the Internet of Things Using Relays

In this article, we first investigate secure communications for a two-hop interference channel relay system with imperfect channel estimation in the wireless Internet of Things (IoT), where K source-destination pairs communicate simultaneously when an eavesdropper exists. We jointly conceive source, relay and destination matrices upon minimizing total mean-squared error (MSE) of all legitimate destinations while keeping the MSE at eavesdropper above a given threshold. We illuminate that the design of the source, relay and destination matrices is subject to both transmit power constraints and secrecy requirements. More specifically, we propose an efficient robust iterative distributed algorithm to simplify the process of the joint design for optimal source, relay and destination matrices. Furthermore, the convergence of the iterative distributed algorithm is described. Additionally, the performances of our proposed algorithm, such as its secrecy rate and MSE, are characterized in the form of simulation results. The simulation results reveal that the proposed algorithm is superior to the traditional approach. As a benefit, secure communications can be ensured by using the proposed algorithm for the multiple input multiple output (MIMO) interference relay IoT network in the presence of an eavesdropper.

Estimation of Time-Varying Channels in MIMO Two-Way Multi-Relay Systems

In this paper, we study time-varying channel estimation and optimal pilot design for multiple-input multiple-output two-way multi-relay systems in the sense of minimizing the total estimation mean square error (MSE) under the power constraints at two source nodes and multiple relays. A particularly challenging issue in the optimal pilot design is to completely eliminate the inter-link interference while most efficiently using the channel resource. To address this challenging issue, we consider a pilot design approach based on the phase rotation technique at multiple relays. First, we establish various optimality conditions for the pilot design in the sense of the minimum total MSE. Then, we propose the optimal pilot scheme by designing the pilot signals, phase rotations, and pilot symbol positions to satisfy the established optimality conditions. Finally, we propose the asymptotically optimal pilot scheme in the high signal-to-noise ratio (SNR) regime with low complexity. Simulation results show that the proposed schemes significantly outperform the existing schemes in terms of the channel estimation and the bit error rate, and the proposed asymptotically optimal scheme provides the near-optimal performance even in the low to moderate SNR range.

Transceiver Design for MIMO Systems with Individual Transmit Power Constraints

This paper investigate the transceiver design for single-user multiple-input multipleoutput system (SU-MIMO). Joint transceiver design with an improper modulation is developed based on the minimum total mean-squared error (TMSE) criterion under two different cases. One is equal power allocation (EPA) and other is the power constraint that jointly meets both EPA and total transmit power constraint (TTPC) (i.e ITPC). Transceiver is designed based on the assumption that both the perfect and imperfect channel state information (CSI) is available at both the transmitter and receiver. The simulation results show the performance improvement of the proposed work over conventional work in terms of bit error rate (BER).