Bias Term Research Articles

RCSA Protocol with Rayleigh Channel Fading in Massive-MIMO System

Introduction: Massive MIMO is a process where cellular BSs a large number of antennas. In this study, we concern about the end-to-end massive-MIMO system under the Rayleigh channel fading effect. Also, it includes both inter-channel interference and intra channel interference in an m-MIMO network system. Method: The major aim is to increase the throughput and network capacity as well as minimizing the channel collision in between the associated pilots. Here, we proposed an RCSA protocol with Rayleigh channel fading effect in the m-MIMO network to create a network like a real-time scenario. Here we have focused on the deployment of urban scenarios with the small timing variation and provided our novel RAP for the UEs, where the UEs want to access the network. To validate the performance of our proposed scheme we are going to compare with the state-of-art technique in the result analysis section. Result: We provide the analysis based upon the two considered scenarios; such as scenario-A considered at intra-channel interference and whereas in scenario-B considered both intra-cell channel interference as well as inter-cell channel interference. Where our RCSA approach is proposed with uncorrelated Rayleigh fading channels (URFC) that used to increase the capacity of network and decrease the collision probability. Conclusion: Here, we proposed the RCSA approach and it consist of four major steps such as; system initialization and querying; response queuing; resource contention and channel state analysis and, resource allocation. The system performs in the TDD mode of operation and the resources of time-frequency are divided into the coherent blocks of channel Discussion: In order to compare our RCSA-URFC approach, here we consider the state-of-art technique such as vertex graph-coloring-based pilot assignment (VGCPA) [35] under URFC. In addition we also consider the bias term randomly to make decision on particular UE. It very difficult to guess the strong probability of UE, therefore as per information obtained via

Valley-contrasting interband transitions and excitons in symmetrically biased dice model

We study the exciton states in the symmetrically biased dice model, the electronic structures of which have an isolated flat band between two dispersive bands. At 1/3 or 2/3 filling, the model describes a two-dimensional semiconductor with the band edge at two degenerate valleys. Because of qualitative changes in the eigenvectors resulting from the bias term, the interband transition between the flat band and a dispersive band is valley contrasting under circularly polarized light. In terms of an effective-mass model and a realistic electron-hole interaction, we numerically calculate the spectrum and wave functions of the intravalley excitons, which are treated as Wannier-Mott excitons. We also discuss the fine structures of the exciton spectrum induced by the intravalley and intervalley exchange interactions. The symmetrically biased dice model thereby proves to be a new platform for valley-contrasting optoelectronics.

Robust Gaussian process regression with a bias model

This paper presents a new approach to a robust Gaussian process regression, creating a non-parametric Bayesian regression estimate robust to outliers. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the Laplace distribution and Student-t distribution. However, the use of a non-Gaussian likelihood would incur the need for a computationally expensive Bayesian approximate computation in the posterior inferences. The proposed approach models an outlier as a noisy and biased observation of an unknown regression function, and accordingly, the likelihood contains bias terms to explain the degree of deviations from the regression function. We introduce two bias models that handle the bias terms differently, treating a bias as an unknown and fixed quantity or treating a bias as a random quantity. We entail how the biases can be estimated accurately with other hyperparameters by a regularized maximum likelihood estimation. Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem with analytical forms of the predictive mean and variance estimates. Therefore, the proposed approach is simple and very computationally attractive. It also gives a very robust and accurate GP estimate for many tested scenarios. For the numerical evaluation, we perform a comprehensive simulation study to evaluate the proposed approach with the comparison to the existing robust GP approaches under various simulated scenarios of different outlier proportions and different noise levels. The approach is applied to data from two measurement systems, where the predictors are based on robust environmental parameter measurements and the response variables utilize more complex chemical sensing methods that contain a certain percentage of outliers. The utility of the measurement systems and value of the environmental data are improved through the computationally efficient GP regression and bias model.

Bias correction for linear discriminant analysis

• We present an asymptotically exact estimator of the optimal intercept for the linear discriminant analysis (LDA). • The proposed accurate estimator is developed based on the theory of random matrices of increasing dimension. • The simple form of the estimator provides analytical insights into the mechanism of the proposed bias correction in LDA. • Analytical insights are complemented by empirical observations. Linear discriminant analysis (LDA) is perhaps one of the most fundamental statistical pattern recognition techniques. In this work, we explicitly present, for the first time, an asymptotically exact estimator of the LDA optimal intercept in terms of achieving the lowest overall risk in the classification of two multivariate Gaussian distributions with a common covariance matrix and arbitrary misclassification costs. The proposed estimator of the optimal bias term is developed based on the theory of random matrices of increasing dimension in which the observation dimension and the sample size tend to infinity while keeping their magnitudes comparable. The simple form of this estimator provides us with some analytical insights into the working mechanism of the bias correction in LDA. We then complement these analytical insights with numerical experiments. In particular, empirical results using real data show that insofar as the overall risk is concerned, the proposed bias-corrected form of LDA can outperform the conventional LDA classifier in a wide range of misclassification costs. At the same time, the superiority of the proposed form over LDA tends to be more evident as dimensionality or the ratio between class-specific costs increase.

When bias contributes to variance: True limit theory in functional coefficient cointegrating regression

Limit distribution theory in the econometric literature for functional coefficient cointegrating regression is incorrect in important ways, influencing rates of convergence, distributional properties, and practical work. The correct limit theory reveals that components from both bias and variance terms contribute to variability in the asymptotics. The errors in the literature arise because random variability in the bias term has been neglected in earlier research. In stationary regression this random variability is of smaller order and can be ignored in asymptotic analysis but not without consequences for finite sample performance. Implications of the findings for rate efficient estimation are discussed. Simulations in the Online Supplement provide further evidence supporting the new limit theory in nonstationary functional coefficient regressions.

Handling Measurement Delay in Iterative Real-Time Optimization Methods

This paper is concerned with the real-time optimization (RTO) of chemical plants, i.e., the optimization of the steady-state operating points during operation, based on inaccurate models. Specifically, modifier adaptation is employed to cope with the plant-model mismatch, which corrects the plant model and the constraint functions by bias and gradient correction terms that are computed from measured variables at the steady-states of the plant. This implies that the sampling time of the iterative RTO scheme is lower-bounded by the time to reach a new steady-state after the previously computed inputs were applied. If analytical process measurements (PAT technology) are used to obtain the steady-state responses, time delays occur due to the measurement delay of the PAT device and due to the transportation delay if the samples are transported to the instrument via pipes. This situation is quite common because the PAT devices can often only be installed at a certain distance from the measurement location. The presence of these time delays slows down the iterative real-time optimization, as the time from the application of a new set of inputs to receiving the steady-state information increases further. In this paper, a proactive perturbation scheme is proposed to efficiently utilize the idle time by intelligently scheduling the process inputs taking into account the time delays to obtain the steady-state process measurements. The performance of the proposed proactive perturbation scheme is demonstrated for two examples, the Williams–Otto reactor benchmark and a lithiation process. The simulation results show that the proposed proactive perturbation scheme can speed up the convergence to the true plant optimum significantly.

Autocalibration and Tweedie-dominance for insurance pricing with machine learning

Boosting techniques and neural networks are particularly effective machine learning methods for insurance pricing. Often in practice, the sum of fitted values can depart from the observed totals to a large extent. The possible lack of balance when models are trained by minimizing deviance outside the familiar GLM with canonical link setting has been documented in Wüthrich (2019, 2020, 2021). The present paper aims to further study this phenomenon when learning proceeds by minimizing Tweedie deviance. It is shown that minimizing deviance involves a trade-off between the integral of weighted differences of lower partial moments and the bias measured on a specific scale. Hence, there is no guarantee that the sum of fitted values stays close to observed totals if the latter bias term is dominated by the former one entering deviance. Autocalibration is then proposed as a remedy. This new method to correct for bias adds an extra local GLM step to the analysis with the output of the first step as only predictor. Theoretically, it is shown that it implements the autocalibration concept in pure premium calculation and ensures that balance also holds on a local scale, not only at portfolio level as with existing bias-correction techniques.

Source enumeration via RMT estimator with adaptive decision criterion based on linear shrinkage estimation of noise eigenvalues using relatively few samples

Estimating the number of signals embedded in noise is a fundamental problem in array signal processing. The classic random matrix theory (RMT) estimator based on RMT does not consider the bias term of the expectation of the eigenvalue being tested, and thus, its detection performance will be affected by this bias term, and it also suffers from noise uncertainty in its decision threshold. In order to overcome these problems, more accurate expressions for the distribution and the bias term of the expectation of the eigenvalue being tested are firstly derived by utilising the linear shrinkage (LS) technique. Then, a novel LS-RMT estimator is proposed by incorporating the bias term of the expectation of the eigenvalue being tested into the decision criterion of the RMT estimator. Moreover, both the increased under-estimation probability and the increased over-estimation probability of the RMT estimator incurred by this bias term are derived according to the sign of this bias term. Based on these results, a novel LS-RMT estimator with adaptive decision criterion (termed as ‘LS-RMT-ADC estimator’) is proposed by utilising the LS-RMT estimator, and the proposed LS-RMT-ADC estimator can adaptively select its decision threshold and determine the noise variance in the selected decision threshold. Therefore, it can overcome both the higher under-estimation probability and the higher over-estimation probability of the RMT estimator, and can also avoid the noise uncertainty in the decision threshold of the RMT estimator. Finally, simulation results are presented to show that the LS-RMT-ADC estimator outperforms the existing estimators.

Splitting Algorithms for Rare Events of Semimartingale Reflecting Brownian Motions

We study rare event simulations of semimartingale reflecting Brownian motions (SRBMs) in an orthant. The rare event of interest is that a d-dimensional positive recurrent SRBM enters the set [Formula: see text] before hitting a small neighborhood of the origin [Formula: see text] as [Formula: see text] with a starting point outside the two sets and of order o(n). We show that, under two regularity conditions (the Dupuis–Williams stability condition of the SRBM and the Lipschitz continuity assumption of the associated Skorokhod problem), the probability of the rare event satisfies a large deviation principle. To study the variational problem (VP) for the rare event in two dimensions, we adapt its exact solution from developed by Avram, Dai, and Hasenbein in 2001. In three and higher dimensions, we construct a novel subsolution to the VP under a further assumption that the reflection matrix of the SRBM is a nonsingular [Formula: see text]-matrix. Based on the solution/subsolution, particle-based simulation algorithms are constructed to estimate the probability of the rare event. Our estimator is asymptotically optimal for the discretized problem in two dimensions and has exponentially superior performance over standard Monte Carlo in three and higher dimensions. In addition, we establish that the growth rate of the relative bias term arising from discretization is subexponential in all dimensions. Therefore, we can estimate the probability of interest with subexponential complexity growth in two dimensions. In three and higher dimensions, the computational complexity of our estimators has a strictly smaller exponential growth rate than the standard Monte Carlo estimators.

Three-Dimensional Nonsingular Cooperative Guidance Law with Different Field-of-View Constraints

In this paper, a distributed three-dimensional (3D) nonsingular cooperative guidance law is designed for multiple missiles with different seeker’s field-of-view (FOV) constraints to achieve salvo attack against a stationary target. The guidance law is derived from an extended biased proportional navigation guidance (PNG). The PNG is augmented by a cooperative guidance term to ensure that times-to-go of the missile group reach consensus in a fixed time before interception. Two auxiliary functions are included into the biased guidance term to guarantee nonsingularity of the guidance law and meet the FOV constraints. The proposed design does not require guidance law switching that is used in some existing biased or multistage guidance designs, which allows for a smooth guidance command. A feasible impact time set is given for the cooperative mission when applying the proposed guidance law. The nonsingularity, FOV constraint satisfaction, and closed-loop stability of the proposed guidance law are theoretically analyzed and proved. Moreover, the criteria for selecting all guidance parameters are provided to facilitate the guidance design. Finally, numerical simulations with comparative studies are conducted to verify the effectiveness of the proposed guidance law and demonstrate the advantages over existing cooperative guidance laws.

Basin and Site Effects in the U.S. Pacific Northwest Estimated from Small-Magnitude Earthquakes

ABSTRACTEarthquake hazards in the U.S. Pacific Northwest (PNW) are increased by the presence of deep sedimentary basins that amplify and prolong ground shaking. To better understand basin and site effects on ground motions, we compile a database of recordings from crustal and intraslab earthquakes. We process 8028 records with magnitudes from 3.5 to 6.8 and hypocentral depths up to 62 km to compute Fourier amplitude spectra of ground acceleration for frequencies of 0–20 Hz. We compute residuals relative to the Bayless and Abrahamson (2019; hereafter, BA18) ground-motion model and perform a series of linear, crossed, mixed-effects regressions. In addition to estimating the bias, event, and site terms, we incorporate groupings for broad regionalized site response in three different regions (Seattle basin, Puget Lowland, non-Puget Lowland), for effects from seismotectonic regime (crustal and intraslab sources), and for interactions between the regions and seismotectonic regimes. We find that the scaling of site response with respect to VS30 (time-averaged shear-wave velocity from the surface to a depth of 30 m) and to basin depth indicators Z1.0 and Z2.5 (depths to the 1.0 and 2.5 km/s shear-wave velocity horizons) is generally consistent with BA18; however, the region terms display strong spatial amplification patterns. For frequencies less than 5 Hz, the Seattle basin amplifies ground motions up to a factor of four, relative to the non-Puget Lowland, with a maximum amplification around near 0.5 Hz. Sites in the Puget Lowland amplify low frequencies up to a factor of 2.5. At higher frequencies (f>5 Hz), the Puget Lowland and Seattle basin show regional deamplification of ground motions, with the smallest average amplification factor of 0.65 occurring at 10.0 Hz. Although we observe slight differences in the seismotectonic regime terms, we find that the region terms are significantly more important for modeling earthquake hazard in the PNW.

Comprehensive evaluation of satellite-based and reanalysis soil moisture products using in situ observations over China

Abstract. Soil moisture (SM) plays a critical role in the water and energy cycles of the Earth system; consequently, a long-term SM product with high quality is urgently needed. In this study, five SM products, including one microwave remote sensing product – the European Space Agency's Climate Change Initiative (ESA CCI) – and four reanalysis data sets – European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis – Interim (ERA-Interim), National Centers for Environmental Prediction (NCEP), the 20th Century Reanalysis Project from National Oceanic and Atmospheric Administration (NOAA), and the ECMWF Reanalysis 5 (ERA5) – are systematically evaluated using in situ measurements during 1981–2013 in four climate regions at different timescales over the Chinese mainland. The results show that ESA CCI is closest to the observations in terms of both the spatial distributions and magnitude of the monthly SM. All reanalysis products tend to overestimate soil moisture in all regions but have higher correlations than the remote sensing product except in Northwest China. The largest inconsistency is found in southern Northeast China region, with an unbiased root mean square error (ubRMSE) value larger than 0.04. However, all products exhibit certain weaknesses in representing the interannual variation in SM. The largest relative bias of 144.4 % is found for the ERA-Interim SM product under extreme and severe wet conditions in northeastern China, and the lowest relative bias is found for the ESA CCI SM product, with the minimum of 0.48 % under extreme and severe wet conditions in northwestern China. Decomposing mean square errors suggests that the bias terms are the dominant contribution for all products, and the correlation term is large for ESA CCI. As a result, the ESA CCI SM product is a good option for long-term hydrometeorological applications on the Chinese mainland. ERA5 is also a promising product, especially in northern and northwestern China in terms of low bias and high correlation coefficient. This long-term intercomparison study provides clues for SM product enhancement and further hydrological applications.

Prioritizing of volatility models: a computational analysis using data envelopment analysis

AbstractEconomic crisis and uncertainty in global status quo affect stock markets around the world. This fact imposes improvement in the development of volatility models. However, the comparison among volatility models cannot be made based on a single‐error measure as a model can perform better in one‐error measure and worst in another. In this paper, we propose a two‐stage approach for prioritizing volatility models, where in the first stage we develop a novel slack‐based data envelopment analysis to rank volatility models. The robustness of the proposed approach has also been investigated using cluster analysis. In the second‐stage analysis, it is investigated whether the efficiency scores depend on model characteristics. These attributes concern the time needed in order to estimate the model, the value of Akaike Information Criterion, the number of models' significant parameters, groups and bias terms, and the error sum of squares (ESS). Further, dummy variables have been introduced to the regression model in order to find whether the employed model includes an in‐mean effect, whether the assumed distribution is skewed, and whether the employed model belongs to the generalized autoregressive conditional heteroskedasticity (GARCH) family. The main findings of this research show that the number of models' statistically significant coefficients, ESS, and in‐mean effects tend to increase the efficiency scores, while time elapsed, the number of statistically significant bias terms, and skewed error distributions tend to decrease the efficiency score.

Extended dynamic mode decomposition for inhomogeneous problems

Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for systems described by homogeneous partial differential equations (PDEs) with homogeneous boundary conditions. We propose an extended dynamic mode decomposition (xDMD) approach to cope with the potential unknown sources/sinks in PDEs. Motivated by similar ideas in deep neural networks, we equip our xDMD with two new features. First, it has a bias term, which accounts for inhomogeneity of PDEs and/or boundary conditions. Second, instead of learning a flow map, xDMD learns the residual increment by subtracting the identity operator. Our theoretical error analysis demonstrates the improved accuracy of xDMD relative to standard DMD. Several numerical examples are presented to illustrate this result.

Modified Linear Scaling and Quantile Mapping Mean Bias Correction of MODIS Land Surface Temperature for Surface Air Temperature Estimation for the Lowland Areas of Peninsular Malaysia

MODIS land surface temperature data (MODIS Ts) products are quantified from the earth surface’s reflected thermal infrared signal via sensors onboard the Terra and Aqua satellites. MODIS Ts products are a great value to many environmental applications but often subject to discrepancies when compared to the air temperature (Ta) data that represent the temperature measured at 2 m above the ground surface. Although they are different in their nature, the relationship between Ts and Ta has been established by many researchers. Further validation and correction on the relationship between these two has enabled the estimation of Ta from MODIS Ts products in order to overcome the limitation of Ta that can only provide data in a point form with a very limited area coverage. Therefore, this study was conducted with the objective to assess the accuracy of MODIS Ts products, i.e., MOD11A1, MOD11A2, MYD11A1, and MYD11A2 against Ta and to identify the performance of a modified Linear Scaling using a constant and monthly correction factor (LS-MBC), and Quantile Mapping Mean Bias Correction (QM-MBC) methods for lowland area of Peninsular Malaysia. Furthermore, the correction factor (CF) values for each MBC were adjusted according to the condition set depending on the different bias levels. Then, the performance of the pre- and post-MBC correction for by stations and regions analysis were evaluated through root mean square error (RMSE), percentage bias (PBIAS), mean absolute error (MAE), and correlation coefficient (r). The region dataset is obtained by stacking the air temperature (Ta_r) and surface temperature (Ts_r) data corresponding to the number of stations within the identified regions. The assessment of pre-MBC data for both 36 stations and 5 regions demonstrated poor correspondence with high average errors and percentage biases, i.e., RMSE = 3.33–5.42 °C, PBIAS = 1.36–12.07%, MAE = 2.88–4.89 °C, and r = 0.16–0.29. The application of the MBCs has successfully reduced the errors and bias percentages, and slightly increased the r values for all MODIS Ts products. All post-MBC depicted good average accuracies (RMSE and MAE < 3 °C and PBIAS between ±5%) and r between 0.18 and 0.31. In detail, for the station analysis, the LS-MBC using monthly CF recorded better performance than the LS-MBC using constant CF or the QM-MBC. For the regional study, the QM-MBC outperformed the others. This study illustrated that the proposed LS-MBC, in spite of its simplicity, managed to perform well in reducing the error and bias terms of MODIS Ts as much as the performance of the more complex QM-MBC method.

Principal Component Wavelet Networks for Solving Linear Inverse Problems

In this paper we propose a novel learning-based wavelet transform and demonstrate its utility as a representation in solving a number of linear inverse problems—these are asymmetric problems, where the forward problem is easy to solve, but the inverse is difficult and often ill-posed. The wavelet decomposition is comprised of the application of an invertible 2D wavelet filter-bank comprising symmetric and anti-symmetric filters, in combination with a set of 1×1 convolution filters learnt from Principal Component Analysis (PCA). The 1×1 filters are needed to control the size of the decomposition. We show that the application of PCA across wavelet subbands in this way produces an architecture equivalent to a separable Convolutional Neural Network (CNN), with the principal components forming the 1×1 filters and the subtraction of the mean forming the bias terms. The use of an invertible filter bank and (approximately) invertible PCA allows us to create a deep autoencoder very simply, and avoids issues of overfitting. We investigate the construction and learning of such networks, and their application to linear inverse problems via the Alternating Direction of Multipliers Method (ADMM). We use our network as a drop-in replacement for traditional discrete wavelet transform, using wavelet shrinkage as the projection operator. The results show good potential on a number of inverse problems such as compressive sensing, in-painting, denoising and super-resolution, and significantly close the performance gap with Generative Adversarial Network (GAN)-based methods.

Dynamic phase transition properties and metamagnetic anomalies of kinetic Ising model in the presence of additive white noise

Using Monte Carlo simulations based on the Metropolis algorithm, we investigate the dynamic phase transition properties of a kinetic Ising model driven by a sinusoidally oscillating magnetic field in the presence of additive white noise, as well as a time independent bias term. By performing a detailed finite-size scaling analysis, we estimate the critical exponent ratios corresponding to the dynamic order parameter and the associated scaled variance, and we calculate the critical field below which the system exhibits a dynamic ferromagnetic phase. As a general result, we show that for a noisy system, DPT does not fall into the conventional universality class of the two-dimensional kinetic Ising model. Finally, as a peculiar phenomenon observed in dynamic phase transitions, we explore the evolution of anomalous metamagnetic fluctuations as a function of the noise. Our results show evidence that the bias field at which the metamagnetic anomaly occurs tends to extend towards the oscillation amplitude of the periodic magnetic field.

Local calibration and Implementation of AASHTOWARE Pavement ME performance models for Oklahoma pavement systems

ABSTRACT AASHTOWare Pavement ME Design software was developed as an advanced pavement design tool based on the mechanistic-empirical pavement design guide. Existing performance prediction models utilised in this design guide are nationally calibrated, and it is essential to calibrate these models based on the specific local materials and environmental conditions, and pavement performance information. In this study, Pavement ME Design prediction models, including IRI, rutting, top-down and bottom-up fatigue cracking, and transverse cracking models were calibrated for the state of Oklahoma. The predictions from distress and international roughness index models were evaluated and compared with the measured distress values, and the accuracy and bias terms of each model were determined. Nationally calibrated models showed large errors and significant bias values, which asserts the need for local calibration. Locally calibrated coefficients of distresses and international roughness index models for the Oklahoma pavement system were determined. Predictions from calibrated models show that the use of calibrated coefficients improves Pavement ME predictions and the design of flexible pavements in the state. The impact of the local calibration of Pavement ME on flexible pavement designs was analysed. Locally calibrated models lead to lower IRI prediction and higher fatigue cracking and rutting in the designs.

An incidental parameters free inference approach for panels with common shocks

This paper develops a novel Method of Moments approach for panel data models with endogenous regressors and unobserved common factors. The proposed approach does not require estimating explicitly a large number of parameters in either time-series or cross-sectional dimension, T and N respectively. Hence, it is free from the incidental parameter problem. In particular, the proposed approach does not suffer from “Nickell bias” of order O(T−1), nor from bias terms that are of order O(N−1). Therefore, it can operate under substantially weaker restrictions compared to existing large T procedures. Two alternative GMM estimators are analyzed; one makes use of a fixed number of “averaged estimating equations” à la Anderson and Hsiao (1982), whereas the other one makes use of “stacked estimating equations”, the total number of which increases at the rate of O(T). It is demonstrated that both estimators are consistent and asymptotically mixed-normal as N→∞ for any value of T. Low-level conditions that ensure local and global identification in this setup are examined using several examples.

Generalized Variant Support Vector Machine

With the advancement in information technology, datasets with an enormous amount of data are available. The classification task on these datasets is more time- and memory-consuming as the number of data increases. The support vector machine (SVM), which is arguably the most popular classification technique, has disappointing performance in dealing with large datasets due to its constrained optimization problem. To deal with this challenge, the variant SVM (VSVM) has been utilized which has the fraction (1/2)b <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in its primal objective function, where b is the bias of the desired hyperplane. The VSVM has been solved with different optimization techniques in more time- and memory-efficient fashion. However, there is no guarantee that its optimal solution is the same as the standard SVM. In this paper, we introduce the generalized VSVM (GVSVM) which has the fraction (1/2t)b <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in its primal objective function, for a fixed positive scalar t. Further, we present the thorough theoretical insights that indicate the optimal solution of the GVSVM tends to the optimal solution of the standard SVM as t → ∞. One vital corollary is to derive a closed-form formula to obtain the bias term in the standard SVM. Such a formula obviates the need of approximating it, which is the modus operandi to date. An efficient neural network is then proposed to solve the GVSVM dual problem, which is asymptotically stable in the sense of Lyapunov and converges globally exponentially to the exact solution of the GVSVM. The proposed neural network has less complexity in architecture and needs fewer computations in each iteration in comparison to the existing neural solutions. Experiments confirm the efficacy of the proposed recurrent neural network and the proximity of the GVSVM and the standard SVM solutions with more significant values of t.