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Imbalanced domain prediction analysis is currently one of the hot research topics. Many real‐world data mining analyses involve using imbalanced data to obtain predictive models. In the context of imbalance, research on classification problems has been extensive, but research on regression problems is negligible. Rare values rarely occur in imbalanced regression problems, but the focus is on accurately predicting the continuous target variables of rare instances. One of the challenges in imbalanced regression is finding a suitable strategy to rebalance the original dataset in order to improve the predictive performance of the model in rare instances. In this study, two algorithms are proposed: sigma nearest over‐sampling based on convex combination for regression (SNOCCR) and affine combination‐based over‐sampling (ACOS). ACOS rebalances the original dataset by generating new instances through the affine combinations of the original examples. The region where the new instances are generated can be adjusted based on the distribution of the data, ensuring that the generated cases better mimic the distribution of the original examples. The comparison among ACOS, SNOCCR, and other preprocessing methods was conducted on 15 datasets to validate the predictive performance of models trained on rebalanced datasets for rare instances. The experimental results indicate that ACOS outperforms other existing methods. In this study, two over‐sampling algorithms are proposed: sigma nearest over‐sampling based on convex combination for regression (SNOCCR) and affine combination‐based over‐sampling (ACOS) in order to improve the predictive performance of the model in imbalanced regression. The experimental results indicate that ACOS outperforms other existing methods. [ABSTRACT FROM AUTHOR]

Classical symmetric distributions like the Gaussian are widely used. However, in reality data often display a lack of symmetry. Multiple distributions, grouped under the name "skewed distributions", have been developed to specifically cope with asymmetric data. In this paper, we present a broad family of flexible multivariate skewed distributions for which statistical inference is a feasible task. The studied family of multivariate skewed distributions is derived by taking affine combinations of independent univariate distributions. These are members of a flexible family of univariate asymmetric distributions and are an important basis for achieving statistical inference. Besides basic properties of the proposed distributions, also statistical inference based on a maximum likelihood approach is presented. We show that under mild conditions, weak consistency and asymptotic normality of the maximum likelihood estimators hold. These results are supported by a simulation study confirming the developed theoretical results, and some data examples to illustrate practical applicability. [ABSTRACT FROM AUTHOR]

The performance of conventional active noise control (ANC) systems degrades under non-Gaussian conditions. In the recent past, generalized filtered-x maximum correntropy criterion (FxGMCC) algorithm has been widely used to tackle such non-Gaussian noises. However, noise reduction performance of maximum correntropy criterion (MCC) based algorithms degrades due to the high steady-state misalignment. To overcome this limitation, a filtered-x exponential hyperbolic cosine adaptive filter (FxEHCAF) algorithm is proposed in this paper. Later, an affine combination technique has been applied and the corresponding affine FxEHCAF (A-FxEHCAF) algorithm has been developed here showing faster convergence rate in transient state along with low residual error in steady-state. Simulation study shows that the proposed FxEHCAF and A-FxEHCAF algorithms provide enhanced noise control performance over other existing algorithms. • A robust FxEHCAF algorithm based ANC technique is proposed. • Affine-FxEHCAF algorithm for enhanced noise control is also proposed. • The theoretical analysis of FxEHCAF and Affine-FxEHCAF are carried out. • Proposed algorithms provide improved ANC performance. [ABSTRACT FROM AUTHOR]

The affine combination of two complex-valued least-mean-squares filters (aff-CLMS) addresses the trade-off between fast convergence rate and small steady-state misadjustment error. However, a rigorous analysis of the aff-CLMS algorithm for second-order non-circular inputs is still under investigation. To this end, the focus in this letter is on the full mean-square analysis of the aff-CLMS algorithm, in which the transient analyses of the mixing parameter, as well as the standard and complementary weight-error covariance matrices, are completed. In addition, we derive the closed-form solutions of the steady-state weight-error power and its complementary version of the aff-CLMS. Finally, the effectiveness of the theoretical analysis is supported by computer simulations. [ABSTRACT FROM AUTHOR]

We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a linear combination of two copulas. This generalizes a recent result of Fernández-Sánchez, Quesada-Molina, and Úbeda-Flores who considered linear combinations of discrete copulas. [ABSTRACT FROM AUTHOR]

Adaptive filters are extensively used in the identification of an unknown system. Unlike several gradient-search based adaptive filtering techniques, the Lyapunov Theory-based Adaptive Filter offers improved convergence and stability. When the system is described by a sparse model, the performance of Lyapunov Adaptive (LA) filter is degraded since it fails to exploit the system sparsity. In this paper, the Zero-Attracting Lyapunov Adaptation algorithm (ZA-LA), the Reweighted Zero-Attracting Lyapunov Adaptation algorithm (RZA-LA) and an affine combination scheme of the LA and proposed ZA-LA filters are proposed. The ZA-LA algorithm is based on ℓ1-norm relaxation while the RZA-LA algorithm uses a log-sum penalty to accelerate convergence when identifying sparse systems. It is shown by simulations that the proposed algorithms can achieve better convergence than the existing LMS/LA filter for a sparse system, while the affine combination scheme is robust in identifying systems with variable sparsity.

This work presents a data driven control strategy able to track a set point without steady‐state error. The control sequence is computed as an affine combination of past control signals, which belong to a set of trajectories stored in a process historian database. This affine combination is computed so that the variance of the tracking error is minimised. It is shown that offset free control, that is zero mean tracking error, is achieved under the assumption that the state is measurable, the underlying dynamics are linear and the trajectories of the database share the same error dynamics and are in turn offset free. The proposed strategy learns the underlying controller stored in the database while maintaining its offset free tracking capability in spite of differences in the reference, disturbances and operating conditions. No training phase is required and newly obtained process data can be easily taken into account. The proposed strategy, related to direct weight optimisation learning techniques, is tested on a process control trainer. [ABSTRACT FROM AUTHOR]

In this paper we prove a recursive identity for the cumulative distribution function of a linear combination of independent exponential random variables. The result is then extended to probability density function, expected value of functions of a linear combination of independent exponential random variables, and other functions. Our goal is on the exact and approximate calculation of the above mentioned functions and expected values. We study this computational problem from different views, namely as a Hermite interpolation problem, and as a matrix function evaluation problem. Examples are presented to illustrate the applicability and performance of the methods. [ABSTRACT FROM AUTHOR]

Spurious induced oscillations have been one of the fundamental problem associated with numerical approximation of the solution of hyperbolic conservation laws. In this note, using notion of data dependent stability, generic three point schemes for scalar case are analysed to show that the induced oscillations depend on initial data too. Further, it is concluded that it is not possible to have an initial data independent, 'uniformly' non-oscillatory three point fixed stencil scheme irrespective of its accuracy. [ABSTRACT FROM AUTHOR]

Adaptive filters are extensively used in the identification of an unknown system. Unlike several gradient-search based adaptive filtering techniques, the Lyapunov Theory-based Adaptive Filter offers improved convergence and stability. When the system is described by a sparse model, the performance of Lyapunov Adaptive (LA) filter is degraded since it fails to exploit the system sparsity. In this paper, the Zero-Attracting Lyapunov Adaptation algorithm (ZA-LA), the Reweighted Zero-Attracting Lyapunov Adaptation algorithm (RZA-LA) and an affine combination scheme of the LA and proposed ZA-LA filters are proposed. The ZA-LA algorithm is based on l-norm relaxation while the RZA-LA algorithm uses a log-sum penalty to accelerate convergence when identifying sparse systems. It is shown by simulations that the proposed algorithms can achieve better convergence than the existing LMS/LA filter for a sparse system, while the affine combination scheme is robust in identifying systems with variable sparsity. [ABSTRACT FROM AUTHOR]

A mental health trial is analyzed using a dose-response model, in which the number of sessions attended by the patients is deemed indicative of the dose of psychotherapeutic treatment. Here, the parameter of interest is the difference in causal treatment effects between the subpopulations that take part in different numbers of therapy sessions. For this data set, interactions between random treatment allocation and prognostic baseline variables provide the requisite instrumental variables. While the corresponding two-stage least squares (TSLS) estimator tends to have smaller bias than the ordinary least squares (OLS) estimator; the TSLS suffers from larger variance. It is therefore appealing to combine the desirable properties of the OLS and TSLS estimators. Such a trade-off is achieved through an affine combination of these two estimators, using mean squared error as a criterion. This produces the semi-parametric Stein-like (SPSL) estimator as introduced by Judge and Mittelhammer (2004). The SPSL estimator is used in conjunction with multiple imputation with chained equations, to provide an estimator that can exploit all available information. Simulated data are also generated to illustrate the superiority of the SPSL estimator over its OLS and TSLS counterparts. A package entitled SteinIV implementing these methods has been made available through the R platform. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a modified Hestenes–Stiefel conjugate gradient method for unconstrained problems is developed, which can achieves the twin goals of generating sufficient descent direction at each iteration as well as being close to the Newton direction. In our methods, the hybridization parameter can also be obtained based on other kinds of conjugacy conditions. Under mild condition, we establish their global convergence for general objective functions. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising. [ABSTRACT FROM PUBLISHER]

We introduce a new combination approach for the mixture of adaptive filters based on the set-membership filtering (SMF) framework. We perform SMF to combine the outputs of several parallel running adaptive algorithms and propose unconstrained, affinely constrained and convexly constrained combination weight configurations. Here, we achieve better trade-off in terms of the transient and steady-state convergence performance while providing significant computational reduction. Hence, through the introduced approaches, we can greatly enhance the convergence performance of the constituent filters with a slight increase in the computational load. In this sense, our approaches are suitable for big data applications where the data should be processed in streams with highly efficient algorithms. In the numerical examples, we demonstrate the superior performance of the proposed approaches over the state of the art using the well-known datasets in the machine learning literature. [ABSTRACT FROM AUTHOR]

In this paper, we study and compare different types of generalized barycentric coordinates in detail, including Wachspress, discrete harmonic and mean value coordinates for convex, n-sided polygons. Contour lines are computed in each barycentric coordinate method, and curvature plots of these contour line curves are visualized. Moreover, different distortions of uniform patterns are also shown, providing exact visual method to compare these methods. To overcome the shortcomings of different generalized barycentric computations, affine combination of methods is provided. [ABSTRACT FROM AUTHOR]

• We propose affine combining of two ACLMS filters and present its optimal mixing parameter, based on which an explicit expression describing the steady state mean behavior of the optimal mixing parameter is quantified for doubly white noncircular Gaussian input data. The so established physical insight shows that in steady state, the optimal mixing parameter is, statistically, negative and monotonically increases against the input SO noncircularity coefficient. • Upon applying the optimal mixing parameter, we perform the MSE analysis of the proposed affine-combined ACLMS filters. The so derived explicit MSE expression not only theoretically presents the universality of the combination scheme, that is, smaller or equal steady state MSE than either of the individual ACLMS subfilters, but also demonstrates that the overall MSE in steady state is approximately a monotonic increasing function of the input SO noncircularity coefficient. • Considering that the optimal affine combiner is unacquirable in practical applications, we provide an error power based scheme to iterate the affine combiner. Numerical examples verify that the proposed iterative combiner converges to the optimal one. The overall MSE curves respectively obtained via the iterative and optimal combiners are shown to be in close agreement. This paper investigates the statistical behavior of an affine combination of two augmented complex least mean-square (ACLMS) adaptive filters for processing noncircular Gaussian signals. First, the optimal affine combiner is studied and its steady state mean behavior is explicitly quantified. This makes it possible to reveal the impact of the input second-order noncircularity coefficient on the combiner. Next, the mean square error analysis of the proposed affine-combined ACLMS filters is provided, proving that the combined scheme performs no less than the best of the individual ACLMS subfilters. Besides, to facilitate physically realization of the combination strategy, an error power based algorithm that can iterate the affine combiner to the optimal one is also proposed. Finally, illustrative numerical simulations are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Affine combination takes a weighted sum of the outputs of two adaptive filters subjected to the same input whose weighting factor is a parameter calculated using an adaptive mechanism (adaptive filters) in order to achieve a better performance. This study operationalized the behavior of Algorithm Accelerator Version γ (ARγ ) in Affine combination in order to achieve greater efficiency and better performance than the algorithm presented in its basic configuration; likewise identify the effects of the Affine Combination Algorithm Accelerator Version γ (ARγ ) adaptive algorithm. The methodological design and operational plan are part of a research process with a descriptive, explanatory and directed experimental answer why the phenomenon occurs (application of adaptive filters in Affine Combination ) and under what conditions it occurs. [ABSTRACT FROM AUTHOR]

In this paper, we combine the application of different forms of Jensen's inequality to convex and affine combinations. Using this approach we obtained several extensions of the functional form of Jensen's inequality for affine combinations of real valued functions. One of the resulting inequalities is applied to quasi-arithmetic means. [ABSTRACT FROM AUTHOR]

Abstract: The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions. [Copyright &y& Elsevier]

In this paper, we propose an approach to the transient and steady-state analysis of the affine combination of one fast and one slow adaptive filters. The theoretical models are based on expressions for the excess mean-square error (EMSE) and cross-EMSE of the component filters, which allows their application to different combinations of algorithms, such as least mean-squares (LMS), normalized LMS (NLMS), and constant modulus algorithm (CMA), considering white or colored inputs and stationary or nonstationary environments. Since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant, its adaptation is also taken into account in the transient analysis. Furthermore, we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance. Good agreement between analysis and simulation results is always observed. [ABSTRACT FROM AUTHOR]

A general affine combination of B-spline subdivision masks is here considered with the aim of generating new subdivision schemes with enhanced properties. This will be done using either stationary or non-stationary coefficients combining both B-splines and their non-stationary counterparts. [ABSTRACT FROM AUTHOR]

This paper studies the statistical behavior of an affine combination of the outputs of two least mean-square (LMS) adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor λ(n) is restricted to the interval (0,1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the mean-square error (MSE). First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSDs of either filter. [ABSTRACT FROM AUTHOR]

Abstract: Generalizing the result in Lemma of Baksalary and Baksalary [J.K. Baksalary, O.M. Baksalary, Commutativity of projectors, Linear Algebra Appl. 341 (2002) 129–142], Baksalary et al. [J.K. Baksalary, O.M. Baksalary, T. Szulc, Linear Algebra Appl. 354 (2002) 35–39] have shown that if P 1 and P 2 are orthogonal projectors, then, in all nontrivial situations, a product of any length having P 1 and P 2 as its factors occurring alternately is equal to another such product if and only if P 1 and P 2 commute, in which case all products involving P 1 and P 2 reduce to the orthogonal projector P 1 P 2 (= P 2 P 1). In the present paper, further generalizations of this property are established. They consist in replacing a product of the type specified above, appearing on the left-hand side (say) of the equality under considerations, by an affine combination of two or three such products. Comments on the problem when the number of components in a combination exceeds three are also given. [Copyright &y& Elsevier]