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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]

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]

• 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]