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Learning with correntropy-induced losses for regression with mixture of symmetric stable noise

机译:使用对称稳定噪声混合的回归损失学习损失

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In recent years, correntropy and its applications in machine learning have been drawing continuous attention owing to its merits in dealing with non-Gaussian noise and outliers. However, theoretical understanding of correntropy, especially in the learning theory context, is still limited. In this study, we investigate correntropy based regression in the presence of non-Gaussian noise or outliers within the statistical learning framework. Motivated by the practical way of generating non-Gaussian noise or outliers, we introduce mixture of symmetric stable noise, which include Gaussian noise, Cauchy noise, and their mixture as special cases, to model non-Gaussian noise or outliers. We demonstrate that under the mixture of symmetric stable noise assumption, correntropy based regression can learn the conditional mean function or the conditional median function well without resorting to the finite-variance or even the finite first-order moment condition on the noise. In particular, for the above two cases, we establish asymptotic optimal learning rates for correntropy based regression estimators that are asymptotically of type O(n(-1)). These results justify the effectiveness of the correntropy based regression estimators in dealing with outliers as well as non-Gaussian noise. We believe that the present study makes a step forward towards understanding correntropy based regression from a statistical learning viewpoint, and may also shed some light on robust statistical learning for regression. (C) 2019 Elsevier Inc. All rights reserved.
机译:近年来,由于其在处理非高斯噪声和异常值的优点,对机器学习中的控制权及其在机器学习中的应用一直在推动不断的关注。然而,理论上了解管道的理解,特别是在学习理论背景下,仍然有限。在这项研究中,我们在统计学习框架内的非高斯噪声或异常值存在中调查基于对的回归。通过产生非高斯噪声或异常值的实际方法,我们引入了对称稳定噪声的混合,包括高斯噪声,Cauchy噪声以及它们的混合物,以模拟非高斯噪声或异常值。我们证明,在对称稳定噪声假设的混合物下,基于正管的回归可以在不诉诸有限差异甚至有限的一阶时刻条件的情况下学习条件平均功能或条件中值函数。特别是对于上述两种情况,我们建立了对渐近的回归估算器的渐近最佳学习率,这些回归估计是o(n(-1))的渐近渐近的。这些结果证明了基于正文基于回归估计的有效性,在处理异常值以及非高斯噪声时。我们认为,本研究向前迈向统计学习观点的基于正文的回归,并可能在稳健的统计学习中对回归的统计学习进行一些光。 (c)2019 Elsevier Inc.保留所有权利。

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