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Robust regression under asymmetric or/and non-constant variance error by simultaneously training conditional quantiles

机译：通过同时训练条件分位数在非对称或/和非恒定方差误差下的稳健回归

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We consider regression problems under asymmetric or/and non-constant variance error. We see this problem in several fields such as insurance premium estimation, medical cost analysis, etc. Applying the method of Least Squares (LS) to this problem yields unstable solution because of outliers that appears on one side of regression surfaces. Conventional robust techniques to deal with outliers, which intend to discard or down-weight the outliers equally from both sides of regression surfaces, does not help for asymmetric error. In this paper, we propose an robust regression estimator (an estimator of the conditional mean) under asymmetric or/and non-constant variance error by simultaneously training conditional quantiles in multi-layer perceptron (MLP). This is considered as a kind of learning from hint or multitask learning approach, i.e., we train the conditional quantile estimator as hints or extra tasks to improve generalization properties of the conditional mean estimator. Numerical experiments and an application to medical cost estimation problem have shown that our proposal has robustness and good generalization properties.
机译：我们考虑在非对称或/和非恒定方差误差下的回归问题。我们在保险费估算，医疗成本分析等多个领域中都看到了该问题。由于在回归曲面的一侧出现异常值，因此将最小二乘（LS）方法应用于此问题会产生不稳定的解决方案。常规的用于处理离群值的鲁棒技术（旨在从回归曲面的两侧均等地丢弃或缩小离群值）无助于非对称误差。在本文中，我们通过在多层感知器（MLP）中同时训练条件分位数，提出了一种在非对称或/和非恒定方差误差下的鲁棒回归估计器（条件均值的估计器）。这被认为是一种从提示或多任务学习方法中学习的方法，即，我们将条件分位数估计器训练为提示或额外任务，以改善条件均值估计器的泛化特性。数值实验及其在医疗费用估算中的应用表明，该方案具有鲁棒性和良好的泛化特性。

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