| 基于指数Laplace损失函数的回归估计鲁棒超限学习机 |
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| 引用本文： | 王快妮,曹进德,刘庆山.基于指数Laplace损失函数的回归估计鲁棒超限学习机[J].应用数学和力学,2019,40(11):1169-1178. |
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| 作者姓名： | 王快妮 曹进德 刘庆山 |
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| 作者单位： | 1西安石油大学 理学院, 西安 710065;2东南大学 数学学院, 南京 211189 |
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| 基金项目： | 国家自然科学基金（61833005；61907033）；中国博士后科学基金（2018M642129） |
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| 摘 要： | 实际问题的数据集通常受到各种噪声的影响，超限学习机(extreme learning machine, ELM)对这类数据集进行学习时，表现出预测精度低、预测结果波动大.为了克服该缺陷，采用了能够削弱噪声影响的指数Laplace损失函数.该损失函数是建立在Gauss核函数基础上，具有可微、非凸、有界且能够趋近于Laplace函数的特点.将其引入到超限学习机中，提出了鲁棒超限学习机回归估计(exponential Laplace loss function based robust ELM for regression, ELRELM)模型.利用迭代重赋权算法求解模型的优化问题.在每次迭代中，噪声样本点被赋予较小的权值，能够有效地提高预测精度.真实数据集实验验证了所提出的模型相比较于对比算法具有更优的学习性能和鲁棒性.
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| 关 键 词： | 神经网络 超限学习机 鲁棒 指数Laplace损失函数 迭代重赋权算法 |
| 收稿时间： | 2019-08-20 |
An Exponential Laplace Loss Function Based Robust ELM for Regression Estimation |
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| Affiliation: | 1School of Science, Xi’an Shiyou University, Xi’an 710065, P.R.China;2School of Mathematics, Southeast University, Nanjing 211189, P.R.China |
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| Abstract: | Datasets are often contaminated by various noises in many practical applications. The classical extreme learning machine (ELM) shows poor prediction accuracy and large fluctuation of prediction results in dealing with such datasets. To overcome this drawback, an exponential Laplace loss function was proposed, which can weaken the influences of noises. The proposed loss function is based on the Gauss kernel function, and is differentiable, non-convex, bounded and able to approach the Laplace function. Then the proposed loss function was introduced into the ELM to build a robust ELM model for regression estimation. The iterative re-weighted algorithm was employed to solve the resultant optimization problem. In each iteration, the training samples with noises were given smaller weights, which can effectively improve the prediction accuracy. Experiments on real-world datasets show that, the proposed model has better learning performance and robustness. |
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