超限学习机鲁棒模型及在金融时间序列预测中的应用

In recent years, some valuable results have been derived on extreme learning machine (ELM). However, most existing ELMs always adopt mean squares error (MSE) to express the empirical risk, which is optimal only under the Gaussian distribution error. In many practical applications, training samples may not be guaranteed the Gaussian distribution error, such as instrument errors, sample errors and modeling errors, which causes the sensitivity to noise samples and poor robustness in considering the performance of ELM. Recent researches found that non-convex loss function and correntropy function in machine learning have been shown better robustness. From this perspective, this project intends to employ non-convex optimization, half-quadratic optimization and kernel trick to study the robust extreme learning machine models and their algorithms. The detailed contents consist of the following aspects: (1) For label noise/target noise and imbalanced data sets, we will establish more practical robust extreme learning machine models based on non-convex loss function, correntropy function and asymmetric loss function. (2) Moreover, we will completely analyze the robustness of these models, the convergence and computational complexity of the algorithms. (3) The project also explores the robust extreme learning machines to the stock closing prices prediction and risk control in the financial time series. The implementation of the project will not only enrich the related theories of ELM, but also lay a practical foundation for its application in more fields.

近年来，超限学习机的研究已涌现出许多有价值的成果，这些成果基本都使用均方误差准则表达经验风险。该误差准则只有在训练点误差服从正态分布时是最优的。然而，许多实际应用问题并不能保证误差服从正态分布，这导致超限学习机对噪声样本点较敏感、鲁棒性差。最新的研究发现非凸损失函数和相关熵函数在机器学习中具有更强的鲁棒性。本项目拟运用非凸优化理论、半二次规划技术和核方法研究基于非凸损失函数、相关熵函数的超限学习机鲁棒模型与求解算法。内容包括：对标签噪声/目标值噪声、不均衡数据集，基于非凸损失函数、相关熵函数、不对称损失函数建立更贴近实际问题的超限学习机鲁棒模型；深入分析所建模型的鲁棒性、求解算法的收敛性和计算复杂度；将超限学习机鲁棒模型应用于金融数据领域，对金融时间序列中股票的收盘价进行预测和风险管控。项目的实施不仅能够丰富超限学习机的理论知识，而且为其在更多领域的应用提供扎实的实践基础。

本项目主要研究在噪声环境下如何提升超限学习机的学习性能。主要包括四方面内容：一是研究超限学习机回归估计鲁棒模型与算法及其应用，通过引入不同的损失函数，针对标签噪声、特征噪声的特点，建立相应的超限学习机模型，来增强模型的抗噪性和泛化能力。二是针对不均衡数据集，利用弹性网络、多层自编码器、相关熵损失函数等技术，研究单分类超限学习机鲁棒模型与算法。三是以零范数正则项、非凸损失函数为基础，研究两种稀疏鲁棒超限学习机模型与算法。四是将超限学习机鲁棒模型推广到多输出数据集，利用L21范数正则项删除超限学习机中的冗余神经元，降低模型的计算复杂度，能够有效提升模型的学习效果。本项目的实施不仅对于超限学习机是一个重要的深入和发展，而且可以促进非凸优化理论、半二次优化技术和超限学习机理论的进一步发展与完善，为超限学习机在更多实际领域的应用提供有力的实践基础。