有序加权平均支持向量回归
Ordered Weighted Average Support Vector Regression
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中文总结 AI 辅助
本文提出一种结合有序加权平均算子的支持向量回归模型，通过两种非线性公式及三种启发式方法，在真实与合成数据上实现高效且准确的回归预测。
中文摘要 AI 辅助
本文提出了一种新颖的支持向量回归（SVR）模型，该模型引入有序加权平均（OWA）算子，以不同方式惩罚观测值相对于ε带的偏差。惩罚取决于每个偏差在所有偏差的有序向量中的位置。本文的一个关键贡献是开发了两种非线性公式：一种用于非递减单调权重向量的连续公式，以及一种用于一般权重向量的混合整数公式。通过利用与这些公式相关的对偶方法，该模型能够容纳非线性核函数。为了提高计算效率，提出了两种启发式方法，用于在减少的计算时间内推导合适的回归超平面，与精确方法相比。此外，还开发了第三种启发式方法，以有效处理非线性核函数。在真实和合成数据集上进行的计算实验表明，精确公式在以下标准指标方面产生了显著的回归函数：平均绝对误差（MAE）和均方误差（MSE）。启发式方法被证明对于较大的数据集特别有效，在解质量和计算工作量之间取得了平衡。
英文摘要
This paper introduces a novel Support Vector Regression (SVR) model that incorporates Ordered Weighted Average (OWA) operators to differently penalize deviations of observations from the ε-strip. The penalty is determined based on the position of each deviation in the ordered vector of all deviations. A key contribution of this work is the development of two nonlinear formulations: a continuous formulation for non-decreasing monotone weight vectors and a mixed-integer formulation for general weight vectors. By leveraging dual approaches associated with these formulations, the model accommodates nonlinear kernel functions. To enhance computational efficiency, two heuristic approaches are proposed for deriving suitable regression hyperplanes in reduced computation times, as compared to exact methods. Additionally, a third heuristic approach is developed to handle nonlinear kernel functions effectively. Computational experiments conducted on both real and synthetic datasets demonstrate that the exact formulations yield remarkable regression functions with respect to the following standard metrics: mean absolute errors (MAE) and mean squared errors (MSE). The heuristic approaches are shown to be particularly efficient for larger datasets, striking a balance between solution quality and computational effort.
发表机构
- Universidad de Cádiz（加的斯大学）
- Instituto de Matemáticas de la Universidad de Sevilla (IMUS)（塞维利亚大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
