In this paper, we propose a novel bounded asymmetric elastic net ($L_{baen}$) loss function and combine it with the support vector machine (SVM), resulting in the BAEN-SVM. The $L_{baen}$ is bounded and asymmetric and can degrade to the asymmetric elastic net hinge loss, pinball loss, and asymmetric least squares loss. BAEN-SVM not only effectively handles noise-contaminated data but also addresses the geometric irrationalities in the traditional SVM. By proving the violation tolerance upper bound (VTUB) of BAEN-SVM, we show that the model is geometrically well-defined. Furthermore, we derive that the influence function of BAEN-SVM is bounded, providing a theoretical guarantee of its robustness to noise. The Fisher consistency of the model further ensures its generalization capability. Since the \( L_{\text{baen}} \) loss is non-convex, we designed a clipping dual coordinate descent-based half-quadratic algorithm to solve the non-convex optimization problem efficiently. Experimental results on artificial and benchmark datasets indicate that the proposed method outperforms classical and advanced SVMs, particularly in noisy environments.

翻译：本文提出了一种新颖的有界非对称弹性网络（$L_{baen}$）损失函数，并将其与支持向量机（SVM）相结合，形成了BAEN-SVM模型。$L_{baen}$损失函数具有有界性和非对称性，并可退化为非对称弹性网络铰链损失、弹球损失以及非对称最小二乘损失。BAEN-SVM不仅能有效处理受噪声污染的数据，还能解决传统SVM中的几何不合理性问题。通过证明BAEN-SVM的违例容忍上界（VTUB），我们表明该模型在几何上是良定义的。此外，我们推导出BAEN-SVM的影响函数是有界的，这为其对噪声的鲁棒性提供了理论保证。模型的Fisher一致性进一步确保了其泛化能力。由于$L_{\text{baen}}$损失是非凸的，我们设计了一种基于裁剪对偶坐标下降的半二次型算法，以高效求解该非凸优化问题。在人工和基准数据集上的实验结果表明，所提出的方法优于经典和先进的SVM，尤其是在噪声环境中。