鲁棒的带帽 lp-范数支持向量序数回归
Robust Capped lp-Norm Support Vector Ordinal Regression
AI总结：
针对支持向量序数回归在含异常值训练数据上性能下降的问题，提出带帽 $\ell_{p}$-范数损失及CSVOR模型，通过权重矩阵识别并抑制轻重异常值，并设计具有收敛保证的重加权优化算法，实验表明其尤其在异常场景下优于现有方法。
摘要：
序数回归是一种特殊的监督学习问题，其标签呈现出固有的顺序。这种顺序将其与普通多分类问题区分开来。支持向量序数回归（SVOR）作为一种出色的序数回归模型，被广泛应用于许多序数回归任务中。然而，与大多数监督学习算法一样，SVOR的设计基于训练数据真实可靠的假设，这在现实世界的数据中很难满足。在许多实际应用中，训练集中经常出现异常值，可能会误导学习过程，导致性能非最优。在本文中，我们提出了一种新颖的带帽 $\ell_{p}$-范数损失函数，该函数在理论上对轻度和重度异常值均具有鲁棒性。带帽 $\ell_{p}$-范数损失可以帮助模型在训练过程中检测并消除异常值。遵循这一概念，我们引入了一个新模型，即带帽 $\ell_{p}$-范数支持向量序数回归（CSVOR），该模型对异常值具有鲁棒性。CSVOR使用权重矩阵在训练过程中检测并消除异常值，以提高对异常值的鲁棒性。此外，我们提出了一种重加权算法，通过我们的理论结果证明了其收敛性，以有效地最小化相应问题。广泛的实验结果表明，我们的模型优于最先进（SOTA）的方法，尤其是在存在异常值的情况下。
英文摘要：
Ordinal regression is a specialized supervised problem where the labels show an inherent order. The order distinguishes it from normal multi-class problem. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is widely used in many ordinal regression tasks. However, like most supervised learning algorithms, the design of SVOR is based on the assumption that the training data are real and reliable, which is difficult to satisfy in real-world data. In many practical applications, outliers are frequently present in the training set, potentially leading to misguide the learning process, such that the performance is non-optimal. In this paper, we propose a novel capped $\ell_{p}$-norm loss function that is theoretically robust to both light and heavy outliers. The capped $\ell_{p}$-norm loss can help the model detect and eliminate outliers during training process. Adhering to this concept, we introduce a new model, Capped $\ell_{p}$-Norm Support Vector Ordinal Regression(CSVOR), that is robust to outliers. CSVOR uses a weight matrix to detect and eliminate outliers during the training process to improve the robustness to outliers. Moreover, a Re-Weighted algorithm algorithm which is illustrated convergence by our theoretical results is proposed to effectively minimize the corresponding problem. Extensive experimental results demonstrate that our model outperforms state-of-the-art(SOTA) methods, particularly in the presence of outliers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
