Robust Capped lp-Norm Support Vector Ordinal Regression

TL;DR

This paper introduces CSVOR, a robust support vector ordinal regression model utilizing a capped $ extit{ ext{l}}_{p}$-norm loss function, designed to effectively detect and eliminate outliers, thereby improving performance on real-world noisy data.

Contribution

The paper proposes a novel capped $ extit{ ext{l}}_{p}$-norm loss function and a robust CSVOR model with a re-weighted algorithm, enhancing outlier robustness in ordinal regression.

Findings

CSVOR outperforms state-of-the-art methods in noisy data scenarios.

The model effectively detects and eliminates outliers during training.

Theoretical convergence of the re-weighted algorithm is established.

Abstract

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.