A significant limitation of one-class classification anomaly detection methods is their reliance on the assumption that unlabeled training data only contains normal instances. To overcome this impractical assumption, we propose two novel classification-based anomaly detection methods. Firstly, we introduce a semi-supervised shallow anomaly detection method based on an unbiased risk estimator. Secondly, we present a semi-supervised deep anomaly detection method utilizing a nonnegative (biased) risk estimator. We establish estimation error bounds and excess risk bounds for both risk minimizers. Additionally, we propose techniques to select appropriate regularization parameters that ensure the nonnegativity of the empirical risk in the shallow model under specific loss functions. Our extensive experiments provide strong evidence of the effectiveness of the risk-based anomaly detection methods.

翻译：一类分类异常检测方法的一个显著局限性在于其依赖于未标记训练数据仅包含正常实例的假设。为克服这一不切实际的假设，我们提出了两种基于分类的新型异常检测方法。首先，我们引入了一种基于无偏风险估计器的半监督浅层异常检测方法。其次，我们提出了一种利用非负（有偏）风险估计器的半监督深度异常检测方法。我们为这两种风险最小化方法建立了估计误差界和超额风险界。此外，我们提出了一些技术来选择合适的正则化参数，以确保在特定损失函数下浅层模型的经验风险非负。大量的实验为基于风险的异常检测方法的有效性提供了有力证据。