用数据分布形状自动调节噪声,让表格异常检测更准更省心。
Kurtosis-Guided Denoising Score Matching for Tabular Anomaly Detection

- 按每列数据分布的峰度自适应设置噪声强度
- 在半监督和全无监督场景下均达顶尖性能
- 无需复杂调参,适合真实数据中异常未知的场景
去噪得分匹配(DSM)通过训练神经网络从加噪样本中恢复得分函数(即对数密度梯度),从而学习数据分布。测试时,得分大小可反映样本与分布的一致性,自然成为异常信号。关键挑战在于扰动尺度选择:噪声过少导致稀疏区域估计不稳定,噪声过多则破坏局部结构、降低异常敏感性。当异常未知且无验证集时,超参数调优尤为困难。本文提出基于峰度的噪声缩放(K-DSM),一种针对每特征的噪声设置方法,根据各边际分布形状动态调整噪声水平,提升低密度区域覆盖率与高密度区域精度,且不增加模型复杂度。不同于以往认为需多尺度或噪声条件训练的观点,我们发现经精心训练的单尺度模型已具备强异常检测能力。在标准表格异常检测基准上,K-DSM 在半监督设置下达到当前最优性能;结合轻量级EMA教师过滤规则(每梯度步前剔除低密度训练点),在完全无监督(含污染)设置下也表现优异,表明数据自适应噪声缩放能实现稳健异常检测,同时减少对超参数调优的依赖。
原文摘要 · Abstract (English)
Denoising score matching (DSM) provides a way to learn data distributions by training a neural network to recover the score function, defined as the gradient of the log density, from noise-corrupted samples. Once trained, the score magnitude at a test point reflects how consistent that point is with the learned distribution, making it a natural anomaly signal. The key practical challenge is selecting the perturbation scale: too little noise yields unstable score estimates in sparse regions, while too much erases local structure and weakens anomaly sensitivity. This is compounded by the difficulty of hyperparameter tuning when anomalies are unknown and no validation set is available. We introduce kurtosis-based noise scaling (K-DSM), a per-feature scheme that sets noise levels from the shape of each marginal distribution, improving coverage of low-density regions and precision in high-density regions without extra model complexity. Contrary to prior claims that multi-scale or noise-conditioned training is necessary, we find that a carefully trained single-scale model is already a strong anomaly detector. On standard tabular anomaly detection benchmarks, K-DSM achieves state-of-the-art performance in the semi-supervised setting. When combined with a lightweight EMA-teacher filtering rule that removes low-density training points before each gradient step, it also achieves strong performance in the fully unsupervised (contaminated) setting, suggesting that simple, data-adaptive noise scaling enables robust anomaly detection while reducing reliance on hyperparameter tuning.
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