Kurtosis-Guided Denoising Score Matching for Tabular Anomaly Detection

TL;DR

This paper introduces kurtosis-based noise scaling for denoising score matching, enhancing tabular anomaly detection by adaptively setting noise levels per feature, achieving state-of-the-art results with minimal hyperparameter tuning.

Contribution

It proposes a novel kurtosis-guided noise scaling method for DSM that improves anomaly detection accuracy without increasing model complexity.

Findings

K-DSM achieves state-of-the-art performance on tabular anomaly detection benchmarks.

A single-scale model with kurtosis-based noise scaling performs well without multi-scale training.

Combining K-DSM with EMA-teacher filtering enhances performance in fully unsupervised settings.

Abstract

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.