Anomaly detection via Gumbel Noise Score Matching

Abstract

We propose Gumbel Noise Score Matching (GNSM), a novel unsupervised method to detect anomalies in categorical data. GNSM accomplishes this by estimating the scores, i.e., the gradients of log likelihoods w.r.t. inputs, of continuously relaxed categorical distributions. We test our method on a suite of anomaly detection tabular datasets. GNSM achieves a consistently high performance across all experiments. We further demonstrate the flexibility of GNSM by applying it to image data where the model is tasked to detect poor segmentation predictions. Images ranked anomalous by GNSM show clear segmentation failures, with the anomaly scores strongly correlating with segmentation metrics computed on ground-truth. We outline the score matching training objective utilized by GNSM and provide an open-source implementation of our work.

Keywords: anomaly; categorical; detection; score matching; tabular; unsupervised.

Figure 1

Correlations with segmentation metrics for Top-K = 50 anomaly scores retrieved from GNSM and Deep SVDD. The arrows next to the metric denote the expected correlation direction. The magnitude of the correlations reflects how well the anomaly scores capture segmentation errors.

Figure 2

Random samples from Top-K = 50 GNSM rankings. Note how the predicted segmentations are either partial/missing or include incorrect classes. The columns (repeated twice) show input image, ground truth segmentations, and model predictions respectively. Different classes are denoted by color. The VOC data includes images obtained from Flickr: https://www.flickr.com/.

Figure 3

Random samples from Top-K = 50 DSVDD rankings. Note how only a few predictions may be considered anomalous. The VOC data includes images obtained from Flickr: https://www.flickr.com/.