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Deep generative networks trained via maximum likelihood on a natural imagedataset like CIFAR10 often assign high likelihoods to images from datasets withdifferent objects (e.g., SVHN). We refine previous investigations of thisfailure at anomaly detection for invertible generative networks and provide aclear explanation of it as a combination of model bias and domain prior:Convolutional networks learn similar low-level feature distributions whentrained on any natural image dataset and these low-level features dominate thelikelihood. Hence, when the discriminative features between inliers andoutliers are on a high-level, e.g., object shapes, anomaly detection becomesparticularly challenging. To remove the negative impact of model bias anddomain prior on detecting high-level differences, we propose two methods,first, using the log likelihood ratios of two identical models, one trained onthe in-distribution data (e.g., CIFAR10) and the other one on a more generaldistribution of images (e.g., 80 Million Tiny Images). We also derive a noveloutlier loss for the in-distribution network on samples from the more generaldistribution to further improve the performance. Secondly, using a multi-scalemodel like Glow, we show that low-level features are mainly captured at earlyscales. Therefore, using only the likelihood contribution of the final scaleperforms remarkably well for detecting high-level feature differences of theout-of-distribution and the in-distribution. This method is especially usefulif one does not have access to a suitable general distribution. Overall, ourmethods achieve strong anomaly detection performance in the unsupervisedsetting, and only slightly underperform state-of-the-art classifier-basedmethods in the supervised setting. Code can be found athttps://github.com/boschresearch/hierarchical_anomaly_detection.

Understanding Anomaly Detection with Deep Invertible Networks through Hierarchies of Distributions and Features