Reliable outlier detection is critical for real-world deployment of deep learning models. Although extensively studied, likelihoods produced by deep generative models have been largely dismissed as being impractical for outlier detection. First, deep generative model likelihoods are readily biased by low-level input statistics. Second, many recent solutions for correcting these biases are computationally expensive, or do not generalize well to complex, natural datasets. Here, we explore outlier detection with a state-of-the-art deep autoregressive model: PixelCNN++. We show that biases in PixelCNN++ likelihoods arise primarily from predictions based on local dependencies. We propose two families of bijective transformations -- ``stirring'' and ``shaking'' -- which ameliorate low-level biases and isolate the contribution of long-range dependencies to PixelCNN++ likelihoods. These transformations are inexpensive and readily computed at evaluation time. We test our approaches extensively with five grayscale and six natural image datasets and show that they achieve or exceed state-of-the-art outlier detection, particularly on datasets with complex, natural images. We also show that our solutions work well with other types of generative models (generative flows and variational autoencoders) and that their efficacy is governed by each model's reliance on local dependencies. In sum, lightweight remedies suffice to achieve robust outlier detection on image data with deep generative models.

Deep networks often make confident, yet, incorrect, predictions when tested with outlier data that is far removed from their training distributions. Likelihoods computed by deep generative models (DGMs) are a candidate metric for outlier detection with unlabeled data. Yet, previous studies have shown that DGM likelihoods are unreliable and can be easily biased by simple transformations to input data. Here, we examine outlier detection with variational autoencoders (VAEs), among the simplest of DGMs. We propose novel analytical and algorithmic approaches to ameliorate key biases with VAE likelihoods. Our bias corrections are sample-specific, computationally inexpensive, and readily computed for various decoder visible distributions. Next, we show that a well-known image pre-processing technique – contrast stretching – extends the effectiveness of bias correction to further improve outlier detection. Our approach achieves state-of-the-art accuracies with nine grayscale and natural image datasets, and demonstrates significant advantages – both with speed and performance – over four recent, competing approaches. In summary, lightweight remedies suffice to achieve robust outlier detection with VAEs.11Code is available at https://github.com/google-research/google-research/tree/master/vae_ood.