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Advances in deep generative and density models have shown impressive capacityto model complex probability density functions in lower-dimensional space.Also, applying such models to high-dimensional image data to model the PDF hasshown poor generalization, with out-of-distribution data being assigned equalor higher likelihood than in-sample data. Methods to deal with this have beenproposed that deviate from a fully unsupervised approach, requiring largeensembles or additional knowledge about the data, not commonly available in thereal-world. In this work, the previously offered reasoning behind these issuesis challenged empirically, and it is shown that data-sets such as MNISTfashion/digits and CIFAR10/SVHN are trivially separable and have no overlap ontheir respective data manifolds that explains the higher OoD likelihood. Modelslike masked autoregressive flows and block neural autoregressive flows areshown to not suffer from OoD likelihood issues to the extent of GLOW,PixelCNN++, and real NVP. A new avenue is also explored which involves a changeof basis to a new space of the same dimension with an orthonormal unitary basisof eigenvectors before modeling. In the test data-sets and models, this aids inpushing down the relative likelihood of the contrastive OoD data set andimprove discrimination results. The significance of the density of the originalspace is maintained, while invertibility remains tractable. Finally, a look tothe previous generation of generative models in the form of probabilisticprincipal component analysis is inspired, and revisited for the same data-setsand shown to work really well for discriminating anomalies based on likelihoodin a fully unsupervised fashion compared with pixelCNN++, GLOW, and real NVPwith less complexity and faster training. Also, dimensionality reduction usingPCA is shown to improve anomaly detection in generative models.

Deep Generative Models Strike Back! Improving Understanding and Evaluation in Light of Unmet Expectations for OoD Data